Algebra
Solve the System
2x+y=8
3x−y=7
(3,2)
The probability of drawing a red card from a standard deck of 52 cards, where half are red.
1/2
The value of x in a triangle with sides 5, 5, and x, where the angle opposite x is 60 degrees
5
Find all positive integer solutions to x2−y2=35
(18,17)
(6,1)
What is the value of X in the following system of equations:
x + 2y + 3z = 20
2x + 3y + z = 11
3x + y + 2z = 17
5/3
A bag contains 4 white, 5 red and 6 green balls. Three balls are drawn at random from the bag. The probability that all of them are green, is
4/91
A triangle has angle measures 40, 60, and 80.
The longest side is 12 units. What is the length of the shortest side (nearest tenth acceptable)?
~8
How many positive integers ≤ 100 are divisible by 2 or 3 but not both?
34
Compute the ordered triple(a,b,c) such that:
a+b+c=4
a+2b+4c=9
a+3b+9c=16
(1,2,1)
How many 4-digit numbers contain no repeated digits?
4536
A trapezoid has parallel sides 8 and 20, height 6, and legs equal in length. Find the leg length.
6(sqrt2)
Find the last digit of (202 − 1)(232−1)
1
Compute the value of:
(25)3-3(25)2+3(25)-1/(7)3+3(7)2+3(7)+1
WITHOUT A CALCULATOR
27
The probability that at least two people share a birthday in a group of 5, assuming 365 days and ignoring leap years.
2.7%
The area of the triangle formed by the points (0,0), (4,0), and (2,3)
6
Call an integer a supaprime if it can be expressed as the product of two distinct prime numbers. For example, 21 is a supaprime because 21 = 3 · 7. Find the positive difference between the smallest supaprime and the largest supaprime less than 50.
40