Which expression is equivalent to cos(2α)cosα−sinα for all values of α for which cos(2α)cosα−sinα is defined?
select the correct answer below:

2

cosα+sinα

cot2α−2cos2α

2tanα1+tanα

2sinα1−tan2α

He graph of f(x) = |x| is stretched by a factor of 0.3 and translated down 4 units. which statement about the domain and range of each function is correct? the range of the transformed function and the parent function are both all real numbers greater than or equal to 4. the domain of the transformed function is all real numbers and is, therefore, different from that of the parent function. the range of the transformed function is all real numbers greater than or equal to 0 and is, therefore, different from that of the parent function. the domain of the transformed function and the parent function are both all real numbers.

Math i have no idea how to do a and b

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.)