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Where did the pendulum’s energy go?
A pendulum that vibrates in the air continues to collide with air molecules in the process of vibrating. Air molecules get their energy from the pendulum. In this process, Air molecules increase their speed. Conversely, the pendulum has lost its energy.
Eventually, the mechanical energy in the pendulum is converted into the air molecule’s heat energy.
Mechanical energy of the pendulum → heat energy of air molecules
A phenomenon that can return to its original state, such as electrons moving in a vacuum, is called a ‘reversible phenomenon.’
However, most natural phenomena are ‘irreversible phenomena’ that occur only in one direction.
Let’s take an example of a pendulum. Can the pendulum move itself using the heat energy of air molecules?
If many air molecules collide with the pendulum in one direction, the pendulum can move by itself. However, this doesn’t happen because each air molecule has a disorderly movement.
As such, most natural phenomena are irreversible, occurring only in one direction.
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It all started with a 1 smart kid
A few weeks ago, Patrick Honner, who is an award-winning math teacher, posted a realization on Twitter. His 7-year-old had just realized discovered that their 300-piece jigsaw puzzle was made out of 324 pieces as it was in an 18 x 18 format.
Calculating number of pieces – DIY
What this means is that a puzzle number is regarded as valid if it is a y x z format. In this format, y is lesser than or equal to z and z is equal to or lesser than 4z. The constant 4 is a random choice and can be any number according to the specification of a certain puzzle. With that in mind, a puzzle number would be something that looks like this, 10x4 = 40, 20x4 = 80, and 30x4 = 120. In the OEIS puzzle, numbers can be found under A071562, where they are described as numbers whose middle divisor is not zero. A middle divisor is the divisor of a number that is between the square root of a number divided by 2 and the square root of a number x 2. This means your middle divisors will have to be 8.660254037844386 and 34.64101615137755 to make a puzzle that will have exactly 300 pieces. However, puzzle piece rows are rarely ever arranged in this manner as they usually get rounded over to the nearest natural number. That is why most manufacturers choose to divide their desired number of pieces with a middle divisor to determine how many pieces will be on one row.
truth vs. Practice
After determining how many rows one side will have using the middle divisor, the remaining number will be used to constitute the other side’s rows. Due to this, the number of pieces advertised on jigsaw puzzle boxes rarely ever represent what you will find inside and math enthusiasts on the internet have realized this.
One of those math enthusiasts is known as John D. Cook once said jigsaw puzzles that claim to have 1,000 pieces mean they approximately have 1,000 pieces. He said the term “1000-piece” is not meant in its literal form because puzzle pieces are normally arranged in a grid-like formation. Since the pieces are in a grid-like formation, this means the number of pieces on one side is a divisor of the total number of pieces. Cook said the grid formation found in many jigsaw puzzles makes it very hard for manufacturers to make a puzzle that has exactly 1,000 pieces. Cook’s assessment of 1,000-piece jigsaw puzzles makes it easier for us to understand why most puzzles have aspect ratios that produce numbers that are around the advertised sum.
Also, there is a puzzle blog that suggests that most 500-piece jigsaw puzzles have 513 pieces. The blog says this because most manufacturers use an aspect ratio of 27 x 19 to make 500-piece puzzles. They also said that most manufacturers also use 38 x 27 aspect ratios to make 1,000-piece puzzles. The 38 x 27 and 27 x19 aspect ratios can be translated as “2Y-piece” and “y-piece.” That makes it a better working model for manufacturers who want to produce both 500-piece and 1,000-piece puzzles.
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The arrival time of an elevator in a 12-story dormitory is equally likely at any time range during the next 3.6 minutes. a. Calculate the expected arrival time. (Round your answer to 2 decimal places.) b. What is the probability that an elevator arrives in less than 2 minutes? (Do not round intermediate calculations. Round your answer to 4 decimal places.) c. What is the probability that the wait for an elevator is more than 2 minutes? (Do not round intermediate calculations. Round your answer to 4 decimal places.)
Use this worksheet to strategize a plan for how you will conduct your study to best examine your hypothesis. Reviewing Chapters 6 and 15 and the chapter that corresponds to your particular design (one of the chapters from 7 through 14) is helpful for this assignment. Please write in complete sentences and please submit a completed worksheet.
TOPIC: How effective is ABA therapy for children with Autism?
Due by 9 pm on June 11th, 2023!
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WBP Math Solution Bengali PDF Download: Dear students, are you looking for WBP Math solutions Bengali PDF? If yes, then here is the right place for you. Because in this post you are going to download WBP Math Somadhan or Solution PDF.
This math solution will be very helpful for West Bengal Police Constable Preliminary Exam. So, if you are preparing for the upcoming WBP Preliminary, then you must download this Math Solution PDF or WBP Preliminary Maths Solved Paper pdf in Bengali.
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WBP Math Solution Bengali PDF Download: Preview:
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But were asked to prove that if B is equal to P. Inverse AP and X is an Eigen vector of a corresponding to an Eigen Value lambda, then PM Verse X is an Eigen vector of B corresponding also to Lambda. So we have that. Yes, A X is equal to Lambda X, where, of course, Lambda is not equal to zero or not. Lambda.
I mean, the Eigen Vector X is non zero by definition. Then we have that P inverse a X well, this is equal to Lambda P Inverse X now since be was PM verse AP It follows that be times p Inverse Times X is equal to p inverse ap times p inverse X which is equal to well, because PM's PM versus the identity. This is the same as P inverse times A. Which times the identity is still a Times X and here I'll group the A and the X together for emphasis. This is the same as P inverse times Lambda X, which is the same as land of times p in verse X.
So it follows that well, we have that X is non zero and we have that p is in vertebral, so it follows that P inverse of X Times X is also a non zero vector. This is actually because p and verses in vertical So we have that p inverse Times X is an Eigen vector of be corresponding to I can value of Lambda..
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Deontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts. It can be used to formalize imperative logic, or directive modality in natural languages. Typically, a deontic logic uses OA to mean it is obligatory that A (or it ought to be (the case) that A), and PA to mean it is permitted (or permissible) that A, which is defined as .
Note that in natural language, the statement "You may go to the zoo OR the park" should be understood as instead of , as both options are permitted by the statement; See Hans Kamp's paradox of free choice for more details.
When there are multiple agents involved in the domain of discourse, the deontic modal operator can be specified to each agent to express their individual obligations and permissions. For example, by using a subscript for agent , means that "It is an obligation for agent (to bring it about/make it happen) that ". Note that could be stated as an action by another agent; One example is "It is an obligation for Adam that Bob doesn't crash the car", which would be represented as , where B="Bob doesn't crash the car".
In Georg Henrik von Wright's first system, obligatoriness and permissibility were treated as features of acts. Soon after this, it was found that a deontic logic of propositions could be given a simple and elegant Kripke-style semantics, and von Wright himself joined this movement. The deontic logic so specified came to be known as "standard deontic logic," often referred to as SDL, KD, or simply D. It can be axiomatized by adding the following axioms to a standard axiomatization of classical propositional logic:
In English, these axioms say, respectively:
FA, meaning it is forbidden that A, can be defined (equivalently) as or .
where . It is generally assumed that is at least a KT operator, but most commonly it is taken to be an S5 operator. In practical situations, obligations are usually assigned in anticipation of future events, in which case alethic possiblities can be hard to judge; Therefore, obligation assignments may be performed under the assumption of different conditions on different branches of timelines in the future, and past obligation assignments may be updated due to unforeseen developments that happened along the timeline.
The other main extension results by adding a "conditional obligation" operator O(A/B) read "It is obligatory that A given (or conditional on) B". Motivation for a conditional operator is given by considering the following ("Good Samaritan") case. It seems true that the starving and poor ought to be fed. But that the starving and poor are fed implies that there are starving and poor. By basic principles of SDL we can infer that there ought to be starving and poor! The argument is due to the basic K axiom of SDL together with the following principle valid in any normal modal logic:
If we introduce an intensional conditional operator then we can say that the starving ought to be fed only on the condition that there are in fact starving: in symbols O(A/B). But then the following argument fails on the usual (e.g. Lewis 73) semantics for conditionals: from O(A/B) and that A implies B, infer OB.
Indeed, one might define the unary operator O in terms of the binary conditional one O(A/B) as , where stands for an arbitrary tautology of the underlying logic (which, in the case of SDL, is classical).
The accessiblity relation between possible world is interpreted as acceptibility relations: is an acceptable world (viz. ) if and only if all the obligations in are fulfilled in (viz. ).
Alan R. Anderson (1959) shows how to define in terms of the alethic operator and a deontic constant (i.e. 0-ary modal operator) standing for some sanction (i.e. bad thing, prohibition, etc.): . Intuitively, the right side of the biconditional says that A's failing to hold necessarily (or strictly) implies a sanction.
In addition to the usual modal axioms (necessitation rule N and distribution axiom K) for the alethic operator , Anderson's deontic logic only requires one additional axiom for the deontic constant : , which means that there is alethically possible to fulfill all obligations and avoid the sanction. This version of the Anderson's deontic logic is equivalent to SDL.
However, when modal axiom T is included for the alethic operator ( ), it can be proved in Anderson's deontic logic that , which is not included in SDL. Anderson's deontic logic inevitably couples the deontic operator with the alethic operator , which can be problematic in certain cases.
An important problem of deontic logic is that of how to properly represent conditional obligations, e.g. If you smoke (s), then you ought to use an ashtray (a). It is not clear that either of the following representations is adequate:
Under the first representation it is vacuously true that if you commit a forbidden act, then you ought to commit any other act, regardless of whether that second act was obligatory, permitted or forbidden (Von Wright 1956, cited in Aqvist 1994). Under the second representation, we are vulnerable to the gentle murder paradox, where the plausible statements (1) if you murder, you ought to murder gently, (2) you do commit murder, and (3) to murder gently you must murder imply the less plausible statement: you ought to murder. Others argue that must in the phrase to murder gently you must murder is a mistranslation from the ambiguous English word (meaning either implies or ought). Interpreting must as implies does not allow one to conclude you ought to murder but only a repetition of the given you murder. Misinterpreting must as ought results in a perverse axiom, not a perverse logic. With use of negations one can easily check if the ambiguous word was mistranslated by considering which of the following two English statements is equivalent with the statement to murder gently you must murder: is it equivalent to if you murder gently it is forbidden not to murder or if you murder gently it is impossible not to murder ?
Some deontic logicians have responded to this problem by developing dyadic deontic logics, which contain binary deontic operators:
(The notation is modeled on that used to represent conditional probability.) Dyadic deontic logic escapes some of the problems of standard (unary) deontic logic, but it is subject to some problems of its own.[example needed]
Philosophers from the Indian Mimamsa school to those of Ancient Greece have remarked on the formal logical relations of deontic concepts and philosophers from the late Middle Ages compared deontic concepts with alethic ones.
In his Elementa juris naturalis (written between 1669 and 1671), Gottfried Wilhelm Leibniz notes the logical relations between the licitum (permitted), the illicitum (prohibited), the debitum (obligatory), the, and the indifferens (facultative) are equivalent to those between the possibile, the impossibile, the necessarium, and the contingens respectively.
Ernst Mally, a pupil of Alexius Meinong, was the first to propose a formal system of deontic logic in his Grundgesetze des Sollens (1926) and he founded it on the syntax of Whitehead's and Russell's propositional calculus. Mally's deontic vocabulary consisted of the logical constants U and ∩, unary connective !, and binary connectives f and ∞.
Mally defined f, ∞, and ∩ as follows:
Mally proposed five informal principles:
He formalized these principles and took them as his axioms:
From these axioms Mally deduced 35 theorems, many of which he rightly considered strange. Karl Menger showed that !A ↔ A is a theorem and thus that the introduction of the ! sign is irrelevant and that A ought to be the case if A is the case. After Menger, philosophers no longer considered Mally's system viable. Gert Lokhorst lists Mally's 35 theorems and gives a proof for Menger's theorem at the Stanford Encyclopedia of Philosophy under Mally's Deontic Logic.
The first plausible system of deontic logic was proposed by G. H. von Wright in his paper Deontic Logic in the philosophical journal Mind in 1951. (Von Wright was also the first to use the term "deontic" in English to refer to this kind of logic although Mally published the German paper Deontik in 1926.) Since the publication of von Wright's seminal paper, many philosophers and computer scientists have investigated and developed systems of deontic logic. Nevertheless, to this day deontic logic remains one of the most controversial and least agreed-upon areas of logic. G. H. von Wright did not base his 1951 deontic logic on the syntax of the propositional calculus as Mally had done, but was instead influenced by alethic modal logics, which Mally had not benefited from. In 1964, von Wright published A New System of Deontic Logic, which was a return to the syntax of the propositional calculus and thus a significant return to Mally's system. (For more on von Wright's departure from and return to the syntax of the propositional calculus, see Deontic Logic: A Personal View and A New System of Deontic Logic, both by Georg Henrik von Wright.) G. H. von Wright's adoption of the modal logic of possibility and necessity for the purposes of normative reasoning was a return to Leibniz.
Although von Wright's system represented a significant improvement over Mally's, it raised a number of problems of its own. For example, Ross's paradox applies to von Wright's deontic logic, allowing us to infer from "It is obligatory that the letter is mailed" to "It is obligatory that either the letter is mailed or the letter is burned", which seems to imply it is permissible that the letter is burned. The Good Samaritan paradox also applies to his system, allowing us to infer from "It is obligatory to nurse the man who has been robbed" that "It is obligatory that the man has been robbed". Another major source of puzzlement is Chisholm's paradox. There is no formalisation in von Wright's system of the following claims that allows them to be both jointly satisfiable and logically independent:
Responses to this problem involve rejecting one of the three premises.
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The mean is the average. For example if you had the numbers 11, 10, 12, 11, 7, and 15. You would add them up and divide by how many numbers there are (which in this case is 6). The number you get is your mean (in this case the means in 11).
The mode is the number that occurs most often. Using the same set of numbers above (11, 10, 12, 11, 7, and 15), the mode would be 11 because that's the only number that occurs the most. In other words, there is more than one of the same number.
It doesn't actually mean difference, but it can be used to get the difference between values. 11 subtract 4 is 7, and 7 is the difference between 4 and 11.
They differ in formula.
Range means finding the difference between the highest number in a set of numbers and the lowest. Mean means dividing the total of a set of numbers by the number of numbers there are Mode means the most frequent number. Median is the number in the middle. To find the median you have to first order the numbers from lowest to highest.
Mean = 21.6 Median = 19.5 Mode = 20 and 21 ------------------------------------------------------------------------ If the "2 1" (between 18 and 20 at the end) is supposed to be "21" then Mean = 26 Median = 20 Mode = 20
3 popular questions about mean,median,mode is whats the mean? whats the mode? whats the median? hope this helps
= What is the difference between real mode and protected mode =
mode is the number that occurs the most and to find the mean/average, add all numbers, then divid that number by the number of numbers there were in your group of numbers.
There is no direct relationship between the mean and mode.
The mean, median, and mode are all measures of central tendency. For symmetrical distributions they all have the same value. For assymetrical distributions they have different values. The mean is the average and the mode is the most likely value.
The Related Link below explains the difference between enhancement mode and depletion mode N channel MOSFETs.
well a spreadsheet is what your making, spreadsheet mode is the view
by average we mean any measure of central tendency and mean is one of the averages. other measures of average are median ,mode, geomatric mean and harmonic mean.
single mode fiber have higher bandwidth than multimode
nothing they are both the same
you do it yourself
Yes they do. All graphs have a mean and a mode. The difference with a double bar graph is that you have to find the mean and mode separately with each different thing you are measuring
The 8251 is a USART (Universal Synchronous Asynchronous Receiver Transmitter). It does not have a minimum and maximum mode.
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On separability finiteness conditions in semigroups
MetadataShow full item record
Taking residual finiteness as a starting point, we consider three related finiteness properties: weak subsemigroup separability, strong subsemigroup separability and complete separability. We investigate whether each of these properties is inherited by Schützenberger groups. The main result of this paper states that for a finitely generated commutative semigroup S, these three separability conditions coincide and are equivalent to every H -class of S being finite. We also provide examples to show that these properties in general differ for commutative semigroups and finitely generated semigroups. For a semigroup with finitely many H -classes, we investigate whether it has one of these properties if and only if all its Schützenberger groups have the property.
Miller , C , O'Reilly , G , Quick , M & Ruskuc , N 2022 , ' On separability finiteness conditions in semigroups ' , Journal of the Australian Mathematical Society , vol. 113 , no. 3 , pp. 402-430 . https://doi.org/10.1017/S1446788721000124
Journal of the Australian Mathematical Society
DescriptionFunding: The first author is grateful to EPSRC for financial support. The second author is grateful to the School of Mathematics and Statistics of the University of St Andrews for financial support.
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.
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In this second part, I will show another metric used in video quality evaluation: the Structural SIMilarity Index (SSIM). In the previuos article, we saw that PSNR and MSE are not always reliable in every situation, so we need a more accurate metric that’s able to cover a wider spectrum of distorsions and losses in video information.
Images are highly structured, so in order to evaluate the quality of a copy you need to measure not only the variations of pixels value than the reference sample, but also the structural distorsions introduced. The first step therefore is to distinguish the structures in a scene. The luminance of the surface of an object is the product of illumination and the reflectance, but its structure is independent of the illumination, so the structural information of an image is defined as the set of attributes that form the structure of the objects represented in the scene, regardless of the average luminance and contrast. Since these two characteristics may vary within the scene, they have to be considered in a local way.
How it works
Let X and Y two NxM arrays representing the (Y) luminance channel of the frames to evaluate; X represents the reference copy, while Y the lossy/distorted sample. Let x and y their monodimensional versions, obtained by merging together the columns (or the rows) of the bidimensional arrays. This is a useful step in order to eliminate a summation in formulas and to write a cleaner code in numerical softwares, but doesn’t affect the generality of this treatment. Let N = NxM for simplicity.
So, the first step is to measure the luminance of x and y, which is understood as the the average of their values, here respectively indicated as μx and μy:
Then, the function for the comparison of the luminance, l(x,y), is defined as follows:
Where C1 = (K1L)2, with K1 is an arbitrary constant (<< 1) usually set to 0.01 and L is equal to the maximum possible pixel value of the image (or, more specifically, of the luminance channel); so, if are used 8 bits per sample, L = 28-1 = 255.
Next, luminance’s information is removed by calculating the standard deviations of the two images (respectively indicated as σx and σy), in order to obtain their average contrast:
And now, the contrasts are compared by using the following function:
As you could expect, C2 is a constant usually equal to (K2L)2, with K2 << 1 and usually set to 0.03.
The third piece of the puzzle is the structure comparison function s(x,y), that remembers Pearson’s correlation index between two signals:
With C3 = C2/2, and
Finally, here is the SSIM Index:
The exponents α, β and γ, greater than zero, are parameters used to calibrate the weight of the three functions in the measurement; typically, α = β = γ = 1, so the SSIM Index can be rewritten as follows:
As the index of structural similarity approaches 1, the greater the degree of fidelity of the encoded copy is close to the original.
