Shape 1 and shape 2 are plotted on a coordinate plane. which statement about the shapes is true? a. shape 1 and shape 2 are not congruent. b. a translation will prove that shape 2 is congruent to shape 1. c. a rotation and a translation will prove that shape 2 is congruent to shape 1. d. a reflection, a rotation, and a translation will prove that shape 2 is congruent to shape 1.

Which sum or difference identity would you use to verify that cos (180° - ∅) = -cos ∅? a. sin (α -β) = sin α cos β – cos α sin β b. cos (α -β) = cos α cos β – sin α sin β c. cos (α -β) = cos α cos β + sin α sin β d. sin (α + β) = sin α cos β + cos α sin β

Unaware that 35% of the 10000 voters in his constituency support him, a politician decides to estimate his political strength. a sample of 200 voters shows that 40% support him. a. what is the population? b. what is the parameter of interest? state its value c. what is the statistics of the interest? state its value d. compare your answers in (b) and (c) is it surprising they are different? if the politician were to sample another 200 voters, which of the two numbers would most likely change? explain

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.