alice and bob take turns to write numbers on a blackboard Alice starts by writing an integral a between 100 and 100 inclusive on the board. On each of Bob's turns he writes twice the number Alice wrote last. On each of Alice subsequent turns she writes the number 45 less than the number Bob wrote last. At some point the number a is written on the board for the second time. Find the possible value of a

Find the volume of the solid generated when the region bounded by y= x and y= 4√x is revolved about the x-axis the volume of the solid is: (type an exact answer cubic units)

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?

Beth divided 9 ounces of her granola recipe into 4 equal-sized amounts. she placed the amounts into individual bowls. the fraction 9/4 represents the number of ounces of granola in each bowl. which other number represents the amount of granola beth has in each bowl? (a) 1 1/4 (b) 2 1/4 (c) 1 3/4 (d) 3 3/4 i need !