In evaluating the quality of the images, however, the given SSIM Index is not applied directly to the entire image: it’s preferred to work locally because the characteristics of a scene are space-varying. Therefore a circular symmetric Gaussian window of size 11×11 and standard deviation of 1.5 is introduced, that moves the entire image pixel by pixel, producing a function with appropriate weights, changing the parameters of brightness, contrast, and covariance as follows:
Let M the number of windows applied to the frames: M previously defined SSIM Indexes are generated, and it’s possible to define a new index (usually called MSSIM) by averaging the M measures:
The adoption of this last version of SSIM Index is widespread.
A great Matlab implementation can be downloaded directly from the web page of the “fathers” of this metric: https://ece.uwaterloo.ca/~z70wang/research/ssim/.
Take a look to (d): it shows a good SSIM Index, but – if you remember Part 1 – it has a very low PSNR (12.95 dB); this is one of the many reasons that makes SSIM more reliable than PSNR in a wide spectrum of situations.
Read more and external sources
- MSE, PSNR and the need of a new index (SSIM):
Mean Squared Error: love it or leave it? A new look at Signal Fidelity Measures. Wang Zhou, A.C. Bovik. Signal Processing Magazine IEEE. Volume: 26, Issue: 1. Publication Year: 2009, Page(s): 98 – 117.
- Kodak lossless true color image suite.
- Xiph.org test media.
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Stable Self-Similar Profiles for Two 1D Models of the 3D Axisymmetric Euler Equations
Global regularity of the Euler equations in the three-dimensional (3D) setting is regarded as one of the most important open questions in mathematical fluid mechanics. In this work we consider two one-dimensional (1D) models approximating the dynamics of the 3D axisymmetric Euler equations on the solid boundary of a periodic cylinder, which are motivated by a potential finite-time singularity formation scenario proposed recently by Luo and Hou (PNAS 111(36):12968–12973, 2014), and numerically investigate the stability of the self-similar profiles in their singular solutions. We first review some recent existence results about the self-similar profiles for one model, and then derive the evolution equations of the spatial profiles in the singular solutions for both models through a dynamic rescaling formulation. We demonstrate the stability of the self-similar profiles by analyzing their discretized dynamics using linearization, and it is hoped that these computations can help to understand the potential singularity formation mechanism of the 3D Euler equations.
© 2016 Springer International Publishing Switzerland.
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Your investment grew from $10000 to $20000 over a period of 5 periods at a compounded growth rate (CAGR) of 14.87%.
14.87% is the average rate of change for the value and assumes this change was compounded every period.
This calculator determined the CAGR (Compound Annual Growth Rate) of an investment or business. This metric is used to measure how much the statistic you're analyzing (can be anything - a stock, a bond, company sales) has changed in each period between the start and end of the analysis. This may also be called an average rate of change calculator.
This is useful when the item being analyzed may have ups and downs over long periods. For Example, consider the stock below:
Assume you were an investor in 2003 and had to make a decision about buying this stock. Earnings have been all over the place! How would you come up with a reasonable estimate of the average rate of change? CAGR is a simple way to smooth out the noise. For example, while earnings dropped in the 2000 reccession, you can point to a longer term trend - if we compared 1998 earnings ($.50) with 2002 earings ($1.25) and feed them into the CAGR calculator, we learn that earnings grew at a compounded rate of 20%.
You can also use this average rate of change calculator as a simple compound interest calculator. If I buy that stock at $14, hold it for 5 years, and sell it for $30 - what is my annual rate of return? By using the CAGR calculator, I can determine that my return was: 16.47%. Not bad!
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We all know the power of compound interest, and the Rule of 72 is a simple and elegant mathematical expression of that concept. It’s also a quick and easy way to figure out how long it will take an investment to double, and the only information you need to make the calculation is a fixed annual rate of return for the investment in question.
How does it work? You divide 72 by the rate of return, and you’ll get a rough estimate of the number of years it will take for your money to double. So, for example, $5,000 invested at 4% would take 18 years (72/4 =18) to become $10,000.
The rule works “in reverse” as well. If you have a certain time period over which you’d like to double your investment, you can use the rule to determine what rate of return you’ll need. For example, if you wanted that same $5,000 to double within a 6 year time period, you’d divide 72 by 6, revealing the need to find an investment with a 12% annual rate of return.
A word of caution: the Rule only provides a rough estimate, and it’s more accurate when it’s applied to lower interest rates. And, of course, it’s best used for quick mental math, and not to guide any major financial decision-making.
You can find a Rule of 72 calculator, plus a calculator that estimates other growth factors, here.
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Quadratic Functions Worksheet With Answers. You can choose the magnitude of the “a” time period and the direction during which the parabola opens. With the help of the group we are ready to proceed to enhance our academic sources. The sides of an equilateral triangle are shortened by 12 items, 13 items and 14 units respectively and a right angle triangle is formed. Find the vertex of the given quadratic functions through the use of the technique of finishing the square.
These Algebra 1 – Quadratic Functions Worksheets produces issues for fixing quadratic equations by factoring. The quadratic equations worksheet will help students apply the usual form of quadratic equations and discover methods to remedy the quadratic equation. These worksheets will help the students of sophistication 10 to practice more for board exams. These Algebra 1 – Quadratic Functions Worksheets produces problems for solving quadratic equations with the quadratic formula.
- Bernadette throws the javelin for her school’s track and subject group.
- You can select the magnitude of the “a” time period and the course by which the parabola opens.
- Find the vertex of the given quadratic capabilities through the use of the strategy of finishing the square.
- With the assistance of the neighborhood we can continue to enhance our academic assets.
- The sides of an equilateral triangle are shortened by 12 items, 13 items and 14 models respectively and a proper angle triangle is shaped.
Also you’ll find a way to change the assorted translated capabilities using the three other enter bins which are labeled a, b, and c. If you want to reposition the display you need to use the tool at the high of the screen that appears like 4 arrows to drag the display screen to a unique place. [newline]Also you have to use the pointer button at the prime of the display screen to tug the perform f to show how the opposite functions change. The file could be run by way of the free on-line application GeoGebra, or run domestically if GeoGebra has been put in on a pc. The sides of an equilateral triangle are shortened by 12 models, thirteen models and 14 units respectively and a proper angle triangle is formed.
- 1 Example Query #1 : Graphing Parabolas
- 2 A 7a Parts Of Quadratic Functions Scavenger Hunt
- 3 Related posts of "Quadratic Functions Worksheet With Answers"
Example Query #1 : Graphing Parabolas
The point $(x,h)$ is identical as $(x,-2f)$ so the graph of $h$ is the same because the reflection of the graph of $2f$ concerning the $x$-axis. So the values of $f$ are first doubled, exaggerating the slope of the graph, after which the graph is mirrored concerning the $x$-axis. Engage your students with efficient distance learning resources.
Deciphering Solutions Of Quadratic Features
In the reasonable stage, the x-values are decimals or fractions. Factorize every quadratic perform and write the function in intercept kind. Practice this array of worksheets to realize expertise in factoring the function, finding zeros and converting quadratic function to intercept type. The graph below exhibits essential attributes of the graph of a parabola that you ought to use to research and interpret the graphs of quadratic capabilities. We’re going to investigate the graphs of quadratic capabilities.
Google Sheets Digital Pixel Artwork Math Linear Equations: Identifying Key Options
Substitute the values of x in the quadratic perform to determine the y values. To facilitate a simple practice, the coefficients and x-values are provided in integers. These Algebra 1 – Quadratic Functions Worksheets produces problems for finishing the sq..
A 7a Parts Of Quadratic Functions Scavenger Hunt
Corbett Maths provides outstanding, unique exam type questions on any topic, in addition to videos, previous papers and 5-a-day. Find if the given values are the answer of the given equations. As a member, you will also get unlimited entry to over eighty four,000 classes in math, English, science, historical past, and more. Plus, get follow checks, quizzes, and personalized teaching that can assist you succeed. With a and c mounted, observe the impact of change of worth of ‘b’on the graph and reply the next questions. By setting every bracket equal to zero and fixing, we get the required solutions.
By contrast, a parabola of the shape rotates concerning the vertical axis, not the horizontal axis. As the adverse check in entrance of theterm makes flips the parabola about the horizontal axis. If the parabola opens downward, the vertex is a maximum level, and if the parabola opens upward, the vertex is a minimal level. The x-intercept is the point, or factors, the place the parabola crosses the x-axis. There may be 0, 1, or 2 x-intercepts, depending on the parabola.
Algebra 1 Unit 7: Quadratic Features
As the title may counsel, this worksheet helps the student follow graphing a quadratic equation from each vertex and intercept form. Good for the Algebra 1 or Algebra 2 pupil, or as a refresher for the Geometry scholar. This set of quadratic operate worksheets incorporates workout routines on evaluating quadratic functions for the given x-values. The x-values are integers in the straightforward stage worksheets.
Pick some earlier than and after the AOS and plug into your equation. This graph represents the peak of a diver vs. the time after the diver jumps from a springboard. Answer the next questions primarily based on the data. As you accomplish that, discover the parabolas being created by the experimenters.
One may be represented with a quadratic perform, and one with a linear operate. Students must graph the heights of the objects over time and reply questions that may lead to important serious about this distinctive system of equations. Math worksheet on quadratic equations will assist the scholars to practice the usual type of quadratic equation. Practice the quadratic equation and discover methods to remedy the quadratic equation. This Algebra 1 – Quadratic Functions Worksheets will produce issues for working towards graphing quadratic perform from their equations.
You can select the magnitude of the “a” time period and the path in which the parabola opens. Students can obtain the PDFs of quadratic equations worksheets here. We’re going to research and analyze graphs of quadratic capabilities and then interpret these graphs inside the context of the state of affairs. Analyze graphs of quadratic features and interpret those graphs throughout the context of the state of affairs. The students can both sketch the graphs by hand or use graphing calculators.
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1. Why did adverse selection occur in the health insurance exchanges? 2. How did health insurers respond to adverse selection? 3. What are alternative approaches for subsidizing health insurance for those with a preexisting condition?
1. What change did the ACA institute that was of major importance in the individual market that any replacement plan would likely maintain in one form or other? 2. How effective was the individual mandate in expanding the exchange risk pools?
1. Why did the government decide not to implement the CLASS Act? 2. What were the ACA’s approaches for reducing the number of uninsured?
1. How can Medicaid be changed so it is not a low-cost substitute for private LTC insurance for the middle-income aged? 2. Why does private LTC insurance, when sold to the aged, have such a high loading charge relative to the pure premium?
1. What should be the objectives of an LTC policy? How do these objectives differ from the LTC goals of the middle class? 2. . Why has the market for LTC insurance grown so slowly?
1. What are alternative ways for treating Medicare under national health insurance? 2. Describe the demographic and economic trends affecting the outlook for LTC.
Outline (and justify) a proposal for national health insurance. As part of your proposal, discuss the benefits package, beneficiaries, method of financing, delivery of services, and role of government. How well does your proposal meet the criteria discussed in the chapter?
1. Discuss the criteria that should be used for evaluating alternative national health insurance proposals. 2. Evaluate the desirability of the following types of taxes for financing national health insurance: payroll, sales, and income tax.
1. How does the ACA employer mandate differ from previous employer mandate proposals? 2. What is the justification for requiring everyone (all those who can afford it) to purchase a minimum level of health insurance?
1. Does an employer-mandated health insurance tax have a regressive, proportional, or progressive effect on the income of employees and consumers? 2. Which groups favor and which groups oppose an employer mandate for achieving national health insurance? Why?
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Written by a pair of math teachers and based on their classroom notes and experiences, this introductory treatment of theory, proof techniques, and related concepts is designed for undergraduate courses. No knowledge of calculus is assumed, making it a useful text for students at many levels. The focus is on teaching students to prove theorems and write mathematical proofs so that others can read them.
Since proving theorems takes lots of practice, this text is designed to provide plenty of exercises. The authors break the theorems into pieces and walk readers through examples, encouraging them to use mathematical notation and write proofs themselves. Topics include propositional logic, set notation, basic set theory proofs, relations, functions, induction, countability, and some combinatorics, including a small amount of probability. The text is ideal for courses in discrete mathematics or logic and set theory, and its accessibility makes the book equally suitable for classes in mathematics for liberal arts students or courses geared toward proof writing in mathematics.
Slightly corrected reprint of the Zinka Press, Wayne, Pennsylvania, 2005 edition.
|Availability||Usually ships in 24 to 48 hours|
|Author/Editor||Amy Babich, Laura Person|
|Dimensions||6 x 9|
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But before taking any final decision, I suggest to check the VSEPR structure and then decide as per the diagram. ), The Lewis structure of SF4 is the combination of 34 valence electron and 5 electron pairs around the Sulfur, in which there are four bonding pairs and one lone pair. or greater than it? In the geometry, three atoms are in the same plane with bond angles of 120°; the other two atoms are on opposite ends of the molecule. So, SF4 is polar. How scientists got that number was through experiments, but we don't need to know too much detail because that is not described in the textbook or lecture. The overall shape is described as see-saw. and types of electrons pairs; magnitude of repulsions between them to arrive at The appearance of SF4 is like a colorless gas. Hint: There is now lone pair on P. Question Determine the electron geometry (eg) and molecular geometry (mg) of SiF4. If the charge distribution is symmetric, it is non-polar. So, this was the explanation about SF4. increase in the volume occupied by electron pair(s). In NSF3, there is a triple bond between N and S. Hence the than in other cases. SO3 Molecular Geometry, Lewis Structure, and Polarity Explained, O3 Lewis Structure, Polarity, Hybridization, Shape and Much More, CS2 Lewis Structure, Hybridization, Polarity and Molecular Shape, NH3 Molecular Geometry, Hybridization, Bond Angle and Molecular Shape, PCL3 Molecular Electron Geometry, Lewis Structure, Bond Angles and Hybridization. question, Next question SF4 covers under ‘Trigonal Bipyramidal’ because of its electron arrangements. electrons pairs on atoms connected to central atom. Some elements in Group 15 of the periodic table form compounds of the type AX 5; examples include PCl 5 and AsF 5. It linked by lines i.e. 109 o 28' In POF 3 , there is a double bond between P and O, which also causes more repulsion than single bond, but less than the triple bond. Isn’t drago’s rule being violated in your answer? This electron arrangement is known as ‘Trigonal Bipyramidal.’. After all this process, the last hybrid orbital contains a lone pair. bonds are single bonds, which exert less repulsion on other bond pairs. Thanks a lot of helping out.. As we have discussed, SF4 has one lone pair and four sigma bonds of F. The central atom is S. So in simple terms, we can say that its bonding regions are four with the one lone pair. Preparation. In this structure, Sulfur is the least electronegative element and so transfers in the middle of the structure, and the diagram gives a three-dimensional structural information. But what about drago’s rule. You can also look at its molecular geometry. * First write the Lewis dot structures for the molecules and find the number The reason is that the lone pair prefers one of the equatorial positions. sif4 polar or nonpolar 3 November 2020 by The three-dimensional arrangement of the fragment or atoms which create a molecule by getting together is known as Molecular Geometry. So, this was the explanation about SF4. >. For bent molecular geometry when the electron-pair geometry is tetrahedral the bond angle is around 105 degrees. the bond angle is maximum i.e. the relative bond angles. This will reduce the bond angle more SF4 Molecular Geometry, Lewis Structure, and Polarity – Explained. Molecule polarity gives the acknowledgment regarding the molecule’s solubility, boiling point, etc. For other informative articles, kindly stay connected with geometry of molecules and if you have any other queries, leave a message in the comments section. valence electrons (associated with an atom. Here, there is only one lone pair around the central atom (Sulfur) which is an odd number. The bond angle is least affected in case of SiF 4, since all the Si-F bonds are single bonds, which exert less repulsion on other bond pairs. in triple bond occupies more space, it exerts more repulsion than that of double 4 I hope you got all the answers of what you were looking for! With 2P-orbitals, there are overlapped four of the hybrid orbitals. Using the example above, we would add that H 2 O has a bond angle of 109.5° and CO 2 would have a bond angle of 180°. A) eg=tetrahedral, mg=trigonal pyramidal B) eg=octahedral, mg=square planar C) eg=trigonal bipyramidal, mg=trigonal pyramidal ... Place the following in order of increasing X-Se-X bond angle, where X represents the outer atoms in each molecule. It is also hazardous as it is highly toxic and corrosive. The reason is that the lone pair prefers one of the equatorial positions. Just like this molecule – SF4. SF4 stands for Sulfur tetrafluoride. The equatorial F atoms are 120 from each other., so the axial/equatorial bond angle is … Here, SF4 bond angles are around 102 degrees in the equatorial plane and around 173 degrees between the axial and equatorial positions. Determine the electron geometry (eg) and molecular geometry (mg) of CO32⁻. A) eg=tetrahedral, mg=trigonal pyramidal B) eg=octahedral, mg=square planar C) eg=trigonal bipyramidal, mg=trigonal pyramidal ... Place the following in order of increasing X-Se-X bond angle, where X represents the outer atoms in each molecule. The bond angles of a molecule, together with the bond lengths (Section 8.8), define the shape and size of the mole-cule. Electron-pair Geometry: Molecular Geometry: Bond Angle: 2: 0: linear: linear: 180: 3: 0: … 1) Write the complete Lewis dot structures of above molecules indicating Therefore, tetrahedrals have a bond angle of 109.5 degrees. The bond angle is least affected in case of SiF4, since all the Si-F The axial F atoms are 180 degrees from each other. (VSEPR – Valence Shell Electron Pair Repulsion theory). The number of valence electrons is 34 and 5 electron pairs. paper, < Previous The other explanation goes like this: Two S-F bonds are opposite from each other, in complete 180 degrees. Amazing Explanation!!! Since the electron density Thanks for your article. You will get a reply from the expert as soon as possible. The advantage of this structure is that it shows the chemical connectivity and bonding of all the particles which are associated with atoms and the reactivity of a molecule. Hunting accurate information is among the biggest issues for the younger generation. Here, SF4 bond angles are around 102 degrees in the equatorial plane and around 173 degrees between the axial and equatorial positions. The molecular formula is number and varieties of particles available in the group of atoms. The shape is like a seesaw. If you want to know that the molecule is polar or nonpolar, first of all, you should draw the Lewis structure of the molecule. … Give the approximate bond angle for a molecule with a tetrahedral shape. But the other two S-F bonds are pointing down, and that is why their bond dipoles do not cancel.
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|15th January 2005, 18:14||#1|
Join Date: Jun 2004
Mercedes-Benz Model List
Hey Guys and Gals,
The Wxxx series of Mercedes always confuses me. If you are like me, i.e. not very Techie when it comes to cars, Especially the Mercs, then this site may help shed some light on the W series.
After looking at this site, I finally know that my Dad actually owned a W110, which I know as Mercedes Benz 200D (1966 model).
enough of talk, here is the link.
Sorry if a similar list has already been posted on the forum.
