The diagonal of a cube is a segment whose endpoints are vertices that are not on the same face. find the surface area of a cube with diagonal length 8 units. round your answer to three decimal places

Find the greatest common factor of the polynomial: 10x^5+15x^4-25x^3 10x^5 x^3 5x^3 5

What is the value of x in the equation (2)3) (x+6)= -18 a. -36 b. -33 c. -24 d. -18

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.)