Proofs
Prove that the diagonals of a triangle are congruent
Check proof
what is the volume of a sphere with radius 1?
4/3 pi
A fair 6 sided dice and a fair coin is flipped. What is the probability that the coin flips head and the dice doesn't roll a 6.
5/12
Find the sum of the answers of x+x+x=x^3
0
what is 1+2*3+4
11
Prove the divisibility rule of 3
Check proof
Square ABCD has side lengths 1. Points P, Q, R, S each lie on a side of ABCD such that APQCRS is an equilateral convex hexagon with side length s. What is s?
2-sqrt(2)
A leap year has 366 days. Find the probability of a year having 53 Sundays if a leap year happens once every four years?
5/28
Solve for all x such that
|x+8|+|x-5|=13
-8<=x<=5
What is d/dx (e^x)
e^x
Prove that 0.99999... = 1
Check proof
What is arcsin(sin(4pi/3))
-pi/3
Each of two boxes contains three chips numbered 1, 2, 3. A chip is drawn randomly from each box and the numbers on the two chips are multiplied. What is the probability that their product is even?
5/9
find floor(a)
16256
A ball is launched vertically at a speed of x and reaches a height of h. The max height of the ball launched at a speed of 5x can be written as mh. Find m.
25
Prove that (a+b)(b+c)(c+a) >= 8abc
Check Proof
On square ABCD, point E lies on side AD and point F lies on side BC such that BE = EF = FD = 30. Find the area of the square.
810
Eight people are sitting around a circular table, each holding a fair coin. All eight people flip their coins and those who flip heads stand while those who flip tails remain seated. What is the probability that no two adjacent people will stand?
47/256
(sqrt(3)/2 + 1/2i)^12 can be written as a+bi. What is a+b?
1
3^32-2^32 has four factors under 100. Find them
5,13,17,97
Find and prove the max value of x + 2y + 3z given x² + y² + z² = 1.
Check proof, max value = sqrt(14)
What is the area of a right triangle whose hypotenuse is 10 and altitude to the hypotenuse is 6?
Triangle Does Not Exist!
!!!DAILY DOUBLE!!!
(This question is worth 1,000 points!)
X, Y, and Z are three random real numbers in the range [0,1] each. What is the probability that X+Y+Z <= 1?
1/6
Let f and g be two quadratic polynomials with real coefficients such that the equation f(g(x)) = 0 has four distinct real solutions: 112, 131, 146, and a. Compute the sum of all possible values of a.
389
What is the 21st Fibonacci Number?
10946