When given the coordinates of the vertices of a triangle, can the slope formula be used to determine whether the triangle is a right triangle? if so, how?

The area of a rectangle is 54x^9y^8 square yards.if the length of the rectangle is 6x^3y^4 yards,which expression represents the width of the rectangle in yards

Select the margin of error that corresponds to the sample mean that corresponds to each population: a population mean of 360, a standard deviation of 4, and a margin of error of 2.5%

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.)