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law relating the apparent contrast,
Note 1 to entry: The formula is sometimes written
where the exponent,
Note 2 to entry: Taking into account the relationship between atmospheric transmissivity,
Note 3 to entry: The contrast is taken to be the quotient of the difference between the luminance of the object and the luminance of the background, and the luminance of the background.
Note 4 to entry: This entry was numbered 845-11-22 in IEC 60050-845:1987.
Note 5 to entry: This entry was numbered 17-629 in CIE S 017:2011.
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You've probably seen this image making the rounds on social media. It shows a method of doing basic subtraction that's intended to appear wildly nonsensical and much harder to follow than the "Old Fashion" [sic] way of just putting the 12 under the 32 and coming up with an answer. This method of teaching is often attributed to Common Core, a set of educational standards recently rolled out in the US.
But, explains math teacher and skeptic blogger Hemant Mehta, this image actually makes a lot more sense than it may seem to on first glance. In fact, for one thing, this method of teaching math isn't really new (our producer Jason Weisberger remembers learning it in high school). It's also not much different from the math you learned back when you were learning how to count change. It's meant to help kids be able to do math in their heads, without borrowing or scratch-paper notations or counting on fingers. What's more, he says, it has absolutely nothing to do with Common Core, which doesn't specify how subjects have to be taught.
I admit it's totally confusing but here's what it's saying:
If you want to subtract 12 from 32, there's a better way to think about it. Forget the algorithm. Instead, count up from 12 to an "easier" number like 15. (You've gone up 3.) Then, go up to 20. (You've gone up another 5.) Then jump to 30. (Another 10). Then, finally, to 32. (Another 2.)
I know. That's still ridiculous. Well, consider this: Suppose you buy coffee and it costs $4.30 but all you have is a $20 bill. How much change should the barista give you back? (Assume for a second the register is broken.)
You sure as hell aren't going to get out a sheet of paper …
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Solving Systems Of Equations (SEO) is based on some very basic axioms and axiom of science. The basic axiom of science is that the patterns cannot be changed and in other words, everything is constant. From this follows the conclusion that there are no exceptions to the rule. In other words everything is constant and we can never change this. Solving systems of equations can be described as finding the solutions of the system of equations (which may be complex mathematical or logical equations) in a deterministic form (without reference to the past or future). In other words solving systems of equations prove that given a set of inputs x, y, z; a certain number of points h, I; and an unknown number k; then the output I = h(x+I) where h is a function of i.
Systems Equations Word Problems Worksheets Best Relations and from solving systems of equations algebraically worksheet , source:alisonnorrington.com
There are many ways to solve systems of equations. One of the most popular ways is to use linear algebra and to do the multiplication and addition operations on the input variables x, y, z. This can be extended to the systems of complex numbers and using it gives solutions of systems of real numbers and vice versa. This is called the discrete math method to solve systems of equations. The finite-math approach uses more operators and functions to multiply and add the inputs and solve the system.
There are two types of linear algebra systems of equations. They are called discrete and non discrete. Discrete systems of equations are easier to understand and implement because the algorithms are well defined and usually the solutions are simple to verify. On the other hand non-discrete systems of equations are less concise and are less efficient because they are more general and include different operations.
Solving Linear Systems In Three Variables Worksheet Fresh 12 Fresh from solving systems of equations algebraically worksheet , source:therlsh.net
Discrete systems of equations can be solved using the dot product, products of several independent variables, integral functions, and quadratic equations. The methods of solving such systems can be done in different ways. These methods are based on either the properties of the inputs or the properties of the function that can be changed. A little-known method of solving systems of different kinds is to use a technique of transpose functions.
There are different ways of implementing the methods. Different approaches in solving systems of different kinds will be needed depending on the nature of the problem being solved. The first and foremost important factor while designing any solver is the method of communication of the user. If there is no proper method of communication then it might create a lot of difficulty in the process of solving the problem and lead to an unsatisfactory output.
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Different people have different levels of experience in solving systems of equations. Some of them know the techniques of solving elliptical equations and cubes and hexagonal equations through the help of mathematical formulae while some of them know how to solve the same problems through the help of programming languages. There are also some people who are experts in solving analytic problems and others specialize in solving finite and integral series. Then, there are some people who are good at solving closed system forms like solutions of spherical or cylindrical problems. There are even some good calculators that come with different algorithms for solving different kinds of equations.
The modern computers which are used for solving the problems come with various algorithms which make the process of solving the system much easy than the older version when the calculations were done manually. One of the popular methods of solving a system of equations is the use of an Algebra solver. It uses both inner and outer algebra operations in the calculation of solutions of a system of equations. The main purpose of using an Algebra solver is to carry out the multiplication and division operations in an efficient way so that the results obtained are both accurate.
Solving Systems Equations by Addition Method Worksheet Lovely from solving systems of equations algebraically worksheet , source:incharlottesville.com
The best part about the Algebra solver is that it can be used anywhere. You can solve solvents online too and get accurate results. Today, almost every college and university use the Algebra solvers to solve problems for their students and graduates as well. If you are interested in getting an advanced degree in Algebra, you can opt for a multi-dimensional analytical course which will cover more mathematical topics. After completing the required courses, you would be equipped to handle almost any problem related to complex mathematical equations.
3 Ways to Solve Systems of Algebraic Equations Containing Two Variables from solving systems of equations algebraically worksheet , source:wikihow.com
Word Problems Worksheet Algebra 1 Best Word Problems Worksheet from solving systems of equations algebraically worksheet , source:nancywang.co
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Kepler's first law:
Planet orbits are ellipses with the sun at one focus of the ellipse.
Kepler's second law:
A line joining a planet to the sun sweeps out equal areas in the ellipse over equal times.
Kepler's third law:
The square of the orbital period of a planet equals the cube of its semi-major axis.
Newton's first law
An object at rest stays at rest. An object in motion stays in motion at a constant speed in a straight line unless acted upon by an unbalanced force.
Newton's second law
The net force on an object is equivalent to the product of object's mass and its acceleration
Newton's third law
Forces come in pairs. For every force, there exists and equal and opposite force.
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TBH Teachers: Coordinate Grid: Mapping an Archeological Site
Grade: 4th grade
Author: Carol Schlenk, revised by Mary Rodriguez (2023)
Time Duration: One 45-minute class period
Overview: Archeologists preserve the context of a site through the use of a rectangular grid or Cartesian coordinate system. Coordinate grids are reflexive frames that extend infinitely in two or more directions from zero. This lesson focuses primarily on distance and pacing, and secondarily on coordinate grids. This activity is intended to help students develop a sense of distance. Students will pace off distances, estimate distances and use reasonable numbers.
TEKS: Mathematics, Grade 4
- (1A), apply mathematics to problems arising in everyday life, society, and the workplace
- (6A), apply knowledge of right angles to identify acute, right, and obtuse triangles
- (8B), convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger into a smaller unit when given other equivalent measures represented in a table
- (8C), solver problems that deal with measurement of length, intervals of time, liquid volumes, mass, money using addition, subtraction, multiplication, or division as appropriate
- Grid paper (included)
- Teacher’s pace list (included)
- Measuring tape
- Rulers (optional)
Activities and Procedures:
Step 1: Ask children how they might calculate the length of the playground. Tell them about the ability to calculate distance using a pacing technique (for example, one of my paces is two feet in length)
Step 2: Go to the playground and have them figure their pace for 10 yards (or use meters, as most archeologists do). To do this, lay out a tape measure that is 10 yards or meters long. Line up the students and have them walk the length of the tape measure, and ask them to count how many steps they take.
Step 3: Record on the chart below the length of their paces. To do this, divide 10 meters/yards by the number of steps to calculate the average length of step for a given student (for example, if a student takes 15 steps over 10 meters, they have a pace of 0.66 meters).
Step 4: Have them figure the length and width of their playground by pacing it (counting their steps and multiplying the number of steps by the length of their steps). Have each student map the playground on a piece of grid paper. You will need to set a scale based on the size of the playground (for example, one square of the paper could equal one foot, or one meter). Rulers can be used to complete the mapping activity.
Closure: Archeologists preserve the context of a site by mapping it on a Cartesian coordinate system. Lead students to understand why pacing is an important tool for the initial mapping of a site by discussing site recording.
Extension Activities: Use these same numbers to begin a lesson on area. Or, create a site on the playground by planting artifacts. The students can then grid the playground and map the artifacts.
Student Product: A map of the playground
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Board Paper of Class 12-Science 2011 Chemistry (SET 3) - Solutions
(i) All questions are compulsory
(ii) Question numbers 1 to 8 are very short-answer questions and carry 1 mark each.
(iii) Question numbers 9 to 18 are short-answer questions and carry 2 marks each.
(iv) Question numbers 19 to 27 are also short-answer questions and carry 3 marks.
(v) Question numbers 28 to 30 are long-answer questions and carry 5 marks each.
(vi) Use Log Tables, if necessary. Use of calculators is not allowed.
- Question 1
Define ‘activation energy’ of a reaction.VIEW SOLUTION
- Question 2
What is meant by ‘reverse osmosis’?VIEW SOLUTION
- Question 3
What type of ores can be concentrated by magnetic separation method?VIEW SOLUTION
- Question 4
Write the IUPAC name of the following compound: CH2 = CHCH2BrVIEW SOLUTION
- Question 5
What is meant by ‘lanthanoid contraction’?VIEW SOLUTION
- Question 6
How would you convert ethanol to ethene?VIEW SOLUTION
- Question 7
Draw the structure of 4-chloropentan-2-one.VIEW SOLUTION
- Question 8
Give a chemical test to distinguish between ethylamine and aniline.VIEW SOLUTION
- Question 9
Calculate the packing efficiency of a metal crystal for a simple cubic lattice.VIEW SOLUTION
- Question 10
Explain how you can determine the atomic mass of an unknown metal if you know its mass density and the dimensions of unit cell of its crystal.VIEW SOLUTION
- Question 11
Differentiate between molarity and molality values for a solution. What is the effect of change in temperature on molarity and molality values?VIEW SOLUTION
- Question 12
The thermal decomposition of HCO2H is a first order reaction with a rate constant of 2.4 × 10−3 s−1 at a certain temperature. Calculate how long will it take for three-fourths of initial quantity of HCO2H to decompose.
(log 0.25 = − 0.6021)VIEW SOLUTION
- Question 13
What do you understand by the rate law and rate constant of a reaction?
Identify the order of a reaction if the units of its rate constant are:
(i) L−1 mol s−1
(ii) L mol−1 s−1VIEW SOLUTION
- Question 14
Describe the principle controlling each of the following processes:
(i) Preparation of cast iron form pig iron.
(ii) Preparation of pure alumina (Al2O3) from bauxite ore.VIEW SOLUTION
- Question 15
Explain giving reasons:
(i) Transition metals and their compounds generally exhibit a paramagnetic behaviour.
(ii) The chemistry of actinoids is not so smooth as that of lanthanoids.VIEW SOLUTION
- Question 16
Complete the following chemical equations:
State reasons for the following:
(i) Cu (I) ion is not stable in an aqueous solution.
(ii) Unlike Cr3+, Mn2+, Fe3+ and the subsequent other M2+ ions of the 3d series of elements, the 4d and the 5d series metals generally do not form stable cationic species.VIEW SOLUTION
- Question 17
Write the main structural difference between DNA and RNA. Of the four bases, name those which are common to both DNA and RNA.VIEW SOLUTION
- Question 18
Write such reactions and facts about glucose which cannot be explained by its open chain structure.VIEW SOLUTION
- Question 19
A solution prepared by dissolving 8.95 mg of a gene fragment in 35.0 mL of water has an osmotic pressure of 0.335 torr at 25°C.
Assuming that the gene fragment is a non-electrolyte, calculate its molar mass.VIEW SOLUTION
- Question 20
Classify colloids where the dispersion medium is water. State their characteristics and write an example of each of these classes.
Explain what is observed when
(i) an electric current is passed through a sol
(ii) a beam of light is passed through a sol
(iii) an electrolyte (say NaCl) is added to ferric hydroxide solVIEW SOLUTION
- Question 21
How would you account for the following:
(i) NF3 is an exothermic compound but NCl3 is not.
(ii) The acidic strength of compounds increases in the order:
PH3 < H2S < HCl
(iii) SF6 is kinetically inert.
- Question 22
Write the state of hybridization, the shape and the magnetic behaviour of the following complex entities:
(i) [Cr(NH3)4 Cl2] Cl
(ii) [Co(en)3] Cl3
(iii) K2 [Ni(CN)4]VIEW SOLUTION
- Question 23
State reasons for the following:
(i) pKb value for aniline is more than that for methylamine.
(ii) Ethylamine is soluble in water whereas aniline is not soluble in water.
(iii) Primary amines have higher boiling points than tertiary amines.VIEW SOLUTION
- Question 24
Rearrange the compounds of each of the following sets in order of reactivity towards SN2 displacement:
(i) 2-Bromo-2-methylbutane, 1-Bromopentane, 2-Bromopentane
(ii) 1-Bromo-3-methylbutane, 2-Bromo-2-methylbutane, 3-Bromo-2-methylbutane
(iii) 1-Bromobutane, 1-Bromo-2, 2-dimethylpropane, 1-Bromo-2-methylbutaneVIEW SOLUTION
- Question 25
How would you obtain the following:
(i) Benzoquinone from phenol
(ii) 2-methyl propan-2-ol from methyl-magnesium bromide
(iii) Propane-2-ol from propeneVIEW SOLUTION
- Question 26
Write the names and structures of the monomers of the following polymers:
(iii) NeopreneVIEW SOLUTION
- Question 27
What are the following substances? Give one example of each.
(i) Food preservatives
(ii) Synthetic detergents
(iii) AntacidsVIEW SOLUTION
- Question 28
(a) Draw the structures of the following molecules:
(b) Complete the following chemical equations:
(i) HgCl2 + PH3 →
(ii) SO3 + H2SO4 →
(iii) XeF4 + H2O →
(a) What happens when
(i) chlorine gas is passed through a hot concentrated solution of NaOH?
(ii) sulphur dioxide gas is passed through an aqueous solution of a Fe (III) salt?
(b) Answer the following:
(i) What is the basicity of H3PO3 and why?
(ii) Why does fluorine not play the role of a central atom in inter-halogen compounds?
(iii) Why do noble gases have very low boiling points?VIEW SOLUTION
- Question 29
(a) What type of a battery is lead storage battery? Write the anode and cathode reactions and the overall cell reaction occurring in the operation of a lead storage battery.
(b) Calculate the potential for half-cell containing 0.10 M K2Cr2O7 (aq), 0.20 M Cr3+ (aq) and 1.0 × 10−4 M H+ (aq)
The half-cell reaction is and the standard electrode potential is given as E0 = 1.33 V.
(a) How many moles of mercury will be produced by electrolysing 1.0 M
Hg (NO3)2 solution with a current of 2.00 A for 3 hours?
[Hg(NO3)2 = 200.6 g mol−1]
(b) A voltaic cell is set up at 25°C with the following half-cells Al3+ (0.001 M) and Ni2+ (0.50 M). Write an equation for the reaction that occurs when the cell generates an electric current and determine the cell potential.
- Question 30
(a) Illustrate the following name reactions:
(i) Cannizzaro’s reaction
(ii) Clemmensen reduction
(b) How would you obtain the following:
(i) But-2-enal from ethanal
(ii) Butanoic acid from butanol
(iii) Benzoic acid from ethylbenzene
(a) Given chemical tests to distinguish between the following:
(i) Benzoic acid and ethyl benzoate
(ii) Benzaldehyde and acetophenone
(b) Complete each synthesis by giving missing reagents or products in the following:
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Refractive Index (n)
The refractive index (n) of a material is the ratio of the speed of light (c) in a vacuum to the velocity of light in the material (cS).
The refractive index of a material is always greater than 1.
water = 1.33
diamond = 2.42
glass = 1.5
air » 1
When a ray of light goes from material (1) into material (2), rather than from a vacuum into a material we talk about the relative refractive index.
Refractive index (relative) when light is travelling from one material to another 1n2
The relative refractive index can more or less than 1. If we go from material 1 with refractive index (n1) into material 2 with refractive index (n2). Then we can find the relative refractive index 1n2 by dividing the speed of light in material 1 (c1) by the speed of light in material 2 (c2) OR by dividing the refractive index of material 2 (n2) by the refractive index of material 1 (n1) OR by dividing the sine of the incident angle (q1) by the sine of the refracted angle (q2).
We can rearrange the last part of the equation above so it looks like this;
If we reverse the direction of the light from material 2 into material 1 the refractive index 2n1 is related to 1n2 like this;
Critical angle qc
When a ray of light goes from a material into an optically less dense material like air. The angle of refraction can become 90o and the ray of light travels along the boundary between the two material. When this happens the angle of incidence is called the critical angle (qc)
If the second material is air then n2 = 1 and so
If the incident angle is greater than the critical angle then light reflects at the boundary between the two material and this is called Total Internal Reflection.
Step index optical fibres
This is has a fine glass core and it is surrounded by a cladding of glass with a lower refractive index than the core. This means that light shone into the core at an angle greater than the critical angle will Total Internally Reflect at the boundary between the core and the cladding. The light then travels down the fibre through a series of reflections before exiting at the other end.
The optical fibre would work without the cladding as air also has a lower refractive index than the core glass. However the cladding is useful as it protects the core, prevents cross talk and prevents the leakage of light.
The core should be narrow as this cuts down on multi-mode dispersion which is where light entering the optical fibre at slightly different angles follow slightly different paths and arrive at the other end a slightly different times this causes the pulse of light to broaden out.
Optical fibres are used in medical instruments called endoscopes and they are used in communications (telephone, Internet, cable TV). The use of optical fibres in communications has improved the transmission of data giving us high speed internet access.
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It did not say why the planets should orbit the sun. Although Halley was dead, the comet reappeared at that time and became known as Halley's comet. Newton expanded upon the earlier work of , who developed the first accurate laws of motion for masses, according to Greg Bothun, a physics professor at the University of Oregon. Newton found that the greater a body's mass the greater the force required to overcome its inertia and mass is taken as a quantitative measure of a body's inertia. Yes No Thanks for your feedback! The block sliding across the floor stops because this frictional force acts on it.
From the acceleration, velocity and distance traveled can be determined for any time. What, then, of the people and objects in the car? The math behind this is quite simple. If there is not, the car continues in a straight line first law moving outward relative to the road. The higher the original speed, of course, the greater the likelihood the tires will squeal. The airplane has a mass m0 and travels at velocity V0. If we decrease the net force than acceleration also decreases.
Momentum, like , is a quantity, having both magnitude and direction. A Tale of Friction High school students learn how engineers mathematically design roller coaster paths using the approach that a curved path can be approximated by a sequence of many short inclines. Newton's three laws Newton, who was born in the year that Galileo died, produced a nearly perfect for the time response to Galileo's suggestion. Real progress on the subject, however, did not resume until the time of 1300-1358 , a French physicist who went much further than Philoponus had eight centuries earlier. Expect students to already know that a force can cause a change in velocity. A block will slide more easily than, for instance, a refrigerator because it has less mass. This force, in other words, is the same as weight.
