You get paid on the first day of each month. You cash your check and pay all of your essential expenses. You use the rest for discretionary expenses. A scatter plot show the number of days that have passed since you were paid and the amount left in your bank account. The explanatory x-variable is the number of days that have passed. The response y-variable is the amount left your bank account. Is there a positive, negative, or no correlation?

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.)