We want to find one of the roots of a cubic equation given by 1 0 3 x + x − = which is between 0 and 1 by an iterative method. Modify the equation above to 2 1 1 x x + = Start with an appropriate initial value and do the iteration above until it is convergent. For example, 0.8, 1 0.5 1 0.5 , 0 1 2 = + x = x = 0.609, 1 0.8 1 2 2 = + x = 0.728,  1 0.609 1 3 2 = + x = The simplest (minimum) code may look like:

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.)