Well, do you think mass affects the acceleration? Newton's laws of motion Earthly and heavenly motions were of great interest to Newton. It depend upon the net force acting on the body. It should also be clear from this example exactly why seatbelts, headrests, and airbags in automobiles are vitally important. The applications of these three laws are literally endless: from the planets moving through the cosmos to the first seconds of a car crash to the action that takes place when a person walks. If the first train is hooked, the second train will go twice the distance of the first train and the force will be twice. For college students there is. Ask them to supply the answers for the blanks in the sentences.
The physicist's definition of velocity includes both speed and direction, so any deviation from straight line motion is a change in velocity and will require an outside force. Acceleration is inversely proportional to mass. Mass is the quantity of matter. The Science Book of Motion. Applications of the second law 1 Objects, when released, fall to the ground due to the earth's attraction. Third law of motion or law of action-reaction Newton questioned the interacting force an outside agent exerted on another to change its state of motion. Conclude the presentation with a quick review of the key concepts, as listed on the slide, with blanks for students to supply the answers.
These pairs of forces exist everywhere. Galileo's observations, in fact, formed the foundation for the laws of motion. Newton's Second Law of Motion Presentation Outline slides 1-16 Open the for all students to view and present the lesson content, guided by the script below and text in the slide notes. We're assuming rightward and upward are the positive directions. The measure of inertia is mass, which reflects the resistance of an object to a change in its motion.
But even this craft would likely run into another object, such as a planet, and would then be drawn into its orbit. Since the moon is about 60 times further from Earth's center than the earth's surface, the acceleration of gravity of the moon is about. Mass: A measure of an amount of matter. The other three were unknown to Newton —yet his definition of force is still applicable. Then click the buttons to view the answers. The given figure shows the general idea about the Atwood machine.
Because velocity indicates movement in a single straight direction, when an object moves in a curve —as the planets do around the Sun —it is by definition changing velocity, or accelerating. There is no such thing as an unpaired force in the universe. In the case of scientific law, disobedience is clearly impossible —and if it were not, the law would have to be amended. For example, a book sitting on a table has a net force of zero. The main outside forces acting on an arrow are friction from air and gravity.
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The energy band diagram for a reverse-biased Si pn-junction diode under steady-state conditions is pictured in Fig. P5.5.
(a) With the aid of the diagram and assuming single-level R-G center statistics, Tn = TP = T, and ET" = Ei, simplify the general steady-state net recombination rate expression to obtain the simplest possible relationship for R at (i) x = 0, (ii) x = - xp,
(iii) x = x nn " (iv) x = - x p, and (v) x = xn•
(b) Sketch R versus x for x-values lying within the electrostatic depletion region (- xp ≤ X ≤ xn).
(c) What was the purpose or point of this problem?
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The rule of 72 is a process for quickly projecting how long it will take for a rate of investment return to make capital double. The number 72 is used in figuring out the answer by dividing the rate of return percentage per period to get an approximation of the number of years in most cases that it will take to double. The rule of 72 is used as a quick mental short cut so spreadsheets or scientific calculators are not needed.
The rule of 72 uses the rate of compounded exponential growth not simple interest year by year, gains are not removed but left in the calculation. The gains are compounded year over year in this system allowing new gains to make more money.
The Rule Of 72 Formula:
Investment rate of return X number of years invested = 72
Number of years invested = 72 / annual investment rate
Investment rate = 72 / number of years invested
The rule of 72 annual rate of return percentage and years to double. (Exact years to double). The formula.
2% annual return takes 36 years to double (35) 2 = 72/36
3% annual return takes 24 years to double (23.45) 3 = 72/24
5% annual return takes 14.4 years to double (14.21) 5 = 72/14.4
7% annual return takes 10.3 years to double (10.24) 7 = 72/10.3
9% annual return takes 8 years to double (8.04) 9 = 72/8
12% annual return takes 6 years to double (6.12) 12 = 72/6
25% annual return takes 2.9 years to double (3.11) 25 = 72/2.9
50% annual return takes 1.4 years to double (1.71) 50 = 72/1.4
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Individual differences |
Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology |
A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of measurement.
For example, length is a physical quantity. The metre is a unit of length that represents a definite predetermined length. When we say 10 metres (or 10 m) or (1 dekameter), we actually mean 10 times the definite predetermined length called "metre".
The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. Different systems of units used to be very common. Now there is a global standard, the International System of Units (SI), the modern form of the metric system.
In trade, weights and measures is often a subject of governmental regulation, to ensure fairness and transparency. The Bureau international des poids et mesures (BIPM) is tasked with ensuring worldwide uniformity of measurements and their traceability to the International System of Units (SI). Metrology is the science for developing nationally and internationally accepted units of weights and measures.
In physics units are standards for measurement of physical quantities that need clear definitions to be useful. Reproducibility of experimental results is central to the scientific method. A standard system of units facilitates this. Scientific systems of units are a refinement of the concept of weights and measures developed long ago for commercial purposes.
Scienceand medicine, often use larger and smaller units of measurement than those used in everyday life and indicate them more precisely. The judicious selection of the units of measurement can aid researchers in problem solving (see, for example, dimensional analysis).
- 1 Systems of units
- 2 Base and derived units
- 3 Calculations with units
- 4 Real-world implications
- 5 See also
- 6 Notes
- 7 External links
Systems of units[edit | edit source]
Traditional systems[edit | edit source]
Historically many of the systems of measurement which had been in use were to some extent based on the dimensions of the human body according to the proportions described by Marcus Vitruvius Pollio. As a result, units of measure could vary not only from location to location, but from person to person.
Metric systems[edit | edit source]
A number of metric systems of units have evolved since the adoption of the original metric system in France in 1791. The current international standard metric system is the International System of Units. An important feature of modern systems is standardization. Each unit has a universally recognized size.
Both the Imperial units and US customary units derive from earlier English units. Imperial units were mostly used in the British Commonwealth and the former British Empire. US customary units are still the main system of measurement used in the United States despite Congress having legally authorized metric measure on 28 July 1866. Some steps towards US metrication have been made, particularly the redefinition of basic US units to derive exactly from SI units, so that in the US the inch is now defined as 0.0254 m (exactly), and the avoirdupois pound is now defined as 453.59237 g (exactly)
Natural systems[edit | edit source]
While the above systems of units are based on arbitrary unit values, formalised as standards, some unit values occur naturally in science. Systems of units based on these are called natural units. Similar to natural units, atomic units (au) are a convenient system of units of measurement used in atomic physics.
Legal control of weights and measures[edit | edit source]
} To reduce the incidence of retail fraud, many national statutes have standard definitions of weights and measures that may be used (hence "statute measure"), and these are verified by legal officers.
Base and derived units[edit | edit source]
Different systems of units are based on different choices of a set of fundamental units. The most widely used system of units is the International System of Units, or SI. There are seven SI base units. All other SI units can be derived from these base units.
For most quantities a unit is absolutely necessary to communicate values of that physical quantity. For example, conveying to someone a particular length without using some sort of unit is impossible, because a length cannot be described without a reference used to make sense of the value given.
But not all quantities require a unit of their own. Using physical laws, units of quantities can be expressed as combinations of units of other quantities. Thus only a small set of units is required. These units are taken as the base units. Other units are derived units. Derived units are a matter of convenience, as they can be expressed in terms of basic units. Which units are considered base units is a matter of choice.
The base units of SI are actually not the smallest set possible. Smaller sets have been defined. For example, there are unit setsTemplate:Which? in which the electric and magnetic field have the same unit. This is based on physical laws that show that electric and magnetic field are actually different manifestations of the same phenomenon.
Calculations with units[edit | edit source]
Units as dimensions[edit | edit source]
Any value of a physical quantity is expressed as a comparison to a unit of that quantity. For example, the value of a physical quantity Z is expressed as the product of a unit [Z] and a numerical factor:
- For example, "2 candlesticks" Z = 2 [candlestick].
The multiplication sign is usually left out, just as it is left out between variables in scientific notation of formulas. The conventions used to express quantities is referred to as quantity calculus. In formulas the unit [Z] can be treated as if it were a specific magnitude of a kind of physical dimension: see dimensional analysis for more on this treatment.
Units can only be added or subtracted if they are the same type; however units can always be multiplied or divided, as George Gamow used to explain:
- "2 candlesticks" times "3 cabdrivers" = 6 [candlestick][cabdriver].
A distinction should be made between units and standards. A unit is fixed by its definition, and is independent of physical conditions such as temperature. By contrast, a standard is a physical realization of a unit, and realizes that unit only under certain physical conditions. For example, the metre is a unit, while a metal bar is a standard. One metre is the same length regardless of temperature, but a metal bar will be one metre long only at a certain temperature.
Guidelines[edit | edit source]
- Treat units algebraically. Only add like terms. When a unit is divided by itself, the division yields a unitless one. When two different units are multiplied, the result is a new unit, referred to by the combination of the units. For instance, in SI, the unit of speed is metres per second (m/s). See dimensional analysis. A unit can be multiplied by itself, creating a unit with an exponent (e.g. m2/s2). Put simply, units obey the laws of indices. (See Exponentiation.)
- Some units have special names, however these should be treated like their equivalents. For example, one newton (N) is equivalent to one kg·m/s2. Thus a quantity may have several unit designations, for example: the unit for surface tension can be referred to as either N/m (newtons per metre) or kg/s2 (kilograms per second squared). Whether these designations are equivalent is disputed amongst metrologists.
Expressing a physical value in terms of another unit[edit | edit source]
Conversion of units involves comparison of different standard physical values, either of a single physical quantity or of a physical quantity and a combination of other physical quantities.
just replace the original unit with its meaning in terms of the desired unit , e.g. if , then:
Now and are both numerical values, so just calculate their product.
Or, which is just mathematically the same thing, multiply Z by unity, the product is still Z:
For example, you have an expression for a physical value Z involving the unit feet per second () and you want it in terms of the unit miles per hour ():
- Find facts relating the original unit to the desired unit:
- 1 mile = 5280 feet and 1 hour = 3600 seconds (3.6 kiloseconds)
- Next use the above equations to construct a fraction that has a value of unity and that contains units such that, when it is multiplied with the original physical value, will cancel the original units:
- Last,multiply the original expression of the physical value by the fraction, called a conversion factor, to obtain the same physical value expressed in terms of a different unit. Note: since valid conversion factors are dimensionless and have a numerical value of one, multiplying any physical quantity by such a conversion factor (which is 1) does not change that physical quantity.
Or as an example using the metric system, you have a value of fuel economy in the unit litres per 100 kilometres and you want it in terms of the unit microlitres per metre:
Real-world implications[edit | edit source]
One example of the importance of agreed units is the failure of the NASA Mars Climate Orbiter, which was accidentally destroyed on a mission to Mars in September 1999 instead of entering orbit, due to miscommunications about the value of forces: different computer programs used different units of measurement (newton versus pound force). Considerable amounts of effort, time, and money were wasted.
On April 15, 1999 Korean Air cargo flight 6316 from Shanghai to Seoul was lost due to the crew confusing tower instructions (in metres) and altimeter readings (in feet). Three crew and five people on the ground were killed. Thirty seven were injured.
In 1983, a Boeing 767 (which came to be known as the Gimli Glider) ran out of fuel in mid-flight because of two mistakes in figuring the fuel supply of Air Canada's first aircraft to use metric measurements. This accident is apparently the result of confusion both due to the simultaneous use of metric & Imperial measures as well as mass & volume measures.
See also[edit | edit source]
Notes[edit | edit source]
- US Metric Act of 1866. as amended by Public Law 110–69 dated August 9, 2007
- (2002). NIST Handbook 44 Appendix B. National Institute of Standards and Technology.
- Emerson, W.H. (2008). On quantity calculus and units of measurement. Metrologia 45 (2): 134–138.
- Unit Mixups. US Metric Association.
- Mars Climate Orbiter Mishap Investigation Board Phase I Report. NASA.
- NTSB. Korean Air Flight 6316. Press release.
- Korean Air incident. Aviation Safety Net.
- includeonly>Witkin, Richard. "Jet's Fuel Ran Out After Metric Conversion Errors", New York Times, July 30, 1983. Retrieved on 2007-08-21. “Air Canada said yesterday that its Boeing 767 jet ran out of fuel in mid-flight last week because of two mistakes in figuring the fuel supply of the airline's first aircraft to use metric measurements. After both engines lost their power, the pilots made what is now thought to be the first successful emergency dead stick landing of a commercial jetliner.”
[edit | edit source]
- A Dictionary of Units of Measurement - Center for Mathematics and Science Education, University of North Carolina
- NIST Handbook 44, Specifications, Tolerances, and Other Technical Requirements for Weighing and Measuring Devices
- NIST Handbook 44, Appendix C, General Tables of Units of Measurement
- Official SI website
- Quantity System Framework - Quantity System Library and Calculator for Units Conversions and Quantities predictions
Legal[edit | edit source]
Metric information and associations[edit | edit source]
- Official SI website
- UK Metric Association
- US Metric Association
- The Unified Code for Units of Measure (UCUM)
Imperial measure information[edit | edit source]
|This page uses Creative Commons Licensed content from Wikipedia (view authors).|
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Algorithms For Approximation of J-Fixed Points of Nonexpansive - Type Maps, Zeros of Monotone Maps, Solutions of Feasibility and Variational Inequality Problems
It is well known that many physically significant problems in different areas of research can be transformed at equilibrium state into an inclusion problem of the form 0 ∈ Au, where A is either a multi-valued accretive map from a real Banach space into itself or a multi-valued monotone map from a real Banach space into its dual space. In several applications, the solutions of the inclusion problem, when the map A is monotone, corresponds to minimizers of some convex functions. It is known that the sub-differential of any convex function, say g, and denoted by ∂g is monotone, and for any vector, say v, in the domain of g, 0 ∈ ∂g(v) if and only if v is a minimizer of g. Setting ∂g ≡ A, solving the inclusion problem, is equivalent to finding minimizers of g. The method of approximation of solutions of the inclusion problem 0 ∈ Au, when the map A is monotone in real Banach spaces, was not known until in 2016 when Chidume and Idu introduced J-fixed points technique. They proved that the J-fixed points correspond to zerosof monotone maps which are minimizers of some convex functions. In general, finding closed form solutions of the inclusion problem, where A is monotone is extremely difficult or impossible. Consequently, solutions are sought through the construction of iterative algorithms for approximating J-fixed points of nonlinear maps. In chapter three, four and seven of the thesis, we present a convergence result for approximating zeros of the inclusion problem 0 ∈ Au. Let H1 and H2 be real Hilbert spaces and K1, K2, · · · , KN , and Q1, Q2, · · · , QP , be nonempty, closed and convex subsets of H1 and H2, respectively, with nonempty intersections K and Q, respectively, that is, K = K1 ∩ K2 ∩ · · · ∩ KN ̸= ∅ and Q = Q1 ∩ Q2 ∩ · · · ∩ QP ̸= ∅. Let B : H1 → H2 be a bounded linear map, Gi : H1 → H1, i = 1, · · · , N and Aj : H2 → H2, j = 1, · · · , P be given maps. The common split variational inequality problem introduced by vi Censor et al. in 2005, and denoted by (CSVIP), is the problem of finding an element u ∗ ∈ K for which ( ⟨u − u∗ , Gi(u∗)⟩ ≥ 0, ∀ u ∈ Ki, i = 1, 2, · · · , N, such that ∗ = Bu∗ ∈ Q solves ⟨v − v ∗ , Aj (v∗ )⟩ ≥ 0, ∀ v ∈ Qj , j = 1, 2, · · · , P. The motivation for studying this class of problems with N > 1 stems from a simple observation that if we choose Gi ≡ 0, the problem reduces to finding u ∗ ∈ ∩N i=1Ki , which is the known convex feasibility problem (CFP) such that Bu∗ ∈ ∩P j=1V I(Qj , Aj ). If the sets Ki are the fixed point sets of maps Si : H1 → H1, then, the convex feasibility problems (CFP) is the common fixed points problem(CFPP) whose image under B is a common solution to variational inequality problems (CSVIP). If we choose Gi ≡ 0 and Aj ≡ 0, the problem reduces to finding u ∗ ∈ ∩N i=1Ki such that the point Bu∗ ∈ ∩P j=1Qj which is the well known multiple-sets split feasibility problem or common split feasibility problem which serves as a model for many inverse problems where the constraints are imposed on the solutions in the domain of a linear operator as well as in the range of the operator. A lot of research interest is now devoted to split variational inequality problem and its gener-alizations.In chapter five and six of the thesis, we present convergence theorems for approximating solu-tions of variational inequalities and a convex feasibility problem; and solutions of split varia-tional inequalities and generalized split feasibility problems.
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Tags: Graphic Design Thesis ReportFraction Problem Solving With SolutionStudent EssayAma Reference Style DissertationCritical Thinking Skills Teaching ResourcesDraw A Picture Problem SolvingEssay On My PetTopic Sentence For A Research Paper
And when a rope pulls, we call that the force of tension, so I'm gonna call this the tension. Now we know what kind of force is acting as the centripetal force. Sometimes, people want to do this, they're like, oh yeah, there's a force of tension, and there's also a centripetal force.But that's just crazy because this tension is the centripetal force. Similarly, over here, I'm not gonna draw the centripetal force twice. I mean, it's possible you could have two forces inward.
Use Newton's second law again for another direction, and that'll get you to where you need to be.
So in other words, let's draw a quality force diagram.
A possible question would be, well, what's the force of tension in the rope?
And so, now's a good time for me to let you in on a little secret.
I wouldn't draw it twice anymore than I'd come over here and say, yeah, there's a normal force, there's also upward force. Maybe there's two ropes and you had a second tension over here pulling inward, but you'd better be able to identify what force it is before you draw it.
Don't just call it F centripetal, so you might be like, yeah, yeah, I get it.
So saying the force that causes this ball to go in a circle is the centripetal force is a little unsatisfying.
It'd be like answering the question, what force balances the force of gravity while the ball's on the table with the answer, the upward force.
And then you use Newton's second law for one of the directions at a time.
And if the direction you chose to analyze Newton's second law for didn't get you to where you needed to be, just do it again.
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Don’t ever ignore the unsightly and unattractive person in your class. Believe me, they turn out to be the ones you’ll kill to get attention from. All that matters is strong willpower and patience.
Lenses, braces, beard, makeup, change of hairstyle, or some lbs down – this is all that takes someone to turn from an ugly duckling into a beautiful and graceful swan.
Our team has compiled the greatest transformations of people who really turned into butterflies. Check them out and tell “what’s your excuse?”
#1. From 13 to 17, a real change
#2. How hair changes everything
#3. Wow, now this is a real glow-up
#4. 5 years apart. Lost some weight, gained some confidence, kept the hoodie!
#5. Can’t believe this is the same men
#6. “Dyed my hair, opened my eyes, got eyebrows…”
#7. Wow, do you think this is the same person?
#8. New style and facial hair seems to help
#9. One of the greatest transformations
#10. Never lose faith
#11. Who’s laughing now?
#12. Working out and Water does wonders!
