Speed Math - Multiple Choice

1. Jerry drives for an hour at 40 miles per hour, and two hours at 55 miles per hour. What is his average speed over these three hours, in miles per hour?

2. What is the units digit of 2^674169420?

3. Evaluate (20-26)^((20/2)-6)

4. Jim and Bob are sharing a pizza with diameter 18 inches. First, Jim eats one half of the pizza. Then, Bob eats one third of the remaining pizza. After this, Jim eats one half of the remaining pizza, and Bob eats one third of what’s left. Jim and Bob continue past infinity because they think they will ever finish the pizza. Which of these numbers is closest to the area of the pizza in square inches Jim eats after 19284857742892 years, given that they eat at a normal rate?

5. Define the function a@b=(5a+9b)/ab for all real numbers a and b. As a common fraction, what is 6@7?

6. My math class has 23 students, including me. My teacher assigns a group project, where students can work in groups of either 2 or 4. Given that I must be in the same group as Jimbob, how many different ways can I choose my group?

7. Which of 3 and 11 is 11979 divisible by?

8. A triangle ABC has side lengths AB=5, AC=12, and BC=13. AD is drawn perpendicular to BC such that D lies on BC. What is the length of AD?

9. The perimeter of a regular 17 sided polygon is 119 inches. There is a cube with the same side length as the 17 sided polygon. What is the volume of the cube in cubic inches?

10. Jacob and Jayden are flipping a fair coin. Jacob has 10 dollars, and Jayden has 20 dollars. Jacob bets 8 dollars that two heads appear before the first tail. If Jacob is wrong, he gives 8 dollars to Jayden. If Jacob is correct, Jayden agrees to give 12 dollars to Jacob because he is a scammer. How much money does Jayden expect to have after money is exchanged?