Given the function f(x)= x^4+6x^3-x^2-30x+4 use the intermediate value theorem to decide which of the following intervals contains at least one zero (there are 4 answers) a) [-5,-4] b) [-4,-3] c) [-3,-2] d) [-1,0] e) [0,1] f) [1,2]

Quick! a survey of 57 customers was taken at a bookstore regarding the types of books purchased. the survey found that 33 customers purchased mysteries, 25 purchased science fiction, 18 purchased romance novels, 12 purchased mysteries and science fiction, 9 purchased mysteries and romance novels, 6 purchased science fiction and romance novels, and 2 purchased all three types of books. a) how many of the customers surveyed purchased only mysteries? b) how many purchased mysteries and science fiction, but not romance novels? c) how many purchased mysteries or science fiction? d) how many purchased mysteries or science fiction, but not romance novels? e) how many purchased exactly two types of books?

Arace is 10 kilometers long.markers will be placed at the beginning and end of the race course and at each 500 meter mark.how many markers are needed to mark the course for the race?

For what values of a is the sum of the fractions 2a−1 / 4 and a−1 /3 positive?