#13. “10 to 20! My nickname used to be ugly”
#14. You go, girl!
#15. Did she change a lot?
#16. Some epic results here
#17. Speaking of glow-ups, who just nailed it?
#18. 13 VS 27. Speechless here
#19. Wow, how did she do this?
#20. Rate this one!
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NCERT Class 10 Maths Chapter 6: Complete Resource for Triangles
The benefits of using NCERT Solutions for Class 10 Maths Triangles PDF is profound. The PDF of Class 10 Maths Chapter 6 NCERT Solutions has been prepared by expert mathematicians at Vedantu after thorough research on the subject matter. All the solutions provided here are written in a simple and lucid manner. With the aid of these NCERT Solutions for Class 10 Chapter 6 of Maths, students can not only improve their knowledge but also aspire to score better in their examinations.
What is even better is that you can now download these NCERT Solutions for Class 10 Chapter Triangles PDF for free. The PDF will allow you to refer to these solutions as per your need and convenience. Download NCERT Solution PDF today to have easy access to all subject solutions for free which also includes Class 10 Science NCERT Solutions.
Exercises under NCERT Solutions for Class 10 Maths Chapter 6 Triangles
NCERT Solutions for Class 10 Maths Chapter 6, "Triangles," is a chapter that deals with the properties and classification of triangles. The chapter contains six exercises, each covering a different aspect of the topic. Below is a brief explanation of each exercise:
Exercise 6.1: In this exercise, you will be introduced to the basic concepts of triangles, including the definition, elements, types, and angles. You will also learn about congruent triangles and the criteria for their congruence.
Exercise 6.2: This exercise focuses on the properties of triangles, such as the angle sum property, the exterior angle property, and the inequality theorem. You will also learn about the Pythagorean theorem and its applications.
Exercise 6.3: In this exercise, you will learn about the similarity of triangles, including the criteria for similarity, the theorem of basic proportionality, and the application of similarity in practical situations.
Exercise 6.4: This exercise covers the mid-point theorem, which states that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half of its length. You will also learn about the converse of this theorem.
Exercise 6.5: In this exercise, you will learn about the altitude and median of a triangle and their properties. You will also learn about the centroid and the orthocenter of a triangle.
Exercise 6.6: This exercise covers the concept of the circumcenter and incenter of a triangle and their properties. You will also learn about the construction of circumcenter and incenter using various methods.
NCERT Maths Class 10 Chapter 6 - Free PDF Download
You can opt for Chapter 6 - Triangles NCERT Solutions for Class 10 Maths PDF for Upcoming Exams and also You can Find the Solutions of All the Maths Chapters below.
NCERT Solutions for Class 10 Maths Other Chapter Solutions PDF Download
NCERT Solutions for Class 10 Maths Chapter 6 Triangles Details
Given below are the details of the various sub-topics included in the Class 10 Chapter 6 Triangles NCERT Solutions:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles: 6.1 Introduction
The PDF of Class 10 Maths Triangles recalls students’ knowledge in this introduction part. Students were already introduced to the concept of Triangles in Class 9 wherein they studied properties such as congruence of Triangles. The introduction part of the chapter basically acts as a window for the students so that they are able to get an insight as to what would they be learning new under the topic of Triangles.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles: 6.2 Similar Figures
In this section of the Class 10 Maths Chapter 6, students are introduced to the concept of similar figures. Students are taught the basis of similarity in figures such as squares or equilateral triangles with the same lengths of the sides, circles with the same radii. As the students progress through this topic, they get to understand that similar figures can have the same shape but not necessarily the exact size. The questions from this topic mostly ask students to prove similarity between figures by applying the theorems.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles: 6.3 Similarity of Triangles
Once the students are made familiar with the concept of similarity, they are then introduced to the criteria under which two or more triangles are deemed similar. The NCERT Solutions for Class 10 Maths Chapter 6 PDF, in this section, explains the theorem of Basic Proportionality. A thorough understanding of this topic will allow students to form the base for solving complex problems in higher mathematics.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles: 6.4 Criteria for Similarity of Triangles
This section outlines and explains the criteria for the similarity of triangles. The basic criteria for two triangles to be called similar include: if their corresponding angles are equal and if the corresponding sides of the triangles are in the same ratio (or proportion). Students will be able to visualise the theorems as they are illustrated with the help of proper examples.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles: 6.5 Areas of Similar Triangles
Students can understand the formula and learn the process for finding the surface area of similar triangles in this section. Maths NCERT Class 10 Chapter 6 allows students to find the area of similar triangles with the utilisation of the different theorems.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles: 6.6 Pythagoras Theorem
The NCERT Solutions Class 10 Chapter 6 explores the use of the Pythagoras theorem in the case of similar triangles. Students have already learnt the theorem and its proof in Class 9. In this section, students will learn how to prove this theorem by employing the concept of similarity of triangles.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles: 6.7 Summary
The summary comprises all the topics that you have studied in the chapter. Going through the summary will allow you to recollect all that you have learnt in the chapter including the important concepts, theorems, etc.
Points to Remember
1. A triangle is a polygon with three angles and three sides. A triangle's interior angles add up to 180 degrees, whereas its exterior angles add up to 360 degrees.
2. A triangle can be classified into the following types based on its angle and sides.
Scalene Triangle: All the three sides of this triangle have different measures.
Isosceles Triangle: Any two sides of this triangle have equal length.
Equilateral Triangle: All the three sides of this triangle are equal and each angle measures 60 degrees.
Acute Angled Triangle: All the angles measure less than 90 degrees.
Right Angle Triangle: Any one of the 3 angles is equal to 90 degrees.
Obtuse-Angled Triangle: One of the angles is greater than 90 degrees.
3. Centroid of a Triangle
The centroid of a triangle is the point where the medians of its three sides intersect. It will always be within the triangle.
4. Incenter of a Triangle
The incenter of a triangle is defined as the point where the angle bisectors of the three angles intersect. It is the point in the triangle where the circle is inscribed. Drawing a perpendicular from the incenter to any of the triangle's sides gives the radius.
5. Circumcenter of the Triangle
The circumcenter of a triangle is defined as the point where the perpendicular bisectors of its three sides intersect. It isn't necessarily located inside the triangle. For an obtuse triangle, it might be outside the triangle, but for a right-angled triangle, it could be at the midpoint of the hypotenuse.
The orthocenter of a triangle is the point where the altitudes of the triangle intersect. It also falls outside the triangle in the case of an obtuse triangle and at the vertex of the triangle in the case of a right-angle triangle, just like the circumcenter.
7. Similarity of Triangles
In triangles, we'll use the same condition that two triangles are similar if their respective angles are the same and their corresponding sides are proportionate.
8. Basic Proportionality Theorem
According to Thales theorem, if a line is drawn parallel to any of the triangle's sides so that the other two sides intersect at a distinct point, the two sides are divided in the same ratio.
9. Converse of Basic Proportionality Theorem
It is the inverse of the basic proportionality theorem, which states that if a straight line divides the two sides of a triangle in the same ratio, that straight line is parallel to the triangle's third side.
Similarity Criteria of Triangles
There are four criteria for determining if two triangles are similar or not. They are as follows:
Side-Side- Side (SSS) Criterion
Angle Angle Angle (AAA) Criterion
Angle-Angle (AA) Criterion
Side-Angle-Side (SAS) Criterion
NCERT Solutions for Class 10 Maths Chapter 6 All Exercises
Vedantu's NCERT Solutions for Class 10 Maths Chapter 6 - Triangles provide a comprehensive and accessible resource for students to grasp the intricacies of triangle geometry. With a diverse range of well-structured exercises and step-by-step explanations, these solutions promote a deeper understanding of key concepts. By incorporating real-life applications, students can appreciate the relevance of triangles in everyday scenarios. Vedantu's expertly crafted solutions foster self-confidence in solving complex problems, bolstering students' problem-solving abilities. The user-friendly platform encourages interactive learning, making the study process engaging and enjoyable. As a reliable aid, Vedantu's NCERT Solutions for Class 10 Maths Chapter 6 empower students to excel in their academics and develop a strong foundation in geometry.
FAQs on NCERT Solutions for Class 10 Maths Chapter 6 - Triangles
1. How Many Exercises are There in NCERT Solutions for Class 10 Maths Chapter 6 Triangles?
The Class 10 Maths NCERT Solutions for the Chapter Triangles contain exercises corresponding to each topic. The chapter contains a total of 6 exercises with a total of 65 questions. The questions include a mix of long and short type questions. Students should attempt to understand all the concepts and theorems given in the chapter and then solve the questions in the exercises. Solving these questions will definitely give the students a competitive edge in the exams.
2. How Many Marks are Allotted to the Class 10 Maths Chapter 6 Triangles in the Board Exam?
The Class 10 Maths Chapter 6 Triangles is a part of a broader unit ‘Geometry’ in the Board exams. The unit of Geometry comprises a total of 15 marks in the Board exams. The Triangles chapter is an important chapter as per the examination point of view and as such is likely to carry around 5-6 marks in the Class 10 Board exams.
3. Which are the Important Topics to Remember Present in CBSE Class 10 Chapter 6 Triangles?
In the CBSE Class 10 Maths Chapter 6, the topic discussed is Triangles. The topics that are important from this chapter are:
Similarity theorems of triangles.
Criteria for triangle similarity.
Area calculation of similar triangles.
Pythagoras theorem and the concept of similar triangles.
Students should make sure that they are thorough with all these topics and should leave no stone unturned to practise as many questions as possible while preparing this topic for the exams.
4. Can the PDF of NCERT Solutions for Class 10 Maths Chapter 6 Triangles be Downloaded for Free?
Yes, at Vedantu you can download the NCERT Solutions for Class 10 Maths Chapter 6 Triangles PDF for absolutely free of cost. The solutions of this chapter have been compiled by some of the best subject experts and provide a clear insight into the various concepts included in the chapter. To download the PDF of the Class 10 Maths Chapter 6, you will just be required to click on the link provided on this page.
You can also choose to take a print out of the PDF and keep it handy for revision purposes. You can also download the Vedantu app n your phone from where you will be able to access the top-notch study material for your Class 10 exam preparation at one go.
5. Do I need to practice all the questions given in the NCERT Solutions Class 10 Maths Triangles?
It is a good idea to practice every question given in the NCERT Solutions for the Class 10 Maths chapter on Triangles. This way you will understand all the topics and concepts clearly and solve all the problems easily. You will also gain confidence about the exam with increased speed and accuracy because the NCERT Solutions provided by Vedantu are curated by subject matter experts. These solutions are therefore guaranteed to help you to clear your concepts easily and effectively for your exam.
6. What are the important topics covered in Class 10 Maths NCERT Solutions Chapter 6?
Chapter 6 of the Class 10 Maths NCERT book deals with Triangles. The most important topics that are covered in this chapter are:
Definition of a triangle
Similarity of two polygons with an equal number of edges
Similarity of triangles
Proving the Pythagorean Theorem
The concepts of Class 10 Maths Chapter 6 may be a bit tricky to understand. Therefore it's a good idea to download and study the NCERT solutions for Class 10 Maths. These solutions are prepared by subject matter experts with decades of experience and will help you to understand all concepts thoroughly and easily.
7. How can I score the best in Class 10 Maths Chapter 6 Triangles?
The following points will help you to score well and get to the best of your potential in Class 10 Maths Chapter 6 Triangles:
Understand the concept of this chapter.
Refer to extra materials like NCERT Solutions of Class 10 Maths Chapter 6 Triangles available at free of cost on the Vedantu app and on the Vedantu website.
Solve model papers.
Maintain a separate notebook for formulas and theorems.
Practice graphs and diagrams.
If you want to score better than all your peers, then your best shot is definitely to download the NCERT Solutions for Class 10 Maths by Vedantu. Vedantu’s NCERT solutions are prepared by the best Maths teachers in India and written in easy to understand language.
8. What are the most important theorems that come in Class 10 Chapter 6 Triangles?
The most important theorems in class 10 Chapter 6 Triangles are:
Angle Bisector Theorem
Inscribed Angle Theorem
To clearly understand the major theorems included in the Class 10 Chapter 6 Triangles, it's best to download the NCERT solutions for Class 10 Maths. These solutions will help you in learning advanced theorems like the ones present in this chapter. This way you can be sure that you will be able to score well in your Class 10 board exams as well.
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** show all your work to earn full credit. mike went to the store. he bought 3 drinks that cost $1.79 each. if he paid $10.00, how much money did he get back?
Get the answer
Category: science | Author: Selma Yafa
*** somebody help me** point p is the circumcenter abc. point p is the point of concurrency of the perpendicular bisector. find as
***15 points*** a truncated cube is a convex polyhedron with 36 edges and 24 vertices. a truncated tetrahedron is a convex polyhedron with 18 edges an
***2 portsa historian notes that many african americans moved from southern ruralareas of the united states to large urban centers farther north betwe
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GATE | GATE CS 2018 | Question 5
The area of a square is ‘d’. What is the area of the circle which has the diagonal of the square as its diameter?
(C) (1/4) πd2
One important observation to solve the question : Diagonal of Square = Diameter of Circle. Let side of square be x. From Pythogorous theorem. Diagonal = √(2*x*x) We know area of square = x * x = d Diameter = Diagonal = √(2*d) Radius = √(d/2) Area of Circle = π * √(d/2) * √(d/2) = 1/2 * π * d
Attention reader! Don’t stop learning now. Practice GATE exam well before the actual exam with the subject-wise and overall quizzes available in GATE Test Series Course.
Learn all GATE CS concepts with Free Live Classes on our youtube channel.
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Cost/Benefit AnalysisReference: System Analysis and Design
(Chapter 8) By Elias M. Awad
Data Analysis The system requirements are: 1. Better customer
service. 2. Faster information retrieval. 3. Quicker notice
preparation. 4. Better billing accuracy. 5. Lower processing and
operating cost. 6. Improve staff efficiency. 7. Consistent billing
procedure to eliminate error.
Data Analysis Several alternative must be evaluated. The
approach can introduction of computer billing system, change in
operation procedure, replacement of staff, improve billing system
or combination of this approach.
Cost and benefit categories In developing cost estimate for a
system, we need to consider the following cost elements: 1.
Hardware 2. Personals 3. Facility cost 4. Operating cost 5. Supply
Procedure for cost/benefit determination Cost and benefit
analysis procedure that gives a picture of various cost, benefits,
and rules associated with a system Determination of cost and
benefits uses the following steps: 1. Identifying the cost and
benefit pertaining to a given project. 2. Categorize the various
costs and benefits for analysis. 3. Select a method for evaluation.
4. Interpreted the result of analysis. 5. Take action.
Procedure for Cost/Benefit Determination Cost and benefit
identification: Certain cost and benefits easily identify than
other. Example:- Direct cost. Categories of cost or benefits that
is not easily identifiable is opportunity costs and benefit.
Classification of Cost and benefits The next step is to
categorize cost and benefits
1. Tangible or Intangible costs and benefits: Tangibility refers
to the easy with which cost or benefit can be measure. Expenditure
of cash for specific item or activity is known as tangible cost.
Cost that are known to exist but whose financial value cannot be
accurately measured are known as intangible cost.
Classification of Cost and benefits1. Tangible or Intangible
costs and benefits: Benefits are also classified as tangible on
intangible. Management often ignore intangibles this may lead to
Classification of Cost and benefits2. Direct or Indirect Cost
and Benefits: Direct cost are those with which a dollar figure can
be directly associated in the project. Direct benefits also can be
specifically attributable to a given project. Indirect cost are the
results of operations that are not directly associated with a given
system or activity. Indirect benefits are realized as a bi product
of another activity or system.
Classification of Cost and benefits3. Fixed or Variable: Fixed
cost are constant they do not change. Variable cost incurred on
regular basis and they are proportional to work volume. Fixed
benefits are constant they do not change. Variable benefit realized
on regular basis.
Saving versus Cost Advantage Saving are realized when there is
some kind of cost advantage. Cost advantage reduce or eliminates
expenditure. True saving reduce or eliminates various cost being
incurred. There are also saving that do not directly reduce the
Select Evaluation Method The common evaluation methods are: 1.
Net benefit analysis. 2. Present value analysis. 3. Net present
value. 4. Payback analysis. 5. Break even analysis. 6. Cash-flow
1. Net benefit analysis Net benefit= (Total benefit)- (Total
cost) Advantage: Easy to calculate, easy to interpret and easy to
present. Disadvantage: It does not account for time value of money.
Time value of money is express as:
2. Present value Analysis Present value analysis calculate the
cost and benefits of the system in terms of today's value of the
Numerical based on Present value AnalysisQ. Suppose that $3,000
is to be invested in a project, and the expected annual benefit is
$1,500 for four year life of the system. Determine the expected
profit or loss.
3. Net Present Value Net Present value:
The net present value is express as percentage of investment.
This approach is relatively easy to calculate and accounts for the
time value of money.
4. Payback Analysis It tells you how long it will take to earn
back the money you'll spend on the project. The shorter the payback
period, sooner a profit is realized and more attractive is the
4. Payback Analysis Payback formula: Elements of the formula:A.
B. C. D. E. F. G. H. Capital investment(development cost).
Investment credit difference(tax incentive). Cost investment(site
preparation). Company federal income tax bracket difference. State
and local tax. Life of capital. Time to install the system. Benefit
4. Payback Analysis Elements of the formula:1. 2. 3. 4. 5.
Project benefits(H). Depreciation (A/F) State and local tax (A X
E). Benefit from Federal Income Tax (FIT): 1 2 3 = 4 Benefits after
FIT: 4 (4 X D)
Payback Analysis Numerical ExampleA. B. C. D. E. F. G. H.
Capital investment=$200,000 Investment credit
difference(100%-8%)=92%. Cost investment=$25000. Company federal
income tax bracket difference (100%-46%)=54% State and local tax=
2%. Life of capital= 5 Years. Time to install the system = 1 years.
Benefit and saving = $250,000.
5. Break even Analysis Break even is the point where the cost of
the candidate system and that of the current one are equal. When a
candidate system is developed, initial costs usually exceed those
of the current system. This is the investment period. When both are
equal its break point. Beyond break point the candidate system
provide more benefit than the old one-return point.
6. Cash flow Analysis Cash flow analysis keep track of
accumulated cost and revenues on a regular basis. The spread sheet
format also provide payback and break point information.
Cash flow Analysis an ExampleReven Jan ue Feb Mar Apr May June
July Aug Sep Oct Nov Dec Reven 22000 22000 26000 27100 41000 48000
59050 59010 66450 64040 69700 71040 ue Expen 51175 34795 27805
27055 28445 28385 29640 29925 28030 30075 30015 30906 se Cash flow
Accu mulat ed cash flow -1805 29175 12795 45 12555 19615 29410
30085 22420 33965 39685 40134
29175 41970 43775 43730 31180 11565 17845 47930 70350 10431
14400 18413 5 0 4
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LONDON (MarketWatch) -- The new search engine Wolfram Alpha won't be replacing Google anytime soon in researching investments, but it does have some nifty features.
Wolfram Alpha was unveiled last week in the latest challenge to the Google empire. See related story.
