Evaluate 19 sin(x) cos(x) dx by four methods. (a) the substitution u = cos(x) − 19 2 sin2(x) + C 19 4 cos(2x) + C 19 4 sin(x) cos(x) + C − 19 2 cos2(x) + C 19 4 sin(2x) + C (b) the substitution u = sin(x) 19 2 sin2(x) + C 19 4 cos(2x) + C 19 2 cos2(x) + C 19 4 sin(x) cos(x) + C − 19 4 sin(2x) + C (c) the identity sin(2x) = 2 sin(x) cos(x) − 19 2 sin2(x) + C − 19 4 sin(x) cos(x) + C − 19 4 cos(2x) + C 19 2 cos2(x) + C 19 4 sin(2x) + C (d) integration by parts − 19 4 sin(x) cos(x) + C 19 4 cos(2x) + C 19 2 sin2(x) + C − 19 4 sin(2x) + C 19 2 cos2(x) + C

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Ascientist studied a population of workers to determine whether verbal praise and/or tangible rewards affect employee productivity. in the study, some workers were offered verbal praise, some were offered tangible rewards (gift cards, presents, and some were offered neither. the productivity of each participant was measured throughout the study by recording the number of daily tasks completed by each employee. which inference might the scientists make based on the given information? a.) the number of daily tasks completed by each employee may influence the dependent variable, which is whether the employee receives verbal praise, tangible rewards, or neither. b.) verbal praise and/or tangible rewards may influence the independent variable, which is the number of daily tasks completed by each employee. c.) verbal praise and/or tangible rewards may influence the dependent variable, which is the number of daily tasks completed by each employee. d.) the dependent variables, which are verbal praise and tangible rewards, may influence the number of daily tasks completed by each employee.

Assume that adults have iq scores that are normally distributed with a mean of mu equals 100 and a standard deviation sigma equals 20. find the probability that a randomly selected adult has an iq between 80 and 120.assume that adults have iq scores that are normally distributed with a mean of mu equals 100 and a standard deviation sigma equals 20. find the probability that a randomly selected adult has an iq between 80 and 120.