Ayaan does push-ups and sit-ups every morning. He does p push-ups and 2p + 5 sit-ups. Which statement describes the number of sit-ups Ayaan does every morning? The number of sit-ups is 5 more than twice the number of push-ups he does.

The number of sit-ups is 5 more than half the number of push-ups he does.

The number of sit-ups is 5 fewer than twice the number of push-ups he does.

The number of sit-ups is 5 fewer than half the number of push-ups he does.

Lassify the function as linear or quadratic and identify the quadratic, linear, and constant terms. f(x) = (3x + 2)(−6x − 3) linear function; linear term: −21x; constant term: −6 linear function; linear term: −18x2; constant term: −6 quadratic function; quadratic term: 6x2; linear term: 24x; constant term: −6 quadratic function; quadratic term: −18x2; linear term: −21x; constant term: −6

In the diagram, the ratio of ab to ae is (1/2) . what is the ratio of the length of to the length of ?

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.