Testing the service this week yielded some interesting dividends.
One nice feature is the ease in which returns are featured, in daily, monthly, year-to-date, annual and five-year performance, for stocks or mutual funds.
Simply enter in General Electric, for example, and those stats come out.
It also compares to rivals: in GE's case, United Technologies and 3M, as well as S&P 500, bonds and T-bills.
Also, entering General Electric will bring up a number of key facts, like market cap, revenue, dividends per share, P/E ratio and dividend yield.
The problem, however, is the Wolfram Alpha data is based on trailing 12-month totals.
MarketWatch's site, for example, has GE's dividend yield at 3.11%, reflecting GE's decision to cut its dividend to 10 cents a share; Wolfram Alpha has it at 9.8%, since GE was paying 31 cents a share each quarter.
The more mathematically inclined can look at return histograms and random-walk projections based on historical parameters.
Probably of more use is the beta calculation to figure out just how closely a stock has tracked the market in the past, though Google Finance and Yahoo Finance also have such data.
Entering "General Electric revenue in 2006" brings up annual results, and quarterly values, as well as a chart showing trailing 12-month revenue. The data does seem to be slightly off, however. For instance, Wolfram says GE revenue was $153.6 billion in 2006. That's close, but not what GE says: $151.6 billion.
That number by GE was revised lower from its original report, which perhaps explains the Wolfram miss. GE results from 2008 yielded better results.
The charting functions bring up some impressive results. It's probably not a huge surprise, but still interesting to observe from entering "market cap Ford / General Motors" that the ratio, 23.7 on Friday, surging off the charts.
Foreign data is harder to come by, however -- it can't figure out "market cap Ford / Volkswagen."
Margins also are foreign to Wolfram.
But the service does feature nice options and mortgage calculators, which can easily be turned into PDF files.
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A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is
We consider a set-theoretic version of mereology based on the inclusion relation ⊆ and analyze how well it might serve as a foundation of mathematics. ... After establishing the non-definability of ∈ from ⊆, we identify the natural axioms for ⊆-based mereology, which constitute a finitely axiomatizable, complete, decidable theory. ... The structure of hereditarily finite sets HF under inclusion is an elementary substructure of the entire set-theoretic universe V under inclusion: HF, ⊆ ≺ V, ⊆ . Proof. ...doi:10.12775/llp.2016.007 fatcat:xrj2bzsp7nf2ho33fwyi2thbx4
We consider a set-theoretic version of mereology based on the inclusion relation ⊆ and analyze how well it might serve as a foundation of mathematics. ... After establishing the non-definability of ∈ from ⊆, we identify the natural axioms for ⊆-based mereology, which constitute a finitely axiomatizable, complete, decidable theory. ... The structure of hereditarily finite sets HF under inclusion is an elementary substructure of the entire set-theoretic universe V under inclusion. HF, ⊆ ≺ V, ⊆ Proof. ...arXiv:1601.06593v2 fatcat:z7twbd7w6fhunk7z77xzdqxpfu
of null hypotheses of statistical independence as a potential source of binary data structure, and second at constructing a discrete structure (Boolean) model of those statistical interactions that remain ... on Boolean patterns that occur in the data) that can be used to simplify (by approximation) the lattice of empirical patterns. ... Cutoffs based on the level of exceptions which maximizes the Pearson Product-moment correlation based on four cells (a, b, c, d) for strong inclusions, as in Table 1 , are repeated for weak inclusion, ...doi:10.1016/0378-8733(95)00273-1 fatcat:cq4waqdahngz3b2cku2gqubf3a
The inclusion relation in the Boolean algebra χ 0 is that of χ, restricted to χ 0 . ... In this paper, we introduce two pairs of rough operations on Boolean algebras. First we define a pair of rough approximations based on a partition of the unity of a Boolean algebra. ... In Section 4, we first define a pair of rough approximations based on a partition of the unity of a Boolean algebra, then propose a pair of generalized rough approximations after defining a basic assignment ...doi:10.1016/j.ins.2004.06.006 fatcat:mwnoxkzsu5fqjhry3xeswaymaa
Communications in Computer and Information Science
The interest of the decision makers in the selection process of suppliers is constantly growing as a reliable supplier reduces costs and improves the quality of products/services. ... Setting logical conditions between attributes was carried out by using the Boolean Interpolative Algebra. ... The principle of structural functionality indicates that the structure of any element of IBA may be directly calculated based on the structure of its components. ...doi:10.1007/978-3-319-08855-6_1 fatcat:q6qxvivr4jaetnxlxha6kp4mnq
It is shown that the Joyal quasi-category model structure for simplicial sets extends to a model structure on simplicial presheaves, for which the weak equivalences are local (or stalkwise) Joyal equivalences ... The article of Jardine gives a proof of the existence of the Jardine model structure based on the technique of Boolean localization. ... Introduction The purpose of this paper is develop an analog of the Jardine model structure on simplicial presheaves in which, rather than having the weak equivalences be 'local Kan equivalences', the weak ...arXiv:1507.08723v2 fatcat:d5koc75mdjfuniqtojfwnglmcy
Boolean models are applied to deriving operator versions of the classical Farkas Lemma in the theory of simultaneous linear inequalities. ... That is what we have learned from the Boolean models elaborated in the 1960s by Scott, Solovay, and Vopěnka. ... The chase of truth not only leads us close to the truth we pursue but also enables us to nearly catch up with many other instances of truth which we were not aware nor even foresaw at the start of the ...arXiv:0907.0060v4 fatcat:qv4xp446pbdj5b4zbv3fpxjheu
The latter do however have limited expressivity, and the corresponding lattice of strong partial clones is of uncountably innite cardinality even for the Boolean domain. ... Sets of relations closed under p.p. denitions are known as co-clones and sets of relations closed under q.f.p.p. denitions as weak partial co-clones. ... Acknowledgements The authors are grateful toward Peter Jonsson, Karsten Schölzel and Bruno Zanuttini, for helpful comments and suggestions. ...doi:10.1093/logcom/exw005 fatcat:vdf5onpuz5a2jplxgi7zaq6say
The author demonstrates that the set of equivalence classes (rough sets) of such a relation is par- tially ordered with respect to the relation of rough (approximate) inclusion. ... Then they study the structure of prime filters of a P-algebra and give a canonical form of any P-algebra homomorphism. ...
The special case of completeness for the Boolean p-calculus is an improvement over that presented in but weaker than the theorem of . ... the Boolean modal p-logics. ... Acknowledgements I wish to thank Robert Goldblatt for spoting an inaccuracy in the way my completeness theorem was phrased in an earlier version. ...doi:10.1016/s0304-3975(97)00233-8 fatcat:bkuwgqcg2fg6lmhw55wds2a5vm
Boolean set operations are computed progressively by reading in input a stream of incremental refinements of the operands. ... Each refinement of the input is mapped immediately to a refinement of the output so that the result is also represented as a stream of progressive refinements. ... generated BSP tree and on a lattice-based Split data structure of the cell decomposition. ...doi:10.2312/sm.20041391 fatcat:gmldqku35vdclpdkufbzxwperu
In this paper, we provide a topological representation for double Boolean algebras based on the so-called DB-topological contexts. ... A double Boolean algebra is then represented as the algebra of clopen protoconcepts of some DB-topological context. Mathematics Subject Classification (2010): 18B35, 54B30, 68T30. ... Each filter of the Boolean algebra D ⊓ is a base of some filter of D; in particular, F ∩ D ⊓ is a base of F . ...doi:10.24193/subbmath.2019.1.02 fatcat:obbh5yufova53bcpsa3hmipgmm
The proof of the last result is based on the author’s theorem [ibid. 94 (1977), no. 2, 121-128; MR 55 #10269] of the finite axiomatizability of any nuclear X,-categorical structure. ... The proof uses the fact that the weak second order theory of linear order is decidable and also the fact that any countable Boolean algebra is isomorphic to a Boolean algebra generated by all left closed ...
The attractors of Boolean networks and their basins have been shown to be highly relevant for model validation and predictive modelling, e.g., in systems biology. ... In the realm of asynchronous, non-deterministic modeling not only is the repertoire of software even more limited, but also the formal notions for basins of attraction are often lacking. ... The work was partially funded by the German Federal Ministry of Education and Research (BMBF), grant no. 0316195. ...arXiv:1807.10103v1 fatcat:aws7v5enczeprcrsy7szv6z5xy
We focus on random microstructures consisting of a continuous matrix phase with a high number of embedded inclusions. ... The basic idea of the underlying procedure is to find a simplified SSRVE, whose selected statistical measures under consideration are as close as possible to the ones of the original microstructure. ... Acknowledgement The financial support of the "Deutsche Forschungsgemeinschaft" (DFG), project no. SCHR 570-8/1, is gratefully acknowledged. ...doi:10.1007/978-90-481-9195-6_2 fatcat:selnjyi6sjh3fodzpfw42kvo5q
« Previous Showing results 1 — 15 out of 20,447 results
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Superb course. I am very impressed with the way the faculty explained real world examples through the probability concepts. I wish we can have more courses from him on statistics and machine learning.
I really enjoyed this course. The explanations are clear and, as suggested by the title, the lecturer uses intuition and daily-life examples rather than abstract and formal definitions and notations.
By Fei Y•
I found so much in probability within this course!
By SARANYA G N•
The course was extremely refreshing and engaging.
By Simone S•
Although very simple it delivers what it promises
By Saminathan G•
Excellent course. Well designed. Very practical.
By Henrique M R P•
Good course and the teaching is at a good pace.
By Sergey B•
Karl is a great techer, thanks for the course!
Thank you for the cool module on probability.
I enjoy this course, and actually I had fun.
By Rocio R•
Very easy to follow!
And very nice exercises.
By Antonio L•
Good teacher and quite enjoyable activities
By Jacqueline T d S•
I really enjoyed and recommend this course.
By Youcheng L•
awesome course materials and presentation!
By Madhu O P S•
I am very much thankful to the teacher.
By hari G•
Can I have more advanced course of this
By Milko V•
One of the best course in Probability!
By HEDFI H•
This how probability should be taught.
By Mohammad A•
I appreciate your effort.
By Nandini R G•
Concepts were precisely explained.
interesting and easy to understand
By Edward M•
Very intuitive and easy to follow.
By Roberto M•
Fun course, excellent professor !
By Sharmila A K•
Really enjoyed doing the course.
By Naimisha J•
Now, I no more hate probability.
By Jack S•
I value the real world approach.
By Ruben W•
Very good and fun to follow MOOC
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Visit the institution website for COVID‑19 updates
A minimum of an upper second-class UK Bachelor’s degree in a relevant discipline or an overseas qualification of an equivalent standard.
Months of entry
The department is home to many internationally renowned mathematicians. Our students go on to pursue successful careers in a variety of settings, primarily as postdoctoral researchers or in the world of finance. Excellent networking opportunities are provided by our central London location and close research links to other London universities.
We offer research supervision across a broad range of pure and applied mathematics. General areas of expertise in pure mathematics include analysis, geometry, number theory, and topology. In applied mathematics key areas of activity include fluid dynamics, mathematical modelling, mathematical physics, applied and numerical analysis and financial mathematics.
Qualification, course duration and attendance options
- full time36 months
- part time60 months
Course contact details
- Dr John Talbot
- +44 (0)20 7679 4102
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3 Mar 2014: Dr. Yann Palu from Universite de Picardie
A talk by Dr. Yann Palu from Universite de Picardie, Amiens France in our monthly “Mathematics Seminar” with following details.
Title: Cluster algebras and representation theory
Date: Monday, March 3, 2014
Time: 15.00 -16.00
Place: Ruang Rapat Gedung Matematika Labtek III ITB (ITN, Labtek III Building, Ruang Rapat)
Cluster algebras were introduced by Fomin and Zelevisky in their study of total positivity and canonical bases. Starting from an oriented graph, one can define the generators of a cluster algebra by means of an inductive operation called “mutation”. This unusual definition forces cluster algebras to satisfy several interesting properties, such as the Laurent phenomenon and positivity. The combinatorics underlying this mutation procedure turned out to appear in many different areas of mathematics: integrable systems, Poisson geometry, algebraic geometry, and representation theory of algebras. This talk will be an introduction to cluster algebras and an illustration of their basic properties with some small examples.
Another talk by same speaker in our bi-weekly “Algebra Seminar” with following details.
Title: An introduction to Caldero-Chapoton maps
Date: Wednesday, March 5, 2014
Time: 14.30 – 15.30
Place: Ruang Seminar I.2 Gedung Matematika Labtek III ITB (ITB, Labtek III Building, Ruang Seminar I.2)
Cluster algebras were introduced by Fomin and Zelevisky. They are defined by giving specific generators, called cluster variables. The Caldero-Chapoton map is an important tool in the theory of categorification of cluster algebras. It gives an “explicit” formula for the cluster variables of a cluster algebra associated with a quiver in terms of the representations of this quiver. The talk will be an introduction to the Caldero-Chapoto map for Jacobi-finite quivers and illustrated with examples.
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A preeminence of polygons is the the amount of the exterior angles constantly equals 360 degrees, however lets prove this for a continual octagon (8-sides).
You are watching: Find the sum of the measures of exterior angles one at each vertex of an octagon
First we must figure out what every of the interior angles equal. To carry out this we usage the formula:
((n-2)*180)/n where n is the variety of sides the the polygon. In our situation n=8 for an octagon, so we get:
((8-2)*180)/8 => (6*180)/8 => 1080/8 = 135 degrees. This means that each internal angle of the consistent octagon is equal to 135 degrees.
Each exterior edge is the supplementary angle to the internal angle at the vertex of the polygon, so in this case each exterior edge is same to 45 degrees. (180 - 135 = 45). Remember that supplementary angles add up come 180 degrees.
And since there room 8 exterior angles, we multiply 45 levels * 8 and we acquire 360 degrees.
This technique works because that every polygon, as long as you space asked to take it one exterior angle every vertex.
upvote 3 Downvote
Either i don"t understand your thinking or you are talking bollocks. The internal angles add up tp 1080 in a polygon, ie 135 each.
All you have to do is division 360/n, n gift the variety of sides in the polygon
I agree with the an initial person. The IS 135!!!
Its wrong the prize is 45, every you have to do it take it 360 and divide that by the number of sides (360/n) so lets say the the variety of sides is 6, her equation would certainly be 360/6 which would be and also the answer would certainly be 60. Inspect my mathematics if you don"t think I"m right.
This aided me so much thank you
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new_Math
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The Shelton Fire Department is urging the public to keep safety in mind when preparing meals and using candles this Thanksgiving. Statistics from U.S. Fire Administration indicate that Thanksgiving is the peak day for home cooking fires. The average number of home fires on Thanksgiving Day is normally double the average number of fires in homes all other days. Most fires that result during cooking can be avoided by paying attention and being organized. To prevent a fire or injury and stay safe when cooking and celebrating Thanksgiving, follow these simple rules: \u00b7\u00a0 \u00a0 \u00a0 \u00a0Stay in the kitchen when you are frying, grilling, or broiling food. If you must leave the home for even a short period of time, turn off the stove or oven. \u00b7\u00a0 \u00a0 \u00a0 \u00a0If you are simmering, baking, boiling, or roasting food, check it regularly and remain in the home while food is cooking. Use a timer to remind you that the stove or oven is on. \u00b7\u00a0 \u00a0 \u00a0 \u00a0Stay alert. Don\u2019t cook if you are sleepy, have been drinking alcohol or have taken medicine that makes you drowsy. \u00b7\u00a0 \u00a0 \u00a0 \u00a0Make your cooking area safe. Move things that can burn away from the stove. Keep things that burn \u2013 pot holders, oven mitts, paper or plastic - off your stovetop. \u00b7\u00a0 \u00a0 \u00a0 \u00a0Turn pot handles toward the back so they can\u2019t be bumped. \u00b7\u00a0 \u00a0 \u00a0 \u00a0Don\u2019t store things that can burn in an oven, microwave, or toaster oven. \u00b7\u00a0 \u00a0 \u00a0 \u00a0Clean food and grease off burners, stovetops, and ovens. \u00b7\u00a0 \u00a0 \u00a0 \u00a0Wear clothing with sleeves that are short, close fitting, or tightly rolled up. \u00b7\u00a0 \u00a0 \u00a0 \u00a0Always keep an oven mitt and lid nearby when you're cooking. If a small grease fire starts in a pan, put on an oven mitt and smother the flames by carefully sliding the lid over the pan. Turn off the burner. Don't remove the lid until it is completely cool. \u00b7\u00a0 \u00a0 \u00a0 \u00a0If there is an oven fire, turn off the heat and keep the door closed to prevent flames from burning you and your clothing. Have the oven serviced before you use it again. \u00b7\u00a0 \u00a0 \u00a0 \u00a0Use turkey fryers outdoors, away from the home and deck. Always monitor oil temperature. Use caution to not overfill or spill hot oil. \u00b7\u00a0 \u00a0 \u00a0 \u00a0Keep children away from the stove. The stove will be hot and kids should stay 3 feet away. Don\u2019t forget about fire dangers posed by lit candles. \u00b7\u00a0 \u00a0 \u00a0 \u00a0Flameless \u201ccandles\u201d, such as battery powered are always preferred for safety. \u00b7\u00a0 \u00a0 \u00a0 \u00a0Flame lit candles should be in a safe location that is kept free of combustible surroundings. Consider where combustible items might be placed and where candles could be knocked over and where they could be forgotten about over time. \u00b7\u00a0 \u00a0 \u00a0 \u00a0Never leave children alone in room with a lit a candle.
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new_Math
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My Students Struggle to Solve Basic Equations
A MiddleWeb Blog
I actually wrote an article about the problem in 2021: Refreshing Students’ Equation Solving Skills. Since then I have been purposefully trying to help students get better at solving equations.
I’ve done things like having students keep their work neater so they don’t make careless errors, drawing a line by the equal sign to help them visualize the equality, and in general just trying to get them to write things down.
Yet my students each year still continue to struggle in this area, and since solving an equation is the foundation that most higher math concepts build off of, we’ll continue to try to improve.
Pinpointing problem areas
I realized I was going to have to be more strategic if I was going to help my students. I needed to know what they are specifically having trouble understanding. So I picked two problems (they were based on 6th and 7th grade standards in our state) for my 11th graders to work.
MA19.6.19 Write and solve an equation in the form of x+p=q or px=q for cases in which p, q, and x are all non-negative rational numbers to solve real-world and mathematical problems.
MA19.7.9a Solve word problems leading to equations of the form px+q=r and p(x+q)=r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
I had my students come up to my desk one at a time. I presented them with the problems and a four-function calculator. They worked a problem and often talked out loud about what they were thinking as they were working. I didn’t ask them to, that was just a bonus!
Here are the two problems:
20 – 7x = 6x -6
2/3b + 7 = -1
I listened as they worked. Then I took the Post-it notes they had worked their problems on and really studied their work. In fact, I often rewrote what the student wrote so I could really understand their thinking. That helped me so much. I have always struggled trying to determine what students were thinking. By rewriting their work, I was able to gain more insight.
