Karen merlott, vp for strategic planning at a recruitment firm, recently conducts a survey to determine customer satisfaction with job placement. she distributed the survey to 45 of the most recently placed executives. two items on a survey questionnaire them to rate the importance of "initial interview process" and "satisfaction of final job placement" on a scale of 1 to 10 (with 1 meaning "not important" and 10 meaning "highly important"). her staff assembled the following statistics on these two items. initial interview process satisfaction of final job placement mean 8.5 7.5 median 9 8.5 mode 9.0 9 standard deviation 1.0 1.5 what can karen conclude from these statistics?

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.

Using only the digits 5, 6, 7, 8, how many different three digit numbers can be formed if no digit is repeated in a number?