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.

Acoffee shop orders at most $3,500 worth of coffee and tea. the shop needs to make a profit of at least $1,900 on the order. the possible combinations of coffee and tea for this order are given by this system of inequalities, where c = pounds of coffee and t = pounds of tea: 6c + 13t ≤ 3,500 3.50c + 4t ≥ 1,900 which graph's shaded region represents the possible combinations of coffee and tea for this order?