Adriena’s strategy for checking that the functions f(x) and g(x) are inverses is to think of them as stacked function machines. she starts by choosing an input to drop into f(x). then she drops the output from f(x) into g(x). if she gets her original number, she is pretty sure that the two equations are inverses. question: is adriena’s strategy sufficient? is there anything else she should test to be sure?

For each sentence below, find the value of x that makes each sentence true. (515) 5 = 25* x= (813)2 = 4* x=

In dire need~! describe how to use area models to find the quotient 2/3 divided by 1/5. check your work by also finding the quotient 2/3 divided by 1/5 using numerical operations only.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.