# tricky

1. ### Tricky Conditional Probability Question

Hi, Having trouble with the following conditional probability question, please see the attachment below titled Capture1. Any help would be appreciated.
2. ### Request for help with tricky Riccati DE with exponential terms.

Hi all, I am developing a model that requires me to derive the solution of a rather tricky Riccati DE, and I am having a devil of a time with it and am beginning to wonder if there is even a closed-form solution. Anyhow, the equation is \frac{dE}{dt} = cB_{t} + bE_{t} + aE_{t}^{2}...
3. ### Tricky Probability question

HELP PLEASE! Been on this for days! There are 17 questions in an quiz with each question having 3 choices(AB&C) but only 1 of the choices is the correct answer. Additionally, In 7 out of the 17 questions, you have the choice of selecting 2 choices (such as A&B or A&C or C&B) if you are not...
4. ### Tricky transposition problem

Hi guys, I'm working on a circuit problem here. I've changed these variables to make them more mathish... if such a word exists. I seem to have got myself in a terrible web here, that I can't get out of. At the moment, I'm here: 1 / x-y = z + 1 / w I need it to be in a form something like...
5. ### Exercises about tricky inequalities (real analysis)

Where can I find some tricky inequalities? (Like this one: $$\sqrt{(\log_9 |x| -1)\log_3(x^2)}>(1/2) - 2\log_9 |x|$$) (I don't know whether it is the correct section of the forum to post this; sorry if it's not.)
6. ### Tricky question of circles

Circle is a shape that cannot be tesselated. But how to optimize the number of circles fitted in a bounded region. Is there any relationship between the number of circles and the dimension of the regions. Design a rack with minimum area or perimeter to fit in 50 coke cans. Restrict the problem...
7. ### A tricky question

When I first see this, I just doubt there's a solution. But actually it has a solution. Anyone wanna try this? :) A man has 3027 STR points. He takes a potion and has a pet. The potion adds 25% of all points. (count as add-on X) The pet adds 6% of all points. (count as add-on Y) The calculation...
8. ### Tricky Spherical coordinates...

Consider the region S inside the cylinder x^2+y^2 = 1, outside the sphere x^2+y^2+z^2 = 1, and with z between 0 and 1. A view from above and a cross section (looking along the positive x axis) are shown below. Set up one or more triple integrals to integrate a function f(x; y; z) over S using...
9. ### Question about general substitution for tricky ODE

as you know, many ODE(Ordinary Differential Equation) have explicit solution, but there are also more ODE which doesn't have. Let's think hypothetical need to find solution for a <Stiff ODE> to calculate area below curvature or more generally, to find primitive or anti-derivative function or...
10. ### Tricky math problem

Hi Guys, I'm new to this forum and would like to put forward a math problem I am struggling to find a solution to, the question is: You have a circle of which you know the radius of. The circle has a 2mm section through the diameter of the circle (which cannot be used). You need to fit 6...
11. ### a simple but tricky problem

I am stuck in this problem. (ex) Tom sells donuts only in boxes of 7, 13 or 24. To buy 14 donuts, you must order 2 boxes of 7, but you cannot buy exactly 15 donuts since no combinations of boxes contain them. What is the maximum number of donuts that cannot be ordered using combinations of...
12. ### Trouble with simple inequality

Hi all. I am having some bother with a seemingly simple question. "Let a, b, c be nonnegative numbers. Show that if a is less than or equal to (b+c) then: a/(1+a) is less than or equal to [ b/(1+b) + c/(1+c) ]" Thank you for your time.
13. ### divisibility proof question

please see image attached. for part (i), i used an induction. I wasn't bothered by this part. For part (ii), i managed to do the first part. The second part involves proving that S is divisible by different things depending on the even/odd status of n, which i was also fine with. The...
14. ### Tricky compound interest problem

Beer soaked ramblings follow. Got stumped by the following problem for about a day. I be sure my friends Sir Denis and Sir Jeff will appreciate it even more than I did. Hated it. Not that it's a bad problem but simply because I couldn't solve it sober. No solution needed. Just for...
15. ### Tricky question

Here's the problem: Let P(k) be a random draw of integers between 1 and k (inclusive). Assume you repeatedly apply P, starting at 10^1000. What's the expected number of repeated applications until you get 1? Why? What is your understanding of the following statement? Assume you repeatedly...
16. ### Tricky Problem.. Help

You enter your local bank to cash a cheque. As usual there is a long queue, and only 1 of 5 cashiers is serving. By the time you get to the cashier you're fed up with waiting and he is in a total mess. In fact he is in such a state that he gives you pounds for pence shown on the cheque and pence...
17. ### Tricky way to generate huge list of prime numbers

Let us concatenate a list of the first primes: 235711131719....... and so on At some point if we stop the list the 10.000th prime we will have a number: A=235711131719.......(10.000th prime). Now assume that we find a function of some form or a particular sequence sequence up to A we could...
18. ### Tricky Distribution

I have an interesting density function of \theta with two parameters a,\lambda and -\pi/2 < \theta < \pi/2: p(\theta) = g(a,\lambda)e^{a\theta}(\cos \theta)^\lambda and g(a,\lambda) is a normalization constant. I can obtain the distribution P(\theta < \theta') and normalization for low...