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?

I understand that anything other than zero to the zero power equals one. But this doesn't seem to make sence to me. Could someone explain how this is, rather than that it is? I'd like as much feedback on this as possible. Thank you.

When you have to multiply two quantities with different units together, how do you interpret the meaning of the combined units? Take the formula for momentum, p=mv, for example - you have (say) kg times m/s. I know how to interpret m/s - for every second that passes by, so many meters are traversed. But what does kgxm mean? For every second, there are so many kilogram-meters. But what is a "kilogram-meter"?

If you're a contestant on Deal or No Deal, and you're down to two cases, you're given the option to switch your cases. I know that, mathematically, it is a good idea to switch the cases, due to the Monty Hall paradox; however, would your chances of getting the better case go to 1/13, or 25/26?

I'm wondering what sort of mathematics one should be looking at pursuing in undergraduate courses with a view applying them to work in paleontology. What kind of math is math is most commonly used? I believe principal component analysis and multivariate statistical techniques like that are pretty important, not that I know at at all what that means. Is there a lot of mathematical ecology, population modeling and what-not, these days? I'm ever leery of calculus.

I decided to go over the probability section in my S1 statistics book. However, it seems i've stumbled at the first hurdle. The first exercise is about the addition rule P(AUB) = P(A) + P(B) - P(AnB). There is a question where it asks about the probabilities events not happening, P(A'), P(A'UB), P(A'nB') etc. I know that P(A') = 1 - P(A), but i'm completely stuck on how to get such probabilities of P(A'nB). Can anyone help unclog my mental block? Thanks once again, Rob

Hi everyone. I have something of a vague question to ask, so I'll try to make it as coherent as possible. I assume that with a perfectly balanced coin, for example, there really is a 50/50 chance of getting either heads or tails each time. But my question deals with situations that may have extenuating circumstances. For example, let's say you ask somebody a physics question. The possible outcomes are that they will either know the answer or not know the answer. So is it safe to say that there is a 50/50 chance that they will either know it or not know it? What if we are told that the person in question is a physicist? It may be impossible to calculate precise odd…

The reverse of a river boat, being the river flow turning the paddle wheel of an anchored boat. How many horsepower would yield a 0.5m/s say-laminar river flow, for 1 m^2 submerged paddles ? Just a pictorial---> http://njscuba.net/zzz_artifacts/paddlewheel.jpg (not homework)

Hi, I have a number of measured data consisting of 10 numerical values. Let’s call these x1 to x10. x1 to x10 have a certain standard deviation, which I calculated by using the formula for the standard deviation for samples (see for example here: https://statistics.laerd.com/statistical-guides/measures-of-spread-standard-deviation.php). Then, I need to convert these values to new values according to the following formula: 2^(-x) From this, I get 10 new numerical values. I can calculate the new sample standard deviation for these based on the formula above or I can use the rules for the Gaussian error propagation to calculate the new standard deviation (see att…

I'm doing a little project at the moment to do with how triangles relate to tetrahedrons and I have some interesting results which have allowed me to calculate what the 4D version would look like. I Made a simple model to test and it worked out right. The only problem now is that none of the shapes I've found have names as far as I know. Is there a name for a 4D shape made from 5 tetrahedrons? It also has 10 faces and 10 edges if that helps. Theres a 5D shape too consisting of 15 tetrahedrons (or 6 of the 4D shapes). Thanks if anyone knows.

How many sides does a shpere have? One or infinite? PS: how does a mobius band work??

