The art class is constructing a sculpture to place as a memorial at the entrance of the school composed of a sphere and a cube-shaped
base. The diameter of the sphere must be equal in length to the edge
of the cube. The formula below represents the length of the edge of
the cube in terms of the total volume of the sculpture.
6V
e=46 +7
If the art class determines that the length of the edge of the cube is
to be 3.5 feet, what volume of sand to the tenth of a cubic foot will
be needed to fill the sculpture?

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.)