Math 513 Final Exam

1. What is the probability of a 9-child family having 5 boys and 4 girls?
2. An inlet pipe on a swimming pool can be used to fill the pool in 24 hours. The drain pipe can be used to empty the pool in 42 hours. If the pool is two-thirds filled and then the drain pipe is accidentally opened, how long will it take to fill the pool?
3. What is the probability of obtaining four heads in five flips of a coin, given that at least three are heads?
4. What is the sum of the whole numbers from 5 – 30,000 inclusive?
5. You have a five gallon container and a 3 gallon container; explain how you can get exactly 4 gallons of water using only these two containers?
6. Two cyclists are pedaling towards each other both at a constant rate of 4 miles per hour. A fly is on one of the handlebars and flies from one handlebar to other continuously until the bikes pass each other. If the two cyclists start out 8 miles apart and the fly’s rate is 15 miles per hour, how far does the fly fly?
7. How many squares are there in a 15 x 15 unit square?
8. Is (p v q) → (~q → p) a tautology?
9. Prove or disprove that the contrapositive of the conditional sentence is the same as the converse of its inverse.
10. Change 2,001 to base two.
11. Given any set, define what properties must be satisfied in order to be a group.
12. Solve for x when 5x³ – 3x² + 70 congruent to 0, (mod 2)
13. Sterling silver contains 92.5% silver. How many grams of pure silver and sterling silver must be mixed to get 80 grams of a 96% alloy?
14. Perform the indicated operation.

7 – 11, (mod 12)

15. Assume that today is Tuesday (day 3). Determine the day of the week it will be 300 days later. (Assume no leap years.)