What are the measures of angles a, b, and c? show your work and explain your answers.

Which of the statements about the graph of the function y = 2x are true? check all of the boxes that apply. the domain is all real numbers x because the exponent of 2 can be any real number when the x-values increases by 1 unit, the y-value multiplies by 2. the y-intercept is (0, 1). the graph never goes below the x-axis because powers of 2 are never negative. the range is all real numbers.

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.

Which is an accurate comparison of the two data sets? the commute to work is typically shorter and more consistent than the commute home. the commute to work is typically shorter but less consistent than the commute home. the commute to work is typically longer and less consistent than the commute home. the commute to work is typically longer but more consistent than the commute home.