gracie played with a remote-controlled car. at first, she made the car travel at a steady speed. then the car remained still while she changed the batteries in the remote. the time it took her to change the batteries was half the time she had played with the car up to that point. after changing the batteries, she made the car travel at a steady speed again, this time at a slower speed than before. the time the car traveled at the slower speed was about twice as long as the time it had traveled at the faster speed.

which sketch represents this situation?

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.)