Applied Mathematics

How thick is a single, 8.5" x 11" sheet of standard printer paper? I saw this article on Cha Chathat said it was about nine millimeters, but that CAN'T be right! How thick is a sheet of printer paper?

https://en.wikipedia.org/wiki/Anscombe's_quartet I would like to know whether or not there is a statistic that can differentiate between the case at the top left versus the top right. Clearly R2 does not do so. One could plot the residuals, and the non-random distribution sometimes becomes apparent. However, what I was hoping to find is some number, preferably one that would be calculated by a statistics program, that could be compared in the two situations. I am reading Motulsky's book Intuitive Biostatistics (that is where I first saw the Anscombe quartet, but I have not found anything in his book yet. I am presently using ProStat, which has both a calculation…

If we can climb one stair, one stair, or two stairs, two stairs, in what ways can we climb n stairs?

Hi, I came up with a word problem that I know the answer to but I have no idea why the solution is what it is or how to reason through it. I posted this on another forum before, but I did not get the answer (explanation) I was looking for. Joe has investments in Company A, Company B, and Company C. Joe is fated to earn $25.00 from Company A within 2 days from now. Joe is fated to earn $45.00 from Company B within 3 days from now. Joe is fated to earn $100.00 from Company C within 5 days from now. Joe is fated to earn no more than $26.00 from Company C and Company B on day 1 (1 day from now). Joe is fated to earn at least $14.00…

For the longest time, I have been trying to understand how to create and understand mathematical models. From the simplest ones growing to the more complex ones. Can anyone recommend to me any reading material, videos, or learning material that can help?

Hello people, Using PSPP, I was doing some basic linear regressions. Examining the following correlation: I included data from over a 100 countries and looked at both baseline values and values 15 years later. Calculating the differences in value for both the independent and dependent variable. Plotting them in a graph. Results were as follows: A weak R-squared value which was highly significant nonetheless (P = < 0.0001). With a negative trendline. No confounding was detected from other variables. I found a "strong" correlation between baseline values of the dependent variable and it's successive changes in values during the 15-y…

Hello, I need your help to calculate (approximate) a double series as shown in the attached. Thank you so much. Best, Steve.double_series.pdf

I'm interested in the following problem: given a random number n (n can be gigantic), how do we find a pair function+input(s) whose output is n such that the input(s) are relatively small in size? This problems arises in data compression; consider the bits that make up a file (or a substring of bits of the file) and treat it as a number (i.e. the bits are the binary representation of this number). If we could write a pair function+input(s) whose output happens to be the substring, this whole substring can be replaced by the function+input(s). I've thought of expressing the number as sums (or differences) of relative big powers of prime numbers. Is this a good ap…

Let's take symmetry of functions as an example of regularity, others may be their periodicity, etc. If one analyzes it, one can conclude that even functions, which are by definition those for which f(-x)=f(x), examples of these are polynomials consisting of even powers of x, and odd functions, for which f(-x)=-f(x), examples of these are polynomials consisting of odd powers of x, are actually exceptions, rather than a rule, ie that functions are generally speaking asymmetric objects with respect to the x=0 axis (or plane in 3D), that do not necessarily have anything to do with those that are symmetric (even and odd). However, the fact is quite the opposite, every asymmetr…

I have it on authority **that tensors enable one to model the electromagnetic interaction between a " moving "charge and an electric conductor in such a way as to dispense with frames of reference . I wonder if anyone might have anything to say on the subject and whether it can be shown in more detail how this is the case. **https://www.markushanke.net/tensors-for-laypeople/

Dear all, In machine learning library scikit-learn of python, the logestic regression function has an argument "class_weight". When you set a higher class weight to a class during fitting the logestic model, you will get higher predictive accuracy of this class. I wish to know what is mathematical principal of setting class_weight. Is it related to modify the target function of logestic regression (https://drive.google.com/open?id=16TKZFCwkMXRKx_fMnn3d1rvBWwsLbgAU) ? Thank you in advance.

Can computation always be reduced to permutation of certain states of a certain subtrate, or be performed by permutation of these, in every possible model of computation, classical or quantum? Or is it too general statement?

