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The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(a) = r where r is the unique remainder obtained when a is divided by b.
(a) What is the range of f? Based on your answer, is f onto?
(b) Determine whether f a 1-1 function.
A bourbon that is 51 proof is 25.5% alcohol by volume while one that is 82 proof is 41% alcohol. How many liters of 51 proof bourbon must be mixed with 1.0 liter of 82 proof bourbo
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