In what direction and by how many units is the graph of f(x) = 5 cos(4x − π) − 1 vertically and horizontally shifted?
up 1, right pi over 4
up 1, left pi over 4
down 1, right pi over 4
down 1, left pi over 4

Jose predicted that he would sell 48 umbrellas. he actually sold 72 umbrellas. what are the values of a and b in the table below? round to the nearest tenth if necessary

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.

Awater truck is filling a swimming pool the equation that represents this relationship is why equals 19.75 x where y is the number of gallons of water in the pool and x is the number of minutes the truck has been filling the pool