Represent the following sentence as an algebraic expression, where "a number" is the letter x. 9 less than the product of 9 and a number.

In the xy-plane, if the parabola with equation passes through the point (-1, -1), which of the following must be true?

What is the length of the segment, endpoints of which are intersections of parabolas y=x2? 11 4 x? 7 4 and y=? 7 8 x2+x+ 31 8 ?

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.)