I worked out a method for predicting what marks I'll get for my exams based on statistics. I first tried it when I wrote my Statistics exam this november. It turned out that the mark I got was only 3% different than the mark I'd predicted with my method, so I deemed it reliable enough to continue using, for all-multiple-choice exmas at least. It might not work with ordinary tests, because very few of them have solely multiple choice questions, and they have far fewer questions, ie sample size. My method is fairly simple, and carried out in steps. Step One: As I answer each question, I give it a rating from 1 to 3 based on how certain I am that I got the question righ…

Ok, this should be interesting, and will hopefully settle a debate between my wife and I. Let's say there's a raffle, with 10 prizes, and you can put your tickets in individual boxes for each prize (thus there will be 10 separate, non-overlapping drawings). 9 other people have already bought 10 tickets each, and as a result, each cup now has 9 tickets in it. If I buy ten tickets myself (and I'm the last person to enter), would I have a better chance of winning if I put one ticket in each cup, or if I put all 10 in one cup?

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…

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…

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.

A man living near me won the lottery twice, both times he got five balls plus the bonus ball The odds of his first win were 2,330,636 to one. But the second time, the odds shot up to 5,400,000, 000,000 to one. Yesterday, Mr McDermott celebrated aboard a yacht at the Port Solent marina near Portsmouth - symbolising the fact that he and his wife are soon heading off to the island of Kerkenah, off Tunisia, where they have bought a house. According to this, winning the lottery once has odds of 2,330,636 : 1 Winning the lottery twice has odds of 5,400,000,000,000 : 1 Now lets assume that I won the lottery last week. If I buy a ticket for next weeks lottery draw, what ar…

hi, I am having a little problem with conterminal angles. I know what they are as defined by my textbook as "...sum of there degree measure is 360 or a multiple of 360". But I am not certain about the "multipe of 360" part. According to what I've read, the rotation has to be multiple of 360. And that's pretty striaght-forward. But in the book following example contradicts the statement, as far as I am concerend: 870 - 360 = 510 510 - 360 = 150 It's stated that 870 and 150 are coterminal angles. But 870+150 =1020 / 3 =340; not 360.

I have a machining problem that I am trying to solve, and it appears that math may be of assistance. Basically, I have a 12mm cylinder and a piece of 10mm brass bar stock, and I want to cut a groove in the bar that approximates the curve of the cylinder fairly closely. Unfortunately, I don't have any tools that can work with a diameter as small as 12mm, so I thought that perhaps using a larger diameter circle, 'tilted' at an angle so it intersects the bar as an ellipse, might get me close enough. (Of course, I never thought before about any formulae relating a 'tilted' circle to the defining particulars of its cross-sectional view based on the angle. Does viewin…

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…

My book says on average the sampling variance [math]\dfrac{\sum (x- \bar{x})}{n} [/math] is biased because it usually gives estimates smaller than the actual variance of a population. We fix this by dividing the sum by n-1 instead of n: [math]\dfrac{\sum (x- \bar{x})}{n-1} [/math] Is there a more intuitive or formal explanation of this?

This article was started as more of a debate than an answer to the question. According to Chaos Theory, any number, n, is defined as being higher than anything with lower value, or higher than any value from 0 to n, and lower than anything with a higher value, or lower than any value from n to infinity. Now, this may seem quite obvious, but also according to Chaos Theory, infinity cannot exist as a number. Both of these are stated in Chaos Theory, and are noted as a flaw in the number system, as how can a definite number be described as being below infinity, yet infinity is not a number in itself? Chaos Theory also states that any number has no definite point of "…

They say the chances of dying in a plane crash are 1 in 9 million. Am I correct in thinking that these chances increase the more you fly in airplanes? If that is true then how do you calculate your chances of dying in a plane crash after every new flight you board? That is, what is the formula for calculating this? Thanks, John

Why don't they use rectangular prisms for dice?

I'm trying to create a budget for a small business. I have to factor in the loan payments, but in order to figure how much they'll be, I'll need to know how much I'm going to be borrowing. Various banks have calculators on their websites that tell you these things, but as I put in the loan payments, my costs fluctuate dramatically. This requires that I modify the amount to borrow for my start up funds, and I end up having to repeat this process over and over again. Specifically, what equation do they use to factor my minimum loan payments? This way, I don't have to keep going back to this website calculator; I can do it myself.