(-1/2+√3/2i)^-2 find out the real and Imaginary part

Ahomeowner plans to hang wallpaper on one wall of a bedroom that is 10 feet long if a stripe of wallpaper is 20 inches wide and stripes or hung vertically how many stripes on wall paper with the homeowner required

Solve the inequaliy: (x^2+2)(x−2)^2(6−2x)> 0

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.)