Suppose b is any integer. Ifb mod 12 = 7,what is 8b mod 12? In other words, if division of b by 12 gives a remainder of 7, what is the remainder when 8b is divided by 12? Your solution should show that you obtain the same answer no matter what integer you start with. Using the definition by mod find an expression for b in terms of 12, 7, and an integer m. (Simplify your answer completely.)

Saline iv fluid bags cost $64.20 for 24, 1000 ml bags from one supplier. a new supplier sells 500 ml bags for $2 each. the hospital uses about 10,000, 1000 ml bags each month. nurses report that about half of the bags are more than half full when they are discarded. if you are going to use only one supplier, which size bag provides the best deal, and how much will you save each month? compare the cost of the new supplier to the current one.

Rewrite the following quadratic functions in intercept or factored form. show your work. f(x) = 3x^2 - 12

White shapes and black shapes are used in a game. some of the shapes are circles. while the rest are squares. the ratio of the number of white shapes to the number of black shapes is 5: 11. the ratio of the number of white cicrles to the number of white squares is 3: 7. the ratio of the number of black circles to the number of black squres is 3: 8. work out what fraction of all the shapes are circles.