Show:
Algebra
Calculus
Logic
Trig
Probability
100
solve for x: 2x-5=3-2x
4x=8 x=2
100
differentiate: f(x)=2x^5+6x³-5x²+3x-5
f'(x)=10x^4+18x³-10x+3
100
this man's father is my father's son. Who is the man?
This man is his son
100
The legs of a right triangle are 5 and 12. what's the hypotenuse?
13
100
what are the odds of rolling doubles when you roll two dice?
6/36 1/6
200
graph: f(x)=4x/5-10
can't put a graph. slope:4/5 y-int:-10
200
maximize: A=xy constraint: x+2y=500
x=250 y=125 A=31,250
200
You are at a fork in the road. one road leads to your destination, the other leads to nowhere. you don't know which one leads to which. there are two men standing at the fork. one always tells the truth. the other always lies. you don't know which one is which. You may ask one question. what do you ask to insure you reach your destination?
"which way would the other guy tell me to go?" and then do the opposite. I believe there are other answers as well.
200
y=2cos(x/2-2) what's the amplitude of the graph?
2
200
A glass jar contains 6 red, 5 green, 8 blue and 3 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of choosing a red marble?
3/11
300
solve for x: 3x²+9x+5=2
x=(-9± √(81-36))/6 =(-9±√45)/6 =(-9±5√3)/6
300
differentiate Ln(3x²)e^3x
ln(3x²)3e^3x+(2e^3x)/2
300
You have three bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble.You pick one marble randomly out of a bag. It is a white marble.What is the probability that the remaining marble from the same bag is also white?
1/2
300
cos(2π/3)
1/2
300
you have a deck of 54 cards (52 cards and two jokers) what are the odds of drawing a card lower than 5? Aces are low.
16/54 8/27
400
Factor: 5x²-x³-20-4x
(5-x)(x-2)(x+2)
400
summation n=1-∞ of 1/(n²+n)
to long to write out. it converges at 1.
400
A solid, four-inch cube of wood is coated with blue paint on all six sides. Then the cube is cut into smaller one-inch cubes. These new one-inch cubes will have either three blue sides, two blue sides, one blue side, or no blue sides. How many of each will there be?
There are 8 with three sides colored, 24 with two sides colored, 24 with one side colored, and 8 with no sides colored
400
what is the sin15°
sin45-sin30 √2/2-1/2 (√(2)-1)/2
400
You roll two dice. what is the probability that the product of the two numbers is a multiple of 3 or 5.
3/4
500
graph: f(x)=2x/(x^2-1)
I can't put a graph. vertical asymp at 1,-1 horizontal at zero graph to the left and below, to the right and above, and between the two that looks somewhat like a -x^3 graph.
500
∫sinx e^x
too long to write out (-e^xcosx+e^xsinx)/2
500
There are twenty coins sitting on the table, ten are currently heads and tens are currently tails. You are sitting at the table with a blindfold and gloves on. You are able to feel where the coins are, but are unable to see or feel if they heads or tails. You must create two sets of coins. Each set must have the same number of heads and tails as the other group. You can only move or flip the coins, you are unable to determine their current state. How do you create two even groups of coins with the same number of heads and tails in each group?
You put ten in one pile, ten in another. then you flip all the coins in one pile.
500
graph: y=3sin(2x-π)
can't put graphs.
500
Two squares are chosen at random on a chessboard. What is the probability that they have a side in common?
1/18