These are counting problems. You cannot simply write down the final answer. You must be sure to give sufficient explanation for your counting method. As always - clarity, legibility, and composition count towards your grade. n 8. Give a proof of the following identity using a double-counting argument: d (1) (9) = 2n-d (1)

The number of ways of choosing r objects from n objects is called the number of ___________ of n objects taken r at a time and is given by the formula C(n, r) = ___________.

Find three arithmetic means between 2 and 8.

Salary Jamal’s boss gives him a 3% raise every year on his birthday. This means that each year, Jamal’s salary is 1.03 times his last year’s salary. If his original salary was $35,000, his salary after 1 year was $35,000(1.03), after 2 years was $35,000(1.03)2, after 3 years was $35,000(1.03)3, as shown in the table below. What will Jamal’s salary be after 10 years? Simplify the expression, to show Jamal’s salary in dollars.