Using five identical index cards, the following structure can be created on a flat, level surface. What is the sum of the two marked angles on the side view of this construction?
What is the maximum number of 3" × 1" × 1" blocks that will fit into a box with interior dimensions of
5" × 5" × 10"?
Mrs. Garcia allowed each student in her class to drop the lowest of their five test scores. When Matt dropped the lowest of his test scores, a 60, his test average increased by 5 points. What is Matt’s new test average?
A 4-person dance team composed of 2 boys and 2 girls is to be selected from a group of 8 girls and 11 boys. How many different dance teams are possible?
A large square is divided into four congruent squares. Then those four squares are each divided into four smaller congruent squares, some of which are shaded, as shown. What is the probability that a dart thrown at random that lands in the largest square will also land in a shaded region? Express your answer as a percent to the nearest tenth.
If \(x+\dfrac{4}{x}=y+\dfrac{4}{y}\) and x ≠ y, then what is the value of the product xy?
How many positive two-digit integers each have the property that the integer's value increases by 75% when its digits are reversed?
How many different pairs of numbers (m, n) can be formed using numbers from the list of integers
{1, 2, 3, … , 99, 100} such that m < n and m + n is even?
In Quaternion, the coin with the least value is the qua. Four quas equal one quab, four quabs equal one quac, four quacs equal one quad, four quads equal one quae and four quaes equal one quaf. What is the least number of coins that have a combined value of 2012 quas?
A two-digit positive integer is randomly selected. What is the probability that the units digit is a multiple of the tens digit? Express your answer as a common fraction.
What is the coefficient of \(x^2y^2z^2\)in the expansion of \(\left(x+y+z\right)^6\)?
Seventy-eight students participate in one or more of three sports: baseball, tennis and golf. Four students participate in all three sports. Five students play only baseball and golf. Two students play only tennis and golf. Three students play only baseball and tennis. If seven students play only tennis, and one student plays only golf, what is the total number of students who play only baseball?
For how many positive integers n is the mean of the set {9, 5, 10, 12, n} equal to its median?
A square measures 80 yd on a side. Bob and Rob begin running from the same corner. Bob runs along a side to an adjacent corner, and Rob runs along a diagonal to an opposite corner. They arrive at their respective corners at the same time. If Bob’s speed was 8 mi/h, what was Rob’s speed? Express your answer as a decimal to the nearest tenth.
The four positive integers P, Q, P + Q and P – Q are all prime and their sum is S. What is the value of S?
The price of a shirt was reduced by 20%. Including the 5% sales tax, Cyndi paid $15.54 for the shirt. What was the original price of the shirt before the discount was applied?
Mollie has fewer than 100 pennies. If she puts the pennies in stacks of five, there are three pennies left over. If Mollie puts them in stacks of seven, there is one penny left over. If she puts them in stacks of three, there are no pennies left over. What is the total number of pennies Mollie has?
In ΔABC, shown here, the measure of angle BCA is 90°, AC = 12 units and BC = 9 units. If D is a point on hypotenuse AB , such that AD = 5 units, what is the length of segment CD? Express your answer in simplest radical form.
For how many positive integers containing no digit of zero is the sum of the digits equal to 5?
Andie bought 3 oldies CDs and 2 current CDs for $78. Deanne bought 2 oldies CDs and 3 current CDs for $82. What is the positive difference in the price of an oldie CD and the price of a current CD?