What is the length of the altitude drawn to the hypotenuse of a right triangle having legs equal to 5 and 12?
60/13
100
sin(45)
sqrt(2)/2
100
Eight coins are tossed. Find the probability of getting two heads and six tails.
7/64
200
Solve for x: (x^2+3x+7)^(1/2) = x+2
x = 3
200
What is the number of sides of a regular polygon for which the number of diagonals is 44 or 45?
11
200
(sin(x))^2 + (cos(x))^2 = ?
1
200
Determine the number of ways a three-person committee can be formed from the five people Al, Barb, Carol, Dawn, and Eric.
10
300
Solve the inequality: x/(x+2) >3
-2<x<-3
300
The length of each leg of an isosceles triangle is x + 1 and the length of the base is 3x - 2. Determine all possible values of x. (The triangle should be nondegenerate; i.e. not just a straight line. Note also that x need not be an integer; your answer should be an inequality.)
2/3<x<4
300
A triangle has a 60 degree angle. The side opposite it has a length of 6. Another side has a length of 6. What is the length of the triangle's third side?
6
300
How many different 11-letter permutations can be formed from the 11 letters of the word MISSISSIPPI?
(use a calculator)
34,650
400
Find the line that contains the point (-1,-2) and is perpendicular to the line 2x-y = 6
y = 2x-6
400
An octahedron is formed by connecting the centers of the faces of a cube. What is the ratio of the volume of the cube to that of the contained octahedron?
6 or 6:1
400
What is the law of cosines?
c^2 = a^2 + b^2 - 2ab*cos(C)
400
A committee of four is chosen at random from a group of five seniors and four juniors. Find the probability that the committee will contain two seniors and two juniors.
10/21
500
What value of x satisfies the equation (x+10)^(1/2) + (x+10)^(1/4) = 12?
x = 71
500
An equilateral triangle is inscribed in a circle. Let D and E be midpoints of two of its sides, and let F be the point where the line from D through E meets the circle. What is the ratio DE/EF
(1+(sqrt(5)))/2
500
cos(x)/(1+sin(x)) + (1+sin(x))/cos(x) = ?
2*sec(x)
500
A player pays $5 to play a game where the probability of winning is 1/5 and the probability of losing is 4/5. If the player wins the game he receives $25. Is this a fair game for the player?
Yes
500
List all three-digit numbers abc for which the 6-digit number 579abc is divisible by 5, 7, and 9.