Uring a downhill bike race, one biker has a total mechanical energy of 8220 Joules. The biker is currently traveling at 12 m/s without having
pedaled, as he speeds down the hill (allowing gravity to do the work). The kinetic energy at this point in time is 5062 J. Calculate the original
(starting) height of the hill. (Round to the nearest tenth place)

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.)

Three friends are comparing the prices of various packages of golf balls at a sporting goods store. hector finds a package of 6 golf balls that costs $4.50.

2f(x)= x+3 if 4 < x < 8 2x if x 28 2