Dear Math Students, This drawing of a cube appears to have a volume of 19 cubic units but, when I built it, I used 27 cubes. What did I do wrong? Your Friend, Puzzled penguin

Find the maximum value of p= 4x + 5y subject to the following constraints :

An elevator travels 310 feet in 10 seconds. at that speed, how far can't his elevator travel in 12 seconds?

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.)