Algebra/NT
Solve for x and y:
x+y=2024
x-y=4
For some number a, the area of an equilaterial triangle with side length a is 30. What is the area of a regular hexagon with side length a?
Two cards are chosen from a regular deck (without replacement). What is the probability of drawing 2 cards of the same suit?
5 cards are randomly chosen from a 52 card deck. If the chance of a three-of-a-kind is m/n, with gcd(m,n) = 1, find m.
Determine the last digit of the number 2^16.
6
A type of rectangular playing card measures 3 by 5 centimeters. Aubrey tiles them out into a rectangular shape that measures 63 by 55 centimeters. How many cards are used?
231 cards
Five regular 6-sided dice are rolled. Of the following probabilities, which is the closest to the chance of not rolling a 1?
(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 50%
(D) 40%
A 1 inch by sqrt(3) inch playing card is rotated 60 degrees. Find the area swept out by the card.
(From AMC) For how many integers n is the expression 4000*(2/5)^n an integer? (Note: n can be nonpositive.)
9
Determine sin(75 degrees).
(1+sqrt(3)) / (2sqrt(2))
or any answer that evaluates to the equivalent.
Spin the wheel of chaos
Basil deals out 6 distinct cards to his four friends Aubrey, Hero, Kel, and Sunny. How many ways can he do this? (People can receive 0 cards.)
84
A standard dice has opposite faces sum to 7. Find the probability a dice with randomly assigned faces is standard.
Given a - 1/a = 3, determine a^8 + 1/a^8 + 300,000.
How many pairs of edges on a cube lie on the same plane?
Omori is trying out a new magic trick with his friends. He has Kel and Aubrey each select a random real number from 0 to 1. However, he suddenly forgot how to do the trick, and in order to save face predicts that the sum of their numbers does not exceed 1/2. What is the chance that he is right?
Playing cards are 2 inch by 4 inch. If a table is 5 inch by 10 inch, find the minimum number of cards needed to cover the table.
Determine the last three digits of the number 9^2024.
Mari draws a picture on a cube, which contains a point P at the center at one of its sides, and a drawing of a roulette table containing all points within N units of P. What is the largest N such that the area of this roulette is exactly pi*N^2?
sqrt(2)
Basil deals out three cards onto the table randomly from a deck of 12 cards, numbered uniquely from 1-12. A winning hand is one where there are two cards that are consecutively numbered. (4,5,6 and 1,10,11 are winning hands, but 3,5,7 is not a winning hand.) What is the chance Basil deals a winning hand?
4 cards are chosen from a 52 card deck. Phil, Tony G and Daniel chose 3 cards with replacement and find the sum of the numbers on them to be 11, 12 and 14. Find the total number of combinations of 4 cards if none of them are face cards.