As mentioned in the text, the notation∃!xP(x) denotes "There exists a unique x such that P(x)is true." If the domain consists of all integers, what are the truth values of these statements? a) ∃!x(x > 1) b) ∃!x(x2 =1) c) ∃!x(x+3=2x) d) ∃!x(x = x +1)

Li buys supplies so he can make and sell key chains. he begins to make a profit only after he sells 4 key chains. what point on the graph makes the most sense in this situation?

Xy x xy if a and b are positive integers such that a*b=9 and b*a=72 what is the value of a/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.)