A computer is printing out subsets of a 5 element set (possibly including the empty set). (a) At least how many sets must be printed to be sure of having at least 3 identical subsets on the list?
(b) At least how many identical subsets are printed if there are 129 subsets on the list?

According to a study conducted in 2015, 18% of shoppers said that they prefer to buy generic instead of name-brand products. suppose that in a recent sample of 1500 shoppers, 315 stated that they prefer to buy generic instead of name-brand products. at a 5% significance level, can you conclude that the proportion of all shoppers who currently prefer to buy generic instead of name-brand products is higher than .18? use both the p-value and the critical-value approaches.

Cos^2x+cos^2(120°+x)+cos^2(120°-x)i need this asap. pls me

The letters g e o r g i a are placed in a bag . if you picked a card and knew it was a vowel , what is the probability that it is an a ?