3. A rectangular prism has dimensions of ½ 2, and 7/2 in. (a) Determine the edge length of the largest unit cube that you could use to pack the prism. Explain.

(b) What is the volume of the prism? Explain.

(c) How many cubes with the edge length from part (a) will fit into the prism? Explain.

Which sentence uses an objective tone? we will plant the best garden of any school in the area. the new campus garden will surely be envied by other schools. a garden would provide numerous benefits to the students. you will probably agree that gardens have many benefits.

Atriangle in the coordinates of (2,3), (-4,5) and (-2,4) it is translated 3 units down. what are it’s new coordinates

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.