# All Questions

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### Prove that for every integer greater than 1. $\dbinom{n}{1}-2\dbinom{n}{2}+3\dbinom{n}{3}+…+(-1)^{n-1}n\dbinom{n}{n}=0$

How do you show the following. Prove that for every integer greater than 1. $\dbinom{n}{1}-2\dbinom{n}{2}+3\dbinom{n}{3}+.....+(-1)^{n-1}n\dbinom{n}{n}=0$ My idea is that is that the whole sequence ...
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### Determine whether each of the following sets is well ordered?

A set is well ordered if every nonempty subset of this set has a least element. Determine whether each of the following sets is well ordered. a) the set of integers b) the set of integers greater ...
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### How to shorten the list of enough conditions of a simple theorem?

Let $f$ be a symmetric binary relation. Let it's known that $f \subseteq \nu$ for a binary relation $\nu$. We need to prove $f \circ f \subseteq \nu$. For this it is obviously enough any one of the ...
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### The most optimal way to solve this set of non-linear equations in high dimensions

So I have a series of non-linear equations which I wish to solve as fast as possible, to illustrate for the case of $n = 4$, I have the following equations: \begin{gather*} ...
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### solution set of linear equation

Is there a system of linear equations with 3 variables and solution set $\{(a, b, c) | a^2 = b\}$? My answer is no but I'm not sure how to explain it. Edit: can't I just say that if ...
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### Question about the logic behind hypothesis testing

Let us say that we have this following problem: "A government agency claims that more than 50% of US tax returns were filed electronically last year. A random sample of 150 tax returns for last year ...
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### Discrete or Continuous Variables

I am having a hard time determining if these are either discrete or continuous. The number of visits to a website in a particular week. I said this was discrete because it is finite. The height ...
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### Find all homogeneous ODE with continuous coefficients with a peculiar property.

My problem is to find all homogeneous ODE with continuous coefficients the such that for any solution $f(t)$ and any $c \in \Bbb R$, $f (t + c)$ is also a solution. Let ...
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### Deciding to place a bet on outcome of a dice roll based on the probability

I have encountered several question of the following format. I have no trouble answering the first half but second half I have no clue on how to proceed. a: If you roll 5 standard six-sided dice, ...
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### Buying the best hard drive, or: Confidence interval for difference between means, variance of ordinal data, etc.

I think my hard drive is on the fritz, and so I've been sorting through my options on Amazon. However, the ratings on Amazon don't really make distinctions as nicely as I'd like; the only readily ...
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### Why is a graph $2$-connected if and only if it has an ear decomposition?

Why is a graph $2$-connected if and only if it has an ear decomposition? Reading the book "Introduction to Graph Theory" I have come across the following definition and statement: why is this ...
I have the Taylor series of cosh $$\sum_{n=0}^\infty \frac {x^{2n}} {(2n)!}$$ and I know that this series converges for all x, but now I want to know if the series represents the function, in other ...