Math 513 Final Exam
- What is the probability of a 9-child family having 5 boys and 4 girls?
- 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?
- What is the probability of obtaining four heads in five flips of a coin, given that at least three are heads?
- What is the sum of the whole numbers from 5 – 30,000 inclusive?
- 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?
- 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?
- How many squares are there in a 15 x 15 unit square?
- Is (p v q) → (~q → p) a tautology?
- Prove or disprove that the contrapositive of the conditional sentence is the same as the converse of its inverse.
- Change 2,001 to base two.
- Given any set, define what properties must be satisfied in order to be a group.
- Solve for x when 5x3 – 3x2 + 70 congruent to 0, (mod 2)
- 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?
- 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.)
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