For each of the following sets, state whether it is finite, countably infinite, or uncountable. With each statement, justify your answer. (Remember that a set S is countably infinite means that |S| = |Z+| and S is uncountable means that |S| > |Z+|.)(a) The set of all finite subsets of Z+(b) The set of all functions from Z+ to {0, 1}.(c) The set of all n × n matrices with binary entries for any n ∈ Z+.

Arandom number generator is used to model the patterns of animals in the wild this type of study is called

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.

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .