Ben swims 50,000 yards per week in his practices. given this amount of training, he will swim the 100-yard butterfly in 51.5 seconds and place 10th in a big upcoming meet. ben's coach calculates that if ben increases his practice to 60,000 yards per week, his time will decrease to 46.4 seconds and he will place 7th in the meet. if ben practices 70,000 yards per week, his time will be 44.6 seconds and he will win the meet. in terms of ben's time in the big meet, what is his marginal productivity of the number of yards he practices?

Aconcession manager at yankee stadium wants to know how temperature affects beer sales. she took a sample of 10 games and recorded the number of beers sold and the temperature in the middle of the game. temperature 80 68 78 79 87 74 86 92 77 84 number of beers 20533 1439 13829 21286 30985 17187 30240 87596 9610 28742 a. draw a scatter plot of the data. b. the manager estimates the regression equation to be: numberofbeers = −100, 678 + 1, 513 ∗ temperature draw this on your scatter plot. c. for one of the estimated points, indicate the residual with ei . d. for that same point, indicate what part of the variation is explained by the model with ˆyi − y¯.