What is the radius of the largest sphere that will fit inside a cube of volume 8 units\(^3\)?

In how many ways can the integers 1 through 6 be written horizontally in a row so that the sum of any two adjacent integers is odd?

Lily made a circle from a length of string measuring 26 cm, and Willow made a circle from a length of string measuring 31 cm. What is the absolute difference in the radii of their circles? Express your answer as a decimal to the nearest tenth.

Kim created decorations for the school dance. It took her 4 minutes to create the first decoration, and each decoration after the first one took 10% less time to create than the one before it. How many minutes did it take her to create the first five decorations? Express your answer as a decimal to the nearest tenth.

It costs $0.12 for the Cheapco Soda Company to manufacture enough cola to fill a cylindrical container that is 2 inches in diameter and 4 inches in height. How much would it cost for Cheapco to manufacture enough cola to fill a cylindrical container that is 6 inches in diameter and 10 inches in height?

If four hamburgers and two hot dogs cost $16.40, and six hamburgers and four hot dogs cost $26.40, what is the combined cost of a hamburger and a hot dog?

Alicia is framing a rectangular photo that measures 8 inches high by 12 inches wide. However, the frame she has was designed to hold a picture with sides in the ratio 4:5. If the frame Alicia has is the smallest possible frame that holds the photo, how much extra area will there be? Express your answer as a decimal to the nearest tenth.

Point A is a vertex of a regular octagon. When all possible diagonals are drawn from point A in the polygon, how many triangles are formed?

Two sides of a triangle are 15 cm and 18 cm in length. The altitude to the 18-cm side is 10 cm. What is the length of the altitude to the 15-cm side?

What is the greatest multiple of 10 that can be expressed using only the numbers 2, 2, 3 and 5, each exactly once, with any or all of the operations +, −, × and ÷, exponentiation and parentheses? Express your answer in scientific notation.

The line that contains (4, −7) and (−3, 14) also contains the point (0, b). What is the value of b?

Jamee is building a two-story house in which the top floor is 12 feet above the bottom floor. The local building code specifies that the height of a step cannot exceed 7.5 inches. What is the maximum height of a step in a staircase that Jamee can construct between the two floors if all steps will have the same height? Express your answer as a decimal to the nearest tenth.

The local gaming club has more than 2 but fewer than 20 members. Every member of the group purchased a signed copy of the latest book from the legendary Dumas, for a grand total of exactly $299. If each member paid the same whole number dollar amount, how many members are in the club? 

The price P, in dollars, that AppCo charges annual subscribers for downloading x smartphone applications is calculated using the formula P = 5 + 1.25x. If a subscriber downloaded 25 applications during a year, what was the average cost per application? 

In Mrs. Abel’s class, there are 16 girls and 14 boys. The mean of the girls’ heights is 63.7 inches, and the mean of the boys’ heights is 65.4 inches. What is the mean of the heights of all 30 students? Express your answer as a decimal to the nearest tenth.

What percent of the prime numbers less than 100 have a units digit of 3? 

On average, a human fingernail grows at a rate of 3 mm per month. At this rate, how many total meters will Deshawn’s 10 fingernails grow over the next 10 years? Express your answer as a decimal to the nearest tenth.

An exponentially talented salesman sells 1 car on his first day, 2 cars on his second day, 4 cars on his third day and so on, so that every day after the first, he sells twice as many cars as the day before. How many days does it take him to sell a total of at least 1000 cars?

Ms. Swift wrote 40 pages of notes, each page containing approximately 240 words. Chanel, who types 36 words per minute, volunteered to type some of Ms. Swift’s notes, beginning at the first page and progressing through them in order. Marcus, who types 54 words per minute, volunteered to type some of Ms. Swift’s notes, beginning at the last page and progressing through them in reverse order. If Chanel and Marcus begin at the same time, working together, how many minutes will it take them to finish typing the notes? Express your answer to the nearest whole number

A very round number is a positive integer that has exactly one nonzero digit. How many integers less than one billion are very round numbers?