Let and be conjugate complex numbers such that . find .

William invested $5000 in an account that earns 3.8% interest, compounded annually. the formula for compound interest is a(t) = p(1 + i)t. how much did william have in the account after 6 years? (apex)

Which expressions equal 9 when x=4 and y=1/3 a. x2+6y b. 2x + 3y c. y2-21x d. 5 (x/2) -3y e. 3x-9y

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.)