Simplify the product.
2n (n² + 3n + 4)
a. 2n^3 + 6n² + 8n
b. 2n^3 + 3n + 4
c. 2n^3 + 6n + 8
d. n² + 5n + 4

You are remodeling your kitchen. you’ve contacted two tiling companies who gladly told you how long it took their workers to tile of a similar size jim completed half the floor in 8 hours. pete completed half of the other floor in 7 hours. if pete can lay 20 more tiles per hour than jim, at what rate can jim lay tiles

If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x)

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.