Let f and g be functions from R to R, with f(x) = ax+b and g(x) = cx+d, where a, b, c, and d are real-number constants. Determine necessary and sufficient conditions on the constants a, b, c, and d so that f ◦ g = g ◦ f.

You use math in day-to-day routines when grocery shopping, going to the bank or mall, and while cooking. how do you imagine you will use math in your healthcare career?

Which of the following can be used to explain a statement in a geometric proof?

Astudy was interested in determining if eating milk chocolate lowered someone's cholesterol levels.ten people's cholesterol was measured. then, each of these individuals were told to eat 100g of milk chocolate every day and to eat as they normally did. after two weeks, their cholesterol levels were measured again. is there evidence to support that their cholesterol levels went down? how should we write the alternative hypothesis? (mud = the population mean difference= before - after)a. ha: mud = 0b. ha: mud > 0c. ha: mud < 0d. ha: mud does not equal 0