A rectangular coordinate system with coordinates in miles is placed with the origin at the center of a city. The figure to the right indicates that a university is located 3.2 miles west and 3.7 miles south of the center of the city. A seismograph on the campus shows that a small earthquake occurred. The quake's epicenter is estimated to be approximately 33 miles from the university. Write the standard form of the equation for the set of points that could be the epicenter of the quake.

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.)