Given: Triangle ABC with AB = 45 and BC = 18. Which of the following are possible lengths for AC?

35

17

7

56

70

27

30

63

Explain step-by-step how to simplify -5(2x – 3y + 6z – 10).

Asquare picture with sides of 32 inches is to be mounted on a square mat with sides of 52 inches. find the area of the mat that will remain uncovered by the picture.

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.)