I then sorted the Post-it notes according to the type of error each student made. I have listed the categories below.
►Confused by Fractions
Not surprisingly, the problem with the fraction was missed much more than the one without. A few students said that they could not begin the problem because it had a fraction in it, and no amount of encouragement could persuade them to try it.
Some students stopped after subtracting both sides by 7 because they simply didn’t know what to do with 2/3, so their answer was -8. Some students multiplied both sides by two thirds instead of multiplying by the reciprocal; their answer was -16/3. One student subtracted 2/3 from both sides, after they subtracted 7 from both sides.
►Combined Unlike Terms
Students combined 20 with -7x to get 13x, while 6x-6 was combined to get x. And others combined 2/3b with 7 to get 14/3b.
►Moved or Lost the Equal Sign
If students subtracted so that they had a zero on one side of the equation, often the equal sign would just disappear. Sometimes the equal sign would never be seen in the students’ work at all.
What does this all mean?
In the broadest sense it means that students who struggle to solve a 6th or 7th grade level equation will definitely struggle to solve quadratic, exponential, or logarithmic equations that are part of the Algebra 2 course of study. More time has to be spent fortifying students’ ability in this area.
Realizing that this was necessary, we allowed for a few weeks at the beginning of the year to refresh students on solving equations. It wasn’t enough. Now I’m thinking it would be better to spiral in problems and continue working on it all year long.
Specifically, I think there are some fundamental skills related to solving equations that students are lacking. Maybe lacking is not the right word; maybe they have the skills but are unable to always apply them correctly or at the right time.
What are students not understanding?
I think the problem they have with fractions indicates they don’t understand reciprocals. Students know that 2/3 is literally 2 divided by 3; so they mistakenly think they should multiply both sides by 2/3. To complicate matters, they are afraid of fractions. They will skip a whole problem if it has a fraction in it.
Why are students still combining unlike terms? I am at a loss. We model constantly the correct way to combine like terms. I think sometimes, if students don’t know what to do, they think they should try anything. I heard a lot of “I know I’m supposed to do something here…”
The moving or missing equal sign is about more than sloppy work. It’s a lack of understanding about equivalence. They haven’t really learned what the equal sign signifies.
What to do about it?
These are my first thoughts about how to help students solve equations.
Model correct vocabulary, It’s not 7x; it’s 7 multiplied by x. It also might be helpful to say one x, as opposed to x. That’s tedious, but I don’t think all students understand the invisible “one” there. Also, do students know that multiplying by 3/2 will yield the same answer as dividing by 2/3?
Make sure students are clear on the definition of solving an equation. To solve an equation means to find all numbers that make the equation true. Source
Help students understand equivalence. Make it mandatory that students plug their solution back in after solving the problem. They will literally be able to see that the correct answer is one that makes the equation true. That will drive home the meaning of the equal sign and help them understand the definition of equivalence.
Be more intentional when teaching students how to “undo” multiplication, division, etc. Explicitly state when to subtract 2x from each side and when to divide both sides by 2.
I also need to diagnose problems sooner. I need to study students’ work in the early weeks of our time together and see what they know and what they don’t know about solving equations.
Much of the problem rests with my assumption that when students arrive in my class, they have mastered solving equations – when they haven’t. Going forward I am going to assume that my students need some coaching and practice and one-on-one help to be proficient at solving equations.
I can’t fall back on the fact that I work a lot of equations on the board. When students watch their teacher solve equations on the board, they don’t know what they don’t know. It’s easy to watch someone do something and think “that’s easy; I can do that.”
I plan to talk with other teachers in my department and see what they suggest. I also want to check with some of our middle school teachers to see if they have any suggestions. And thanks in advance for sharing any ideas you might have in the comments below.
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new_Math
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Individual differences |
Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology |
The error of measurement is the observed differences in obtained scores due to chance variance.
The standard error of measurement or estimation is the estimated standard deviation of the error in that method. Specifically, it estimates the standard deviation of the difference between the measured or estimated values and the true values. Notice that the true value of the standard deviation is usually unknown and the use of the term standard error carries with it the idea that an estimate of this unknown quantity is being used. It also carries with it the idea that it measures not the standard deviation of the estimate itself but the standard deviation of the error in the estimate, and these are very different.
In applications where a standard error is used, it would be good to be able to take proper account of the fact that the standard error is only an estimate. Unfortunately this is not often possible and it may then be better to use an approach that avoids using a standard error, for example by using maximum likelihood or a more formal approach to deriving confidence intervals. One well-known case where a proper allowance can be made arises where the Student's t-distribution is used to provide a confidence interval for an estimated mean or difference of means. In other cases, the standard error may usefully be used to provide an indication of the size of the uncertainty, but its formal or semi-formal use to provide confidence intervals or tests should be avoided unless the sample size is at least moderately large. Here "large enough" would depend on the particular quantities being analysed.
Standard error of the mean
The standard error of the mean (SEM), an unbiased estimate of expected error in the sample estimate of a population mean, is the sample estimate of the population standard deviation (sample standard deviation) divided by the square root of the sample size (assuming statistical independence of the values in the sample):
- s is the sample standard deviation (i.e. the sample based estimate of the standard deviation of the population), and
- n is the size (number of items) of the sample.
A practical result: Decreasing the uncertainty in your mean value estimate by a factor of two requires that you acquire four times as many samples. Worse, decreasing standard error by a factor of ten requires a hundred times as many samples.
This estimate may be compared with the formula for the true standard deviation of the mean:
- σ is the standard deviation of the population.
Note: Standard error may also be defined as the standard deviation of the residual error term. (Kenney and Keeping, p. 187; Zwillinger 1995, p. 626)
If values of the measured quantity A are not statistically independent but have been obtained from known locations in parameter space x, an unbiased estimate of error in the mean may be obtained by multiplying the standard error above by the square root of (1+(n-1)ρ)/(1-ρ), where sample bias coefficient ρ is the average of the autocorrelation-coefficient ρAA[Δx] value (a quantity between -1 and 1) for all sample point pairs.
Assumptions and usage
If the data are assumed to be normally distributed, quantiles of the normal distribution and the sample mean and standard error can be used to calculate confidence intervals for the mean. The following expressions can be used to calculate the upper and lower 95% confidence limits, where x is equal to the sample mean, s is equal to the standard error for the sample mean, and 1.96 is the .975 quantile of the normal distribution.
- Upper 95% Limit =
- Lower 95% Limit =
In particular, the standard error of a sample statistic (such as sample mean) is the estimated standard deviation of the error in the process by which it was generated. In other words, it is the standard deviation of the sampling distribution of the sample statistic. The notation for standard error can be any one of , (for standard error of measurement or mean), or .
Standard errors provide simple measures of uncertainty in a value and are often used because:
- If the standard error of several individual quantities is known then the standard error of some function of the quantities can be easily calculated in many cases;
- Where the probability distribution of the value is known, it can be used to calculate an exact confidence interval; and
- Where the probability distribution is unknown, relationships like Chebyshev’s or the Vysochanskiï-Petunin inequality can be used to calculate a conservative confidence interval
- As the sample size tends to infinity the central limit theorem guarantees that the sampling distribution of the mean is asymptotically normal.
- Consistency (measurement)
- Least squares
- Observational error
- Sample mean and sample covariance
- Scoring (testing)
- Statistical estimation
- Statistical measurement
- Test bias
- Test reliability
- Test scores
Survival function - Kaplan-Meier - Logrank test - Failure rate - Proportional hazards models
|This page uses Creative Commons Licensed content from Wikipedia (view authors).|
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new_Math
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You will never believe this, but it is a known fact amongst many lottery players that the combination of numbers: one two three four five six is a definite losing combination. Are you surprised?
Although many wise, yet inexperienced lotto players, mathematicians believe that no matter which six numbers you choose/predict in a lotto game, they all have equal chance of being the winning combination. Well, so they believe, but the question remains, are they right? No, they’re not.
Once you actually study the statistics and analyse each lottery game’s drawing outcomes, and not only in your country alone, but world-wide since as early as the year ninety fifty five, you will confidently be able to confirm all logical probabilities by applying one plain and simple rule.
The most probable will happen most frequently, and the least probable will happen less frequently. Therefore, if you always play the probabilities you stand a much better chance of winning at a lotto game. For example if you use a pattern of numbers which has only won five % of lottery games, then you can be certain of a ninety five % chance of losing. Or if you chose a combination of six numbers which has never in the history of any lottery game been chosen, then plain common sense will tell you that you have a zero chance at winning.
Surely those mathematicians who believe the opposite to be true should listen to their common sense instead of mathematical calculations and realise their calculations and beliefs are totally absurd when it comes to a lottery game.
If you really want to win at a lottery game one day, take note of these ten reasons why you should never play these six lotto numbers:
1. One number combination
2. Sequential numbers
3. Pattern betting
4. Bordering Numbers
5. Calendar Figures
6. All numbers are low, and not half only
7. Tail end of a bell bend
8. Twenty thousand tickets sold at each lotto draw
9. Not a well-adjusted game
10. Falls short of the seventy % of the possible range of sums
So now you know. If you are playing these numbers, try and avoid them the next time you get your lotto ticket from http://luckynumbers.co.za/
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new_Math
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This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group, a theory that is more complicated than the study of the classical non-modular case. Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the better understood non-modular setting. It details techniques for the computation of invariants for many modular representations of finite groups, especially the case of the cyclic group of prime order. It includes detailed examples of many topics as well as a quick survey of the elements of algebraic geometry and commutative algebra as they apply to invariant theory. The book is aimed at both graduate students and researchers—an introduction to many important topics in modern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter.
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new_Math
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In this paper, we give a construction of optimal families of N-ary perfect sequences of period N2, where N is a positive odd integer. For this, we re-define perfect generators and optimal generators of any length N which were originally defined only for odd prime lengths by Park, Song, Kim, and Golomb in 2016, but investigate the necessary and sufficient condition for these generators for arbitrary length N. Based on this, we propose a construction of odd length optimal generators by using odd prime length optimal generators. For a fixed odd integer N and its odd prime factor p, the proposed construction guarantees at least (N/p)p-1φ(N/p)φ(p)φ(p-1)/φ(N)2 inequivalent optimal generators of length N in the sense of constant multiples, cyclic shifts, and/or decimations. Here, φ (·) is Euler's totient function. From an optimal generator one can construct lots of different N-ary optimal families of period N2, all of which contain pmin-1 perfect sequences, where pmin is the least positive prime factor of N.
Bibliographical notePublisher Copyright:
© 2018 IEEE.
All Science Journal Classification (ASJC) codes
- Information Systems
- Computer Science Applications
- Library and Information Sciences
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new_Math
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Accurate Ohm's Law Calculator | Voltage, Current, Resistance & Power | Free Online Tool
Ohm's Law Calculator is an online tool that calculates the relationship between electric current, voltage, and resistance, based on Ohm's Law. It is a useful tool for electricians, engineers, and students who want to calculate the value of any of the three variables and solve problems related to electrical circuits.
Using the Ohm's Law Calculator is very easy. There are three input fields where you can enter the values of the two variables you know, and the calculator will automatically calculate the third variable. The three variables are:
- Voltage (V): The electrical potential difference between two points in a circuit, measured in volts (V).
- Current (I): The flow of electric charge through a conductor, measured in amperes (A).
- Resistance (R): The property of a material that opposes the flow of electric current, measured in ohms (Ω).
To use the Ohm's Law Calculator, follow these simple steps:
- Choose the variable you want to calculate (voltage, current, or resistance).
- Enter the values of the two known variables in the input fields.
- Click on the "Calculate" button, and the calculator will display the result in the third input field.
The main advantage of using the Ohm's Law Calculator is its speed and accuracy. Instead of manually calculating the value of the unknown variable using Ohm's Law formula (V = IR, I = V/R, or R = V/I), you can get an instant result with just a few clicks. This saves time and reduces the chance of making calculation errors. Additionally, the calculator is user-friendly and provides a clear interface for easy navigation.
Moreover, the Ohm's Law Calculator also includes a graphical representation of the circuit and its values, making it easier to understand the relationship between the variables. The calculator also allows you to switch between different units of measurement, such as volts, millivolts, kilovolts, amperes, milliamperes, kiloamperes, ohms, kiloohms, and megohms, which makes it more versatile and convenient to use for a wide range of applications.
In conclusion, the Ohm's Law Calculator is a useful tool for anyone who deals with electrical circuits and needs to calculate the values of voltage, current, and resistance quickly and accurately. Its user-friendly interface, graphical representation, and the ability to switch between different units of measurement make it an essential tool for electricians, engineers, and students.
It is believed that these calculations are accurate, but not guaranteed. Use at your own risk!
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new_Math
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Math problems to solve
Here, we debate how Math problems to solve can help students learn Algebra. Our website can help me with math work.
The Best Math problems to solve
Apps can be a great way to help students with their algebra. Let's try the best Math problems to solve. So before you choose any of the websites on this list, it’s a good idea to do some research on them and make sure they are a good fit for your child’s needs. Many sites have free trial periods that allow you to try out their services without paying anything at all, which is great because it allows you to see if it’s right for your child before you have to commit to anything. Some sites also offer free trial periods for certain plans, so be sure to check those out as well. In addition, make sure that the site has an easy-to-use interface and that there are no hidden fees or charges. And lastly, make sure that the site offers a 24/7 support line so that your child can get help whenever they need it.
Expression is a math word that means to write something as an equation. For example, 2 + 3 would be written as (2+3). There are many types of expressions in math. One type of expression is an equation. An equation is just a math word that means to write something as an equation. For example, 2 + 3 would be written as (2+3). Another type of expression is an equation with variables. In this type of expression, the variables replace the numbers in the equation. For example, x = 2 + 3 would be written as x = (2+3). A third type of expression is a variable in an equation. In this type of expression, the variable stands for one of the numbers in the equation. For example, x = 2 + 3 would be written as x = (2+3). A fourth type of expression is called a fraction in which you divide something by another thing or number. Fractions are written like regular numbers but with a '/' symbol before the number. For example, 4/5 would be written as 4/5 or 4 5/100. Anything that can be written as a number can also be used in an addition problem. This means that any number or group of numbers can be added together to solve an addition problem. For example: 1 + 1 = 2, 2 + 1 = 3, and 5 -
The partial fraction decomposition solver is used to solve the boundary value problem of a partial fraction expression. This method is widely used in scientific, engineering, and finance fields. This solver works in two steps: The first step requires finding the roots of the following equation. br>The second step requires solving for one variable at a time. br>For each root, use the formula for that variable to obtain an approximate value for the remaining variables. br>Then combine these approximate values using an algorithm to obtain a final answer. br>For more information on solving boundary value problems using partial fraction decomposition, see Partial fraction decomposition Solver.
To solve a trinomial, first find the coefficients of all of the terms in the expression. In this example, we have ("3x + 2"). Now you can start solving for each variable one at a time using algebraic equations. For example, if you know that x = 0, y = 9 and z = -2 then you can solve for y with an equation like "y = (0)(9)/(-2)" After you've figured out all of the variables, use addition or subtraction to combine them into one final answer.
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new_Math
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The Dirichlet function χ presents a particular problem for the theory of the Riemann integral. Consider this sequence of functions:
f (t) = lim (cos (n! πt))
(1 if t = k/n! for k an integer and 0 otherwise), all of which are clearly Riemann integrable. This sequence of functions fn
(t) converges to χ(t), where χ(t) = 0 when t is irrational and χ(t) = 1 when t is rational (the characteristic function
of the rational numbers over the set of real numbers). This is not
Riemann integrable because for any partition P you can make the Riemann sums
equal either 0 or 1, by taking the points ci
to be either rational or irrational. Thus, the space of all Riemann integrable functions is incomplete, since taking a Cauchy sequence
will converge to χ, which is not Riemann integrable.
This function motivated the theory of the Lebesgue integral, and is indeed Lebesgue integrable, with an integral (over any interval) of zero, because χ(t) is zero almost everywhere, i.e. zero everywhere except on a set of measure zero.
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new_Math
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- How do I insert a vertical bar in Word?
- How do I insert a vertical line in Gmail signature?
- Is a vertical line a function?
- What is the vertical line symbol called?
- What is a vertical line?
- How do you use the vertical line test to identify a function?
- How do you tell if a graph represents a function?
- What is vertical bar on keyboard?
- How do you type a vertical line?
- How do I get a vertical bar on my keyboard?
- What do two vertical lines mean in math?
- What does vertical line test mean?
- What does a vertical line mean on a graph?
- Is a vertical line a linear equation?
How do I insert a vertical bar in Word?
Use a Bar Tab to Add a Vertical LineSelect the paragraph where you want to add the vertical line.Go to Ribbon > Home.
Click the Tabs button at the bottom of the dialog.In the Tab stop position box, enter the position where you want the vertical line to appear.
Click the Bar button in the Alignment section..
How do I insert a vertical line in Gmail signature?
Scroll down until you see the ‘Signature’ box. Type in your name and title separated by a vertical line. The vertical line key is above the ‘enter/return’ key on your keyboard and is the same key as the forward slash “\”.
Is a vertical line a function?
For a relation to be a function, use the Vertical Line Test: Draw a vertical line anywhere on the graph, and if it never hits the graph more than once, it is a function. If your vertical line hits twice or more, it’s not a function.
What is the vertical line symbol called?
The vertical line, also called the vertical slash or upright slash ( | ), is used in mathematical notation in place of the expression “such that” or “it is true that.” This symbol is commonly encountered in statements involving logic and sets. Also see Mathematical Symbols.
What is a vertical line?
: a line perpendicular to a surface or to another line considered as a base: such as. a : a line perpendicular to the horizon. b : a line parallel to the sides of a page or sheet as distinguished from a horizontal line.
How do you use the vertical line test to identify a function?
To use the vertical line test, take a ruler or other straight edge and draw a line parallel to the y-axis for any chosen value of x. If the vertical line you drew intersects the graph more than once for any value of x then the graph is not the graph of a function.
How do you tell if a graph represents a function?
Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
What is vertical bar on keyboard?
Alternatively referred to as a vertical bar, the pipe is a computer keyboard key “|” is a vertical line, sometimes depicted with a gap. This symbol is found on the same United States QWERTY keyboard key as the backslash key. … Keyboard help and support.
How do you type a vertical line?
You can type a straight vertical line, or “|,” on most modern keyboards dating back to some of the 1980s IBM PCs. It’s generally found above the backslash, so you can type a “|” by holding down the shift key and hitting the “” key.
How do I get a vertical bar on my keyboard?
google said,Shift-\ (“backslash”).German keyboard it is on the left together with < and > and the Alt Gr modifier key must be pressed to get the pipe.Note that depending on the font used, this vertical bar can be displayed as a consecutive line or by a line with a small gap in the middle.More items…
What do two vertical lines mean in math?
Every number on the number line also has an absolute value, which simply means how far that number is from zero. The symbol for absolute value is two vertical lines. … For example, the absolute value of “negative 10” is ten, and the absolute value of “positive 10” is also 10.
What does vertical line test mean?
The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.
What does a vertical line mean on a graph?
