Practice Set 7
- Problem #1: In triangle ABC, angle B is a right angle. Select a point D on side AC, such that line segment BD is perpendicular to side AC. If AB=8 and BC=15, what is BD? Express your answer as a common fraction.
- Problem #2: When Amy, Elizabeth, and Meg were little, they used to play with Barbie dolls. The number of dolls that Elizabeth had was equal to the square root of the number of dolls that Amy had. The number of dolls that Meg had was equal to the square root of the number of dolls that Elizabeth had. Each of the girls had more than 1 doll but fewer than 50 dolls. How many dolls did Amy, Elizabeth, and Meg have put together?
- Problem #3: On the first day of a dare, Timmy ate 2 worms. On each day after that, he ate 2 more worms than he did on the previous day. Timmy ate his 50th worm on the nth day. What is the value of n?
- Problem #4: *Calculator use is assumed on this problem.* I live in Michigan, and I drove to Ohio to visit a friend. I drove for a total of 3.1 hours on the freeway, partly in Michigan and partly in Ohio. Since the freeway speed limits in the two states are different, I drove at 70 miles per hour in Michigan and 65 miles per hour in Ohio. In all, I drove 212 miles on the freeway. How many of these miles did I drive in Michigan?
- Problem #5: In a game of tag, It is running toward you at a constant speed of 10 meters per second. You are running away from It at 8 meters per second. If It is 50 meters behind you, how many seconds will it take before It catches you?
- Problem #6: How many positive three-digit integers can be formed using only odd digits?
- Problem #7: A rectangular prism has side, front and bottom faces having areas of 2 square feet, 4 square feet and 8 square feet, respectively. What is the volume of the rectangular prism, in cubic feet?
- Problem #8: A swimming pool in the shape of a rectangular prism has a length of 75 ft and a width of 40 ft. It is empty now, but it needs to be filled to a depth of 5 ft. There are 4 pumps that will pump water into the pool at the same time, and each pump will work at a rate of 125 gallons of water per minute. If a cubic foot of water is equivalent to 7.5 gallons, how many minutes will it take to fill the pool?
- Problem #9: Anastasia, the most popular girl at school, has 65 girls in her clique. Each day, Anastasia randomly chooses 5 girls from her clique to eat lunch with. If Lucy is a member of Anastasia's clique, what is the probability that Anastasia and Lucy will have lunch together today? Express your answer as a common fraction.
- Problem #10: There are 1000 millimeters in a meter, and there are 1000 meters in a kilometer. The number of cubic millimeters in a cubic kilometer is 10n. What is the value of n?
Solutions
