Type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. the domain of the function f(x) = 3x3 is {2, 5}. what is the function’s range? the range of the function f(x) = 3x3 when its domain is {2, 5}

Use the formulas a = x 2 – y 2, b = 2xy, c = x 2 + y 2 to answer this question. one leg of a right triangle has length 11 and all sides are whole numbers. find the lengths of the other two sides. the other leg = a0 and the hypotenuse = a1

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.

At a pizza shop 70% of the customers order a pizza 25% of the customers order a salad and 15% of the customers order both a pizza and a salad if s customer is chosen at random what is the probability that he or she orders either a pizza or a salad