The function f(x) = 582(7)x represents the growth of a mosquito population every year in a remote swamp. troy wants to manipulate the formula to an equivalent form that calculates every 2 months, not every year. which function is correct for troy's purposes?
a: f(x) = 582(7 to the one sixth power)6x
b: f(x) = 52(7)x
c: f(x) = 582(712)the x over 12 power
d: f(x) = 5852(7)x

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.)