Karl starts the engine on his small private airplane. The engine drives a propeller with a radius of 9 feet and its centerline 12.5 feet above the ground. At idle, the propeller rotates at a constant speed of approximately 750 revolutions per minute. The height of one propeller tip as a function of time is given by h = 12.5 + 9 sin(750t), where h is the height in feet and t is the time in minutes. Find h when t = 3.5 minutes.
a.
21.1 ft
b.
14.8 ft
c.
3.8 ft
d.
10.2 ft

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)