I'd like to choose one solution technique and write the finite difference form of the solution. Can you please explain how that leads to the next estimate(s), the accuracy of the method, and why you chose that method. I'd use only each technique once? Methods are Backward, Forward Euler, Crank–Nicolson, Runge–Kutta or Adams–Bashforth. I tried to find an analytical solution for each first, then compare the results with the exact results of the point for each time step. However, solving the equations are so difficult. Is there any way to determine a method without solving the equations? df/dt=f^(1/3)(1/4t) df/dt=2*t df/dt=−e^(f*t) df/dt=f(∂2f/∂x2)

In my spare time I work as a substitute teacher. In High School math today, students were working on a standardized practice test to prepare for the ACT exam. The following question baffled me. Given x and y are positive integers, such that both x2Y2 and xy3 have a greatest common factor (GCF) of 27, which of the following could be a value of y? The available answers are 81, 27, 18, 9 and 3 I ruled out 81, 27, 18 and 9 as values of y because in all cases y2 would be greater than 27, so the GCF could not be 27. It appears the intended answer is y = 3. However, if y = 3, then x2 y2 becomes 9x2. In order for this to have a GCF of 27, x2 must…

Does this thought experiment posit that BETWEEN the monkeys the complete works of Shakespeare can be compiled from individual words they type? Or does it posit that ONE monkey, given infinite time, will produce an error-free complete works. If it is the first scenario I can see this happening and I could actually imagine it working with just a large number of monkeys and a long time. If it's the second scenario I have a problem. Not just that it is totally counter-intuitive or that infinite time is impossible to comprehend. I realise that monkeys and typewriters are (fun) devices used to help think about complex theories pertaining to pro…

Greetings: Before anything, I am a 50 year young man with Aspergers and ADHD that considers himself a free-thinking Catholic. This question is in two parts. And my sincere apology for the length of the second one, it might seem like a wall of words, but i saw no other way to properly post it without changing anything in the question's content, interpretation or meaning. 1) First, a personal question, this is to see just how far math and science is related, in your person: "How important is mathematics to you, what place has mathematics to you, and how far does mathematics have an impact on your thinking/accepting?" 2) Here we have the actual math quest…

There is a 4 digit number which spells like "abcd". Jack, John and James tries to find this number. Jack only know the range of the digits(biggest -smallest).John only knows a+b+c+d.James knows a*b*c*d. Jack says: I dont know all the digits but James doesn't either. James says: I dont know all the digits but John doesnt either. John says: I just found it and Jack should be just found it as well. What is the four digits ?

I am looking for a rigorous proof for the following theorem (which I quote from Schaum Differential Geometry book): "If K#0 at a point P on a surface, show that there is a neighborhood of P in which the points can be put into a 1-1 correspondence with the spherical image of the neighborhood (see Problem 9.57)". Note: K is Gauss curvature.

application of toplogy

I'm not sure if this is the correct place to post this. On a piece of equipment, I purchased new, the clock ran slow. The second clock that was installed ran slow---it lost approximately 4.1 minutes in one month. Below is what I sent the Service Manager who I understand thinks it is possible to test the newly installed clock immediately after installing it with a cell phone (the NH Rep thinks it's possible also, I understand. (I did not measure the time initially with the precision indicated below but just included all the digits displayed by the Windows computer calculator and actually, if you round up, the clock loses approximately 27.8 ms per hour.) Even if a person ha…

I want to convert a stochastic formula into a proper equation describing the probability of a specific card draw in a card game. Example: A and B are people playing cards. They each have a 52 card deck and four cards in hand. A has an ace, a ten, and 2 fours. If A draws 3 more cards from his deck, and he wants to draw one more ace, what is the probability? That is, there are: 48 cards in the deck (52 card deck, minus the 4 cards in A's hand); 3 target cards (4 aces in the deck, minus the one in A's hand); and 3 cards to be drawn. [1] The original formula: probability=1−((D−T)!−(D−T−H)!)(D!−(D−H)!−1))=17.96%, where: D is the current deck size, T is the number o…

Hello everyone For my thesis, I'd like to log transform a variable that represents a certain angle between 2 peaks on a curve. The problem, of course, is that this angle can be negative. As no angle is smaller than -90°, would it be allowed to add 90° to all angles, and log transform the results into a new log-transformed variable? Thanks F

Most forums are rehashing the same stuff, which gets boring. Went back to a few projects started a dozen yrs ago. This is one of them. The graphic is an incomplete 'tree'. Vixra postings don't provide any constructive feedback! The PDF file is here

Hello y'all In my thesis, I have this variable, which is expressed in a percentage (%). It's not an option to, e.g., display 20 % as 0.20, since that is absolutely not common for that variable. Now, this variable does not satisfy the conditions for parametric testing. However, its square-root variant does. But if I report both this variable, in %, then do I have to change the "unit" (which in itself is demensionless) to something else than %? Now I would report: Mean Var ± SD - % Mean VarROOT ± SD - % But I'm not sure if this is quite right. After all: e.g., in the case of 20 %, I took the root of 20, and not of 0.20. So ... sqrt(2…

Hi friends I am a high school student from india and have been trying to prove the collatz conjecture. Physics and maths have always been my favourite and recently I have been able to develop a proof for this conjecture. What should I do? Whom should I send it to? What is its value? Please do help me out.