EBOLA MATH CONTEST L - SENIOR DIVISION PLAYERS First 2 players with the correct answers detailed and elaborately explained answers get $25 each. Send all solutions to email address: mett01@yahoo 1. What is the ratio V^2 / A^3, where V is the volume of a regular octahedron and A is the surface area? 2. Let F(n) denote the Fibonacci numbers, defined by F(1) = F(2) = 1, F(3) = 2, F(4) = 3, F(5) = 5, F(6) = 8 and F(n+2) = F(n+1) + F(n) for n >=1. Express the infinite sum S as a reduced fraction. S = F(1)/5 + F(2)/5^2 + F(3)/5^3 + F(4)/5^4 +…+… 3. Suppose f(x) = ax + b and a and b are real numbers. We will define f1(x) = f(x) and f2(x) = f(f1(x)) and f3(x) = f(f2(x)) and f4(x) = f(f3(x)) and fn+1(x) = f(fn(x)) for all positive integers n. If f7(x) = 128x + 381, what is the value of a + b? 4. Assume that for every person the probability that they have exactly one child is 1/4, the probability that they have exactly two children is 1/2, and the probability that they have exactly three children is 1/4. What is the probability that a person will have exactly four grandchildren? 5. Compute all integers r such that a circle of radius r with diameter AC has a point B on the circle such that AB = 30 and BC is a positive integer.
Posted on: Mon, 24 Nov 2014 01:15:59 +0000
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