GEOMETRY
What is the perimeter of a square that has an area of 25?
20
If x^-2 = 64, what is the value of x^(1/3) + x^0?
3/2
If 1/3 of a number is 4 less than 1/2 of the number, the number is
24
Let x represent the unknown number. Since 1/3 of x is 4 less than 1/2 of x, x/3 = x/2 - 4. So, 2x = 3x - 24, giving x = 24.
If (2^3)^2 = 4^p, then 3^p =
27
In how many different ways can five students be seated in three chairs?
60
5x4x3=60
What is the circumference of a circle in which a 5 by 12 rectangle is inscribed? (In terms of pi)
13pi.
The length of a diagonal of a 5 by 12 rectangle is 13 (pythagorean theorem). The diagonal of the rectangle is the diameter of the circle inscribed, and C = 2(pi)r.
Let the function f be defined by f(x) = 3x-1 and let the function g be defined by g(x) = x^2. If m is a positive number such that f(7) = g(m) + g(2), what is the value of m?
4
if x+3=6, then what is x-3?
0
When the number of people who contribute equally to a gift decreases from four to three, each person must pay an additional $10. What is the cost of the gift?
$120.
What is the area of the circle whose radius is the average of the radii of two circles with areas of 16pi and 100pi?
49pi.
A rectangular prism shaped fish tank is 15 inches tall and has a width of 12 inches and a length of 30 inches. It is filled 2 inches high with water. If the water needs to be filled to 3 inches from the top, how many cubic inches of water are needed to fill the tank?
3600 cubic inches
A culture of 5000 bacteria triples every 15 minutes. What is the size of the bacteria population after 2 hours have elapsed?
32,805,000
The regular price of software at a computer superstore is 12% off the retail price. During an annual sale, the same software is 25% off the regular price. If the retail price is p, what is the sale price in terms of p?
0.66p
Since the regular price of software is 12% off the retail price p, the regular price of the software can be expressed as 0.88p. So the sale price is 0.75 x 0.88p = 0.66p.
Simplify (4a+a-3)(4b-2b-b)
5ab-3b
Three fair coins are tossed at the same time. What is the probability that all three coins will come up heads OR all will come up tails?
1/4. 1/8 (all heads) + 1/8 (all tails) = 1/4.
If the integer lengths of the three sides of a triangle are 4, x, and 9, what is the least possible perimeter of the triangle?
19. In the given triangle, 9-4
What is the equation of the graph obtained by shifting the graph of y=x^2 horizontally to the left 4 units and vertically down 3 units?
y = (x+4)^2 - 3
30% of the 200 students are athletes who play a sport. If 20% of the athletes play basketball, how many students are basketball players?
12
For the system of three equations: x-z=7, x+y=3, z-y=6, what is x?
8
The ratio of sophomores to juniors is 5:9. If there are 126 students in the class, how many are sophomores?
45
Each edge in a cube is 5cm. What is the surface area in square cm?
150
Working alone, Bill takes three times the amount of time to paint a fence that Mike takes. If Bill and Mike work together, they can paint the fence in 2 hours. If Mike works at the same rate as when he worked with Bill, how long would it take Mike working alone to paint the same fence?
2 hours and 40 minutes.
If x represents the number of hours it takes Mike working alone to paint the fence, then 3x is the number of hours it takes Bill working alone to paint the fence. So 2(1/x) + 2(1/3x) = 1 gives x=8/3 hours.
Fruit for a dessert costs $1.20 a pound. If 5 pounds of fruit are needed to make a dessert that serves 18 people, what is the cost of the fruit needed to make enough of the same dessert to serve 24 people?
$8.00. If 5 pounds of fruit serve 18 people, then 5/18 pound serves one person, so 24 x 5/18 = 20/3 pounds. Since the fruit costs $1.20 a pound, the cost of the fruit needed to serve 24 people is 20/3 x $1.20 = $8.00.
For how many integer values of b is b+3>0 and 1>2b-9?
Seven. b>-3, and b<5. Since b is an integer, b may be equal to any of the following: -2, -1, 0, 1, 2, 3, or 4.
x, y, 22, 14, 10... In this sequence, each term after the first term x is obtained by halving the term that comes before it and then adding 3 to that number. What is the value of x-y?
32. x=70, y=38. 70-38=32.