Which pair of complex factors results in a real-number product? 15(–15i) 3i(1-3i) (8 + 20i)(–8 – 20i) (4+7i)(4-7i)

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

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.)

The point (-7, -24) is on the terminal ray of angle 0 which is in standard position. a student found the six trigonometric values for angle e. the student's answers are shown. which value(s) are incorrect? sin(8) cos(8) 24 tan(0) sin(0)=25 cos(0) -- tan(ⓡ) - - 24 csc(o)=2 sec(0) --25 cot(6) - za csc(o) sec(0) cot(0) done