Algebra
If a bakery owner starts a doughnut machine at 8:30 AM, and by 11:10 AM, the machine is 1/3 done with the daily job, this is the time that the machine will be done with this job.
What is 4:30 PM?
The volume of a cube with a surface area that is two times the surface area of a cube with side length 1.
What is 2√2?
It is the probability of getting three heads for a fair coin if you flip the coin five times.
What is 5/16 or 0.3125?
Considering angle A, if sin(A)=-0.6 and tan(A)>0, then this is the value of cos(A).
What is -4/5 or -0.8?
The prime factorization of 864.
What is 25 x 32?
It is the reciprocal of the quantity (1/2 + 2/3).
What is 6/7?
Older television screens have a ratio of the width to the height is 4/3. But some movies do not have such a ratio, so dark strips need to be at the top and bottom of scenes. Suppose a movie has a width-to-height ratio of 2/1 and is shown on an older television screen with a diagonal of length 27. If h is the height of each strip, this is h.
What is 2.7?
A bag contains 4 red marbles and 6 blue marbles. If two marbles are chosen at random from the bag without replacement this is the probability that both marbles chosen are red.
What is 2/15 or 0.13333...?
Considering angle B, if m∠B<90 degrees, and sin(B)=1/3, then this is cos(2B).
What is 7/9 or 0.777...?
If P=2m and Q=3n, then this is how one would express 12mn in terms of P, Q, m, and n only (hint: express your answer as PxQy, where x and y are arbitrary variables).
What is P2nQm?
What is [-1,1] and [0,1]?
Consider points A and B that lie on circle O, where ∠AOB=60 degrees. Then, consider another smaller circle P, which is tangent to all sides and arc of sector AOB. This is the ratio of the areas of circle P and circle O.
What is 1/9?
Four coins are picked out of a piggy bank that contains a collection of pennies, nickels, dimes, and quarters. Within these numbers (15, 25, 35, 45, 55), this is the number that cannot be the total number of cents of the four coins.
What is 15?
Suppose that sin(a)+sin(b)=√(5/3) and cos(a)+cos(b)=1. This is cos(a-b).
What is 1/3
Consider the function Ik=10k+2+64. The function N(k) represents the number of times that Ik is divisible by 2. In that case, this is the largest value of N(k).
What is 7?
If k = 20082+22008, then this is the units digit of k2+2k.
What is 6?
Consider the trigonal pyramid OXYZ, where O is the origin of the 3d coordinate plane, X is (4,0,0), Y is (0,3,0), and Z is (0,0,5). This is the volume of this pyramid.
What is 10?
Consider three numbers x, y, and z, which are randomly-chosen numbers between -1 and 1. This is the probability that x2+y2+z2<1.
What is π/6?
The value of x within the interval (0, π] if sin3x+sin(x)+(sin(x))-1+(sin(x))-3=85/8
What is π/6?
It is a number that can be rewritten as the long summation
9+6+3+4/3+5/9+2/9+7/81+8/243...
What is 81/4 or 20.25?
What is 224?
A round table has radius 4. Six rectangular place mats are placed on the table. Each place mat has width 1 and length x as shown. They are positioned so that each mat has two corners on the edge of the table, these two corners being end points of the same side of length x. Further, the mats are positioned so that the inner corners each touch an inner corner of an adjacent mat. If 2x can be expressed as (a√(b)-√(a)), this is a+b.
What is 4?
This is the number of integers less than 1000 that is 6 times the number of their digits.
What is 1?
The solutions of the equation z4+4z3i-6z2-4zi-i=0 are the vertices of a convex polygon in the complex plane. This is the area of the polygon. (Express your answer as 2a where a is some fraction)
What is 25/4 or 21.25?
It's the value of x in the arithmetic progression log12162, log12x, log12y, log12z, log121250.
What is 270?