Paco's cell phone carrier charges him $0.20 for each text message he sends or receives, $0.15 per minute for calls, and a $15 monthly service fee. Paco is trying to keep his bill for the month below $30. Which best describes the possible values of t, the number of texts he can send or receive? t can be any real number where 0 ≤ t < 75. ~~ t can be any whole number where 0 ≤ t < 75. t can be any real number where 0 ≤ t < 150. t can be any whole number where 0 ≤ t < 150.

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.

Using the rise/run counting method, the slope of the line is

To start to solve the system of equations below, which number would you multiply in the equation -2x-5y=-1? the two equations are -2x-5y=-1 and 4x+2y=8