Describe how you can find the roots for any quadratic function written in factored form by looking at just the equation.

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.

Tyler reads 2/5 of a book on monday, 1/3 of it on tuesday, 2/9 of it on wednesday, and 3/4 of the remainder on thursday. if he still has 14 pages left to read on friday, how many pages are there in the book?

The price for gasoline is represented by the equation y=3.69x, where y represents the total price for x gallons of gasoline. on a graph, the number of gallons is represented on the horizontal axis, and the total price is represented on the vertical axis. determine whether each statement describes the graph of the equation. select true or false for each statement