# number

1. ### Generate a random number folowing a given distribution

Hello, I have a question, Im not sure if there even exists a solution. I read that one can generate normally distributed random values from uniformly distributed ones. Is there a way of generating a random number, folowing a given distribution, out of a limited count of given uniformly...
2. ### How do I find the least number of times a shuttle can go from one place to another?

I often see this situation in exams and I'd like to know if there is any kind of algorithm or shortcut that I can use to solve this riddle instead of just guessing or trying to play Where's wally with the question. The problem is as follows: A space station must be evacuated to a nearby...
3. ### How do I find the least number tickets from a jar if the number isn't given?

The problem is as follows: In a jar there are tickets of the same size and color which have a number printed from $10$ to $\left(4n+10\right),\, n\geq 2,\,n \in \mathbb{N}$ .How many tickets could be taken out at random from the jar the least possible to be certain that among the tickets...
4. ### Need help to verify the number of solutions

Given equation x^2 +x +\lambda =0 \; ,x\in \mathbb{R}. Verify N - the number of solutions, using any software (matlab, calculators... etc.) N_{\lambda } =\frac{\displaystyle 1 + \lim_{s\rightarrow \infty} \left[-2\left(1+e^{-2s(-1-4\lambda)}\right)+1\right]}{2}\lim_{s\rightarrow \infty}...
5. ### Number of solutions

Express the number of solutions of equation(EQ) in terms of \lambda. (EQ) x^2 +x +\lambda =0 \; ,x\in \mathbb{R}.
6. ### What would be the number of electrons in a spectroscopic notation?

I found this a bit "trivial" question regarding quantum numbers but I'm still confused over the given alternatives in the answer. Could it be that whoever posed the question made a mistake or made the question in a silly way? The problem is as follows: How many electrons are in the...
7. ### Number of solutions of transcendental equation

Find how many solutions the equation has ? x^2 -2x =(-1)^x \; , x\in \mathbb{Z}.
8. ### How do I find the least number of spheres from a jar when taken at random?

The problem is as follows: A porcelain jar has $x$ yellow colored spheres, $2x$ lightblue spheres and $3x$ black spheres. What is the number of spheres to be taken out of the jar at random and at least to affirm that we have $\frac{x}{2}$ spheres of each color?. (Assume that you are not...
9. ### Linear Approximation to Estimate a number

I have a couple of online hw questions that have got me stumped. The first states: "Use a linear approximation to estimate the following number" and then provides the number (2.9)^4. the practice problems from the textbook indicate that the answer is simply 2.9^4 which would be 70.7281. This...
10. ### Irrational -> Rational Number

Hey, I was using guess and check to find a value, and it ended up being close to 15.83007499. I am certain it could be represented by an equation, but I can't find out what that would be. There is a good chance it would be a log natural. If you do find out what it is, I'd love to know. Thanks!!
11. ### [Help] The number of possible k-sided polygons in an m by n grid of dots

Hello. :spin: This is my first post, so sorry for the potential mistakes below. A grid of dots has the dimensions m by n, where m is greater than or equal to n. Pick k dots from this grid in such a way that they form a polygon with k sides. In other words, no three dots can be collinear...
12. ### Express any number greater than 35 as sum of x 5s and y 9s

How can we prove that any number greater than or equal to 35 as a sum of x 5s and y 9s Probably by induction
13. ### Number of solutions

(eq1) F(x)=0 ; (eq2) F(x/2)=0 . If (eq1) has two solutions , how many solutions are for (eq2) ?
14. ### why do we represent rational number by p/q?

why do we represent rational number by p/q, why can't you not use m/n, x/y, c/y, a/c, etc. is there any meaning by (p/q)?
15. ### Number theory maybe?

Hello. So someone gave me this question that I do not know how to solve (nor does he). We can take a whole lot of cases, but is their a better solution for this problem? Problem: Let n be a natural number more than 1. Prove that their are not more than 23 primes in the range 10n to...
16. ### Linear combination of random variables, convergence for a large number of variables

Hi, I have positive random variables X1, X2, X3, ..., Xn such that their sum=1 (so they are random, subject to constraints that each Xi is positive their sum has to be 1.. so all are fractions). Now, I have a function f=C1.X1+C2.X2+C3.X3.....+Cn.Xn where C1, C2, ....Cn are known...
17. ### Number of trials until success for successful participants

Hello, I have the following problem: Given a Bernoulli trial with probability of success p and a number of trials x, what is the expected number of trials until success among those that succeed in x trials? e.g. if p = 0.02 and x = 60, (1-0.02)^50 = 0.36 attempts fail all 60 trials, and I...
18. ### For what natural n is the number (5^(2*n+1))*(2^(n+2))+(3^(n+2))+(2^(2*n+1)) divisibl

For what natural n is the number (5^(2*n+1))*(2^(n+2))+(3^(n+2))+(2^(2*n+1)) divisible by 19? I get that (19*(50^n + 12^n) + (50-19)(50^n +....+19^n). So it means that n can be any natural number? Or I did some mistake there?
19. ### Sum of number's number

Hey, I have a number theory problem: determine the sum of the digits of a natural number. I have been thinking about it for a lot time during this days, but I can't still find a solution. Can someone give me an idea or advise me a book/internet site with something useful? Thank a lot.
20. ### How to find functions & inputs whose output is a specific number

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...