Suppose that a positive integer is written in decimal notation as n = akak−1 · · · a2a1a0 where 0 ≤ ai ≤ 9 (i. e. the ai are the digits of n). (a) prove that n is divisible 9 iff the sum of the digits ak + · · · + a0 is divisible by 9. for example, 123453 is divisible by 9 (try it! ) because 1 + 2 + 3 + 4 + 5 + 3 = 18, which is divisible by 9.

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¯.