A vertical line is one the goes straight up and down, parallel to the y-axis of the coordinate plane. All points on the line will have the same x-coordinate. … A vertical line has no slope. Or put another way, for a vertical line the slope is undefined.
Is a vertical line a linear equation?
Besides horizontal lines, vertical lines are also special case of linear equations. Similar to the lesson for the horizontal lines case, we will practice on determining the equations for graph where all the x points have the same value.
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We propose a method for studying symmetric global Hopf bifurcation problems in a parabolic system. The objective is to detect unbounded branches of non-constant periodic solutions that arise from an equilibrium point and describe their symmetric properties in detail. The method is based on the twisted equivariant degree theory, which counts orbits of solutions to symmetric equations, similar to the usual Brouwer degree, but on the report of their symmetric properties.
Equivariant Global Hopf Bifurcation in Abstract Nonlinear Parabolic Equations
Arnaja Mitra, The University of Texas at DallasAuthors: Zalman Balanov, Wieslaw Krawcewicz, Arnaja Mitra, Dmitrii Rachinskii
2023 AWM Research Symposium
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A new approximation algorithm for the multilevel facility location problem
Discrete Applied Mathematics , Volume 158 - Issue 5 p. 453- 460
In this paper we propose a new integer programming formulation for the multilevel facility location problem and a novel 3-approximation algorithm based on LP-rounding. The linear program that we use has a polynomial number of variables and constraints, thus being more efficient than the one commonly used in the approximation algorithms for these types of problems.
|Econometric Institute Reprint Series|
|Discrete Applied Mathematics|
|Organisation||Erasmus Research Institute of Management|
Gabor, A.F, & van Ommeren, J.C.W. (2010). A new approximation algorithm for the multilevel facility location problem. Discrete Applied Mathematics, 158(5), 453–460. doi:10.1016/j.dam.2009.11.007
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The title "Associate Professor", which is commonly used in North America, is "usually connected to tenure" in that it is almost exclusively given to tenured or permanent professors who are higher in rank than Assistant Professors. This has also been explained in previous Academia.SE questions, for example:
Within the last year, someone also asked here about the awarding of the Associate Professor title to people without doctorates: Is it true, that there are associate professors, full professors and University provosts without a doctorate in the Western Continental Europe?, and we learned there that in UK there are Professorships awarded in Law and Engineering (and I wouldn't be surprised if also in Medicine) to people without doctorates.
I wonder if there's any precedent for people being given this title without a PhD in Canada? I wouldn't be surprised if people have this title after getting a JD, MD, PharmD, PEng, etc., so even more specifically I am wondering about people who have only an undergrad degree and/or Masters.
The reason for my question, is because it looks like a U15 university in Canada (I might as well just say openly that it's University of Waterloo) says that they will be re-labeling Continuing Lecturers into Associate Professors:
Continuing Lecturers (soon to become Associate Professors), often enough do not have a PhD (for example here and here). I understand that other Canadian universities (e.g. University of Toronto and McMaster University) also have the "teaching-stream Professor" positions, but advertisements for applying to those positions suggest that a PhD is required.
Since Charles Grant astutely pointed out that Freeman Dyson's full professorship at Cornell was without a PhD, I'd like to be clear that I'm not looking for "one-time exceptional cases" that lasted only 1 year and went to someone who helped Feynman get the Nobel Prize, but more for "regular" positions that are offered frequently (e.g. there's at least one job advertisement at the university per year for a job with the "Associate Professor" title).
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#1 The Ratchet Eye
This transcends ratchet with it’s amazing creativity!
#2 The Ratchet Rainbow
Looks kinda like a cartoon superhero?
#3 Strawberry Blonde
Looks pretty crazy, but I think it’s just extensions
#4 Sparkle Princess
Okay, at least you gotta respect the time and effort that must’ve gone into this.
#5 Hot Mess
Does this weave come with super powers?
Dolla Dolla Bills Y’all!
#7 Hair By Skittles
Well, if she has little kids I bet they like it.
Is that a patch?
#9 Cottn Candy?
Wonder what it looks like down? Wonder if it comes down at all?
#10 The Tribal Bun
Looks pretty good from the front, though?
#11 Mr. Ratchet
This actually looks really difficult and complicated.
#12 The Super Sayyan
Wonder if she transforms?
#13 The Crazy Hat
Think she went hunting that day?
#14 The Jolly Ranchers
LMFAOOOOO….IM DONE!! XD
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How to find an eigenvector?
Step 1: Determine the eigenvalues of the given matrix A using the equation det (A – λI) = 0, where I is equivalent order…
How to find eigenvalues and eigenvectors?
Characteristic Polynomial. That is, start with the matrix and modify it by subtracting the same variable from each…
How to find the eigenvalues of a matrix?
Step 1: Make sure the given matrix A is a square matrix. Also, determine the identity matrix I of the same order.
How do you calculate matrix?
Multiply the entry in the first row and second column by the entry in the second row and first column. If we are finding the determinant of the 2×2 matrix A, then calculate a12 x a21. 3. Subtract the second value from the first value 2×2 Matrix. 2×2 Matrix Determinant Formula.
Can an eigenvector be a zero vector?
Eigenvalues may be equal to zero. We do not consider the zero vector to be an eigenvector: since A 0 = 0 = λ 0 for every scalar λ, the associated eigenvalue would be undefined. If someone hands you a matrix A and a vector v, it is easy to check if v is an eigenvector of A: simply multiply v by A and see if Av is a scalar multiple of v.
What is an eigenvector of a covariance matrix?
Eigen Decomposition of the Covariance Matrix Eigen Decomposition is one connection between a linear transformation and the covariance matrix. An eigenvector is a vector whose direction remains unchanged when a linear transformation is applied to it. It can be expressed as
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A related point is that Kelly assumes the only important thing is long-term wealth. Most people also care about about the path to get there. Two people dying with the same amount of money need not have had equally happy lives. Kelly betting leads to highly volatile short-term outcomes which many people find unpleasant, even if they believe they will do well in the end.
More recently, the strategy has seen a renaissance, in response to claims that legendary investors Warren Buffet and Bill Gross use a variant of the Kelly criterion. The formula is used to determine the optimal amount of money to put into a single trade or bet. Kelly began to develop investing strategies according to probability theory. These theories also applied to gambling strategies, too, and these investing strategies are part of what is now called game theory. Here you bet the full “single bet Kelly” percentage of 1,4% on every bet.
While most calculators compute the Kelly Criterion in terms of odds and edges , this calculator is designed to sneak a peek here work in terms of current and future prices . Please check your local laws or consult with legal counsel before attempting to play poker online. This paper defines an equivalent stake for performance index bets, and from this are derived several measures of over-round for a performance index.
Top Recommended Arbitrage Betting Software:
If you wager one buck at a time, you win almost certainly. First, they require punters to be able to accurately assess the probability of something happening and compare this number to the odds they are getting. If you are tossing a coin, this is easy, because you are dealing with the mathematical certainty that heads will come up, in the long run, 50% of the time. If you are then offered odds of $3.50, which imply heads will only come up 29% of the time, it is relatively simple to work out how “wrong” the odds are and bet accordingly. Juxtaposed against inebriated party-goers, Bill and a small group of newfound nerdy friends sat assiduously at the blackjack tables and discussed probability theory between rounds.
Using Hash Ai To Simulate Company Survival Rates
Results obtained for the Triple Kelly portfolio confirm that over-investment can have disastrous outcomes, with a maximum drawdown very close to 95%. Recently, few researchers are starting to study how the Kelly criterion can be used on option portfolios. Aurell et al. are the first to use the Kelly criterion in order to specify a model to price and hedge derivatives in incomplete markets. Wu and Chung implement an algorithm that seems able to find the most profitable option portfolio using the Kelly criterion. Using data from the Taiwan Stock Exchange Index they demonstrate that trading signals obtained from traditional strategies were not necessary when using the Kelly criterion. Finally, Wu and Hung use the Kelly criterion within a framework where a strategy involving trading on options exercised on the simple index futures is defined.
We need you, and we want you to be able to keep improving your strategies so you win more. However, the bettor has assessed the true odds of Hawthorn winning the Grand Final to be $1.90 which is implying a percentage chance of victory at 52.63%. In essence, the Kelly Criterion calculates the proportion of your own funds to bet on an outcome whose odds are higher than expected.
Kelly Vs Optimal Video Poker Strategy
1) for a 2X bet you should not bet anything unless the probability of winning is above 50%. In fact, if the probability is below 50%, you should try to find a way to take the other side of the bet or trade . In this example you have a 60% probability of doubling your money; the Kelly Criterion says that you should bet 20% of your bankroll .
The Kelly Criterion is based on solid mathematics and informative post has a lot to recommend it. For those adept at calculating true probabilities, it offers a dynamic way of maximising their rewards. It is important to remember, however, that the Kelly Criterion is essentially a staking system. It will not identify potential bets and is not an automatic route to profit. It should therefore be used with caution, particularly by those new to betting.
Even though the formula says that one should bet 98% of your bankroll when you have a 99% chance of winning a 2X bet, that still leaves you with a 1% chance of going broke—too high for me, at this stage in my life. For sports betting, there is the added complication that the true odds on an outcome are not known. When calculating your Kelly bet, your estimate may well differ significantly from the true odds.
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Mateo Dordi ‘23, University of California Berkeley
I major in Applied Mathematics at UC Berkeley. It’s the application of mathematical methods by different fields such as science, engineering, business, computer science, and industry. I’ve always enjoyed doing math and it was something that came naturally to me so I decided to make it my major.
I am currently taking Math 53 here at Berkeley which is Multi Variable Calculus. In high school, I took AP Calculus AB/BC in the 11th grade which really peaked my interest for math. I enjoyed working through each problem and really understanding the fundamentals and basics behind each and every problem in math. It showed me the simplicity and beauty behind mathematics and its implications in our day to day life.
Though I didn’t really complete any projects, I did work on proving a theorem in Calculus class which was really fun, even though it took my friend and I almost a week to complete it.
The department is a little smaller than the big name majors, but there are still a plethora of facilities and research opportunities for math majors to pursue. There aren’t too many applied math majors I know here but a lot of people I know are taking the same level math class as I am. The few people that are majoring in math really love the faculty. They’re very helpful since it’s a smaller program compared to something like Computer Science.
Math is in every single thing that you do. It teaches you valuable lessons and if you can get a math degree, you can pretty much do anything. I hope to eventually get into software and use the math knowledge I have to advance the company I am working at. Some other fields that math majors can get into include being Statisticians, Mathematicians, Math Professors, and basically anything Economics or Finance related.
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Problem solving relates to using a wide range of mathematical skills. Problems may involve your use of shape and space, addition and subtraction, multiplication and division- any area of maths in fact.
However, reasoning skills will need to be used such as logical thinking, working systematically (doing things in a particular order) and reading comprehension skills.
Try and follow the steps below to help you solve the problems given.
1) As with any maths problem you ALWAYS need to carefully READ what the problem is asking/ telling you. Read it aloud if you can.
2) UNDERSTAND which area of maths the problem is related to and which OPERATIONS you may need to use (if any).
- First I will need to... Then I will...
3) Realise what you ALREADY KNOW about the problem (the problem itself will often give you all the information you need to solve it).
- I know that... so I also know that...
4) CONTINUE solving the problem- BREAK IT DOWN into smaller steps if you need to. Build it/ draw it/ say it
5) CHECK your solution- work backwards using inverse operations (if appropriate).
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In materials that undergo martensitic phase transformation, macroscopic loading often leads to the creation and/or rearrangement of elastic domains. This paper considers an example involving a single-crystal slab made from two martensite variants. When the slab is made to bend, the two variants form a characteristic microstructure that we like to call “twinning with variable volume fraction.” Two 1996 papers by Chopra et al. explored this example using bars made from InTl, providing considerable detail about the microstructures they observed. Here we offer an energy-minimization-based model that is motivated by their account. It uses geometrically linear elasticity, and treats the phase boundaries as sharp interfaces. For simplicity, rather than model the experimental forces and boundary conditions exactly, we consider certain Dirichlet or Neumann boundary conditions whose effect is to require bending. This leads to certain nonlinear (and nonconvex) variational problems that represent the minimization of elastic plus surface energy (and the work done by the load, in the case of a Neumann boundary condition). Our results identify how the minimum value of each variational problem scales with respect to the surface energy density. The results are established by proving upper and lower bounds that scale the same way. Themore »
Minimizers for the Cahn--Hilliard energy functional under strong anchoring conditions
We study analytically and numerically the minimizers for the Cahn-Hilliard energy functional with a symmetric quartic double-well potential and under a strong anchoring condition(i.e., the Dirichlet condition) on the boundary of an underlying bounded domain. We show a bifurcation phenomenon determined by the boundary value and a parameter that describes the thickness of a transition layer separating two phases of an underlying system of binary mixtures. For the case that the boundary value is exactly the average of the two pure phases, if the bifurcation parameter is larger than or equal to a critical value, then the minimizer is unique and is exactly the homogeneous state. Otherwise, there are exactly two symmetric minimizers. The critical bifurcation value is inversely proportional to the first eigenvalue of the negative Laplace operator with the zero Dirichlet boundary condition. For a boundary value that is larger (or smaller) than that of the average of the two pure phases, the symmetry is broken and there is only one minimizer. We also obtain the bounds and morphological properties of the minimizers under additional assumptions on the domain.Our analysis utilizes the notion of the Nehari manifold and connects it to the eigenvalue problem for the negative Laplacian more »
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Variational boundary conditions based on the Nitsche method for fitted and unfitted isogeometric discretizations of the mechanically coupled Cahn-Hilliard equation.The primal variational formulation of the fourth-order Cahn-Hilliard equation requires C1-continuous finite element discretizations, e.g., in the context of isogeometric analysis. In this paper, we explore the variational imposition of essential boundary conditions that arise from the thermodynamic derivation of the Cahn-Hilliard equation in primal variables. Our formulation is based on the symmetric variant of Nitsche's method, does not introduce additional degrees of freedom and is shown to be variationally consistent. In contrast to strong enforcement, the new boundary condition formulation can be naturally applied to any mapped isogeometric parametrization of any polynomial degree. In addition, it preserves full accuracy, including higher-order rates of convergence, which we illustrate for boundary-fitted discretizations of several benchmark tests in one, two and three dimensions. Unfitted Cartesian B-spline meshes constitute an effective alternative to boundary-fitted isogeometric parametrizations for constructing C1-continuous discretizations, in particular for complex geometries. We combine our variational boundary condition formulation with unfitted Cartesian B-spline meshes and the finite cell method to simulate chemical phase segregation in a composite electrode. This example, involving coupling of chemical fields with mechanical stresses on complex domains and coupling of different materials across complex interfaces, demonstrates the flexibility of variational boundary conditions in the context ofmore »
Inverting the variable fractional order in a variable-order space-fractional diffusion equation with variable diffusivity: analysis and simulationAbstract Variable-order space-fractional diffusion equations provide very competitive modeling capabilities of challenging phenomena, including anomalously superdiffusive transport of solutes in heterogeneous porous media, long-range spatial interactions and other applications, as well as eliminating the nonphysical boundary layers of the solutions to their constant-order analogues.In this paper, we prove the uniqueness of determining the variable fractional order of the homogeneous Dirichlet boundary-value problem of the one-sided linear variable-order space-fractional diffusion equation with some observed values of the unknown solutions near the boundary of the spatial domain.We base on the analysis to develop a spectral-Galerkin Levenberg–Marquardt method and a finite difference Levenberg–Marquardt method to numerically invert the variable order.We carry out numerical experiments to investigate the numerical performance of these methods.
In this work we present a systematic review of novel and interesting behaviour we have observed in a simplified model of a MEMS oscillator. The model is third order and nonlinear, and we expressit as a single ODE for a displacement variable. We find that a single oscillator exhibits limitcycles whose amplitude is well approximated by perturbation methods. Two coupled identicaloscillators have in-phase and out-of-phase modes as well as more complicated motions.Bothof the simple modes are stable in some regions of the parameter space while the bifurcationstructure is quite complex in other regions. This structure is symmetric; the symmetry is brokenby the introduction of detuning between the two oscillators. Numerical integration of the fullsystem is used to check all bifurcation computations. Each individual oscillator is based on a MEMS structure which moves within a laser-driven interference pattern. As the structure vibrates, it changes the interference gap, causing the quantity of absorbed light to change, producing a feedback loop between the motion and the absorbed light and resulting in a limit cycle oscillation. A simplified model of this MEMS oscillator, omitting parametric feedback and structural damping, is investigated using Lindstedt's perturbation method. Conditions are derived on the parameters of the modelmore »
Abstract We prove a regularity theorem for the free boundary of minimizers of the two-phase Bernoulli problem, completing the analysis started by Alt, Caffarelli and Friedman in the 80s. As a consequence, we also show regularity of minimizers of the multiphase spectral optimization problem for the principal eigenvalue of the Dirichlet Laplacian.
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Realistically, no! There are 6,670,903,752,021,072,936,960 possible solvable Sudoku grids that yield a unique result (that’s 6 sextillion, 670 quintillion, 903 quadrillion, 752 trillion, 21 billion, 72 million, 936 thousand, 960 in case you were wondering). That's way more than the number of stars in the universe.
Think of it this way: if each of the approximately 7.3 billion people on Earth solved one Sudoku puzzle every second, they wouldn’t get through all of them until about the year 30,992.
But surely not every possible grid layout is all that different from every other one, right? That number is so inconceivably huge – and seemingly random – that within those seven commas there’s got to be at least a few similar or even near duplicate puzzles. So how many are truly distinct?
Combinatorics is a field of math concerned with problems of selection, arrangement, and operation within a finite or discrete system. A Latin square is an n-by-n grid filled with n distinct symbols in such a way that each symbol appears only once in each row and column. A solved Sudoku grid is a Latin Square of order nine, meaning n=9. So it is a finite system on which combinatorics can be applied.
Using combinatorics, we can take any one Sudoku grid and, with various simple tricks, create enough unique grids for you to do one each day for the next century. Simply by transposing and rotating the grid or interchanging columns and rows we get exponentially more unique puzzles.
But all of the puzzles created this way are essentially the same; the difficulty and probable starting points won’t vary drastically. Of all the unique possibilities for a Sudoku puzzle only a (theoretically) more manageable 5,472,730,538 are essentially different and can't be somehow derived from each other. That would still take a single person more than 173 years to get through even if he or she could finish one every second. So no need to pace yourself.
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Notes on a Problem Involving Permutations as Subsequences
STANFORD UNIV CA DEPT OF COMPUTER SCIENCE
Pagination or Media Count:
The problem attributed to R. M. Karp by Knuth is to describe the sequences of minimum length which contain, as subsequences, all the permutations of an alphabet of n symbols. The paper catalogs come of the easy observations on the problem and proves that the minimum lengths for n5, n6 and n7 are 19, 28 and 39 respectively. Also presented is a construction which yields for n2 many appropriate sequences of length n sup 2-2n4 so giving an upper bound on length of minimum strings which matches exactly all known values.
- Theoretical Mathematics
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