number

  1. F

    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. Chemist116

    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. Chemist116

    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. idontknow

    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. idontknow

    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. Chemist116

    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. idontknow

    Number of solutions of transcendental equation

    Find how many solutions the equation has ? x^2 -2x =(-1)^x \; , x\in \mathbb{Z}.
  8. Chemist116

    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. B

    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. A

    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. 7

    [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. D

    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. idontknow

    Number of solutions

    (eq1) F(x)=0 ; (eq2) F(x/2)=0 . If (eq1) has two solutions , how many solutions are for (eq2) ?
  14. A

    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. S

    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. K

    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. M

    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. M

    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. V

    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. D

    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...