Two ferries depart from opposite banks of a river simultaneously, and cross the river moving at constant speeds and perpendicularly to the river banks. The ferries meet each other at a point that is 700 meters away from the closest riverbank. When they reach the respective river banks toward which they are moving, they immediately turn around and travel back the other way, meeting again. This time they meet at a point that is 400 meters away from the second riverbank. How wide is the river, in meters?

The table respent two linear functions the equation respented by the first tables is given

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.

The slope of the line passing through the points (2, 7) and (-4, 8) is