You wait in line for 45 minutes to get on the Superman ride at Six Flags. The ride lasts 180 seconds. What is the
ratio of time spent in line to the time spent on the ride?

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.

He trapezoid is composed of a rectangle and two triangles. what is the area of the rectangle? what is the total area of the triangles? what is the area of the trapezoid? ? a) 42 cm2; 27 cm2; 69 cm 2 b) 54 cm2; 27 cm2; 81 cm 2 c) 108 cm2; 27 cm2; 135 cm 2 d) 108 cm2; 13.5 cm2; 121.5 cm 2

The image of abc is a'b'c. what transformations would result in this image? abc is reflected over the line x = 1, then is rotated -90° around the origin. abc is reflected over the line y = x - 1, then t: (x, y) → (x - 1, y - 1). abc is rotated 90° around the origin, then is reflected over the y-axis. abc is rotated -90° around the origin, then is reflected over the line y = -1.