Show that if a, b, c, and m are integers such that m ≥ 2, c > 0, and a ≡ b (mod m), then ac ≡ bc (mod mc). rosen, kenneth. discrete mathematics and its applications (p. 259). mcgraw-hill higher education. kindle edition.

Walter is to make cookies for a basketball tournament. he's made 15 cookies so far. his coach asked him to make at least 20 cookies but no more than 55. solve the inequality and interpret the solution. 20 ? x + 15 ? 55

The price of a box of 15 cloud markers is $12.70. the price of a box of 42 cloud markers is $31.60. all prices are without tax, and the price of the packaging is the same for any size. how much would 50 cloud markers in a box cost? write an equation which will tell the price p for the number n markers in the box.

At all trials and hearings, a court reported types every word spoken during the proceedings so that there is a written record of what transpired. because they must type every word, the average court reporter must be able to type a minimum rate of 3.75 words per second in order to be certified. suppose a trial transcript contains 25 pages with an average of 675 words per page. assuming the court reporter typed the transcript at the minimum rate, how long was she actively typing? a) 1 hour, 15 minutes b) 1 hour, 45 minutes c) 2 hours, 30 minutes d) 3 hours