John and Phil were playing tennis. They each hit a tennis ball at the same time and measured the how high the tennis balls went and how long it took for each one to
land on the tennis court. The graph represents the height of the tennis ball 1
seconds after it was hit by john

The function f given by $ (1) = (-161 – 2) (1 – Zepresents the height of the
tennis ball t seconds after it was hit by Phil. In both functions, height is measured in feet.
Part 1. Whose tennis ball hit the tennis court first? When did that happen?
Part 2. Phil's tennis ball reached its maximum height after a seconds. Did Phil's
tennis ball reach a higher maximum than John's tennis ball?
Part 3. What was the maximum height of Phil's tennis ball? Round your answer to
the nearest whole number.

Suppose we have a set of small wooden blocks showing the 26 letters of the english alphabet, one letter per block. (think of scrabble tiles.) our set includes 10 copies of each letter. we place them into a bag and draw out one block at a time. (a) if we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) now suppose we just toss our chosen blocks into a pile, and whenever we draw a letter we already have, we put it back in the bag and draw again. how many different piles of 5 blocks could result? possible? piles will contain at least one repeated letter? (c) if we draw out 5 blocks wit hout looking at them, how many different piles are (d) if we draw out 5 blocks without looking at them, how many of the possible 2. (4) consider the following formula. 12 give two different proofs, one using the factorial formulas and the other combina torial.