Find the length and width of a rectangle with maximum area that has a perimeter of 9P units.

Factor the polynomial 4x4 – 20x2 – 3x2 + 15 by grouping. what is the resulting expression? (4x2 + 3)(x2 – 5) (4x2 – 3)(x2 – 5) (4x2 – 5)(x2 + 3) (4x2 + 5)(x2 – 3)

Atown has a population of 12000 and grows at 3.5% every year. what will be the population after 7 years, to the nearest whole number?

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.)