A tortoise and a hare are competing in a 2000-meter race. The arrogant hare decides to let the tortoise have a 550-meter head start. When the start gun is fired the hare begins running at a constant speed of 8 meters per second and the tortoise begins crawling at a constant speed of 5 meters per second. a. Write an expression in terms of t that represents the hare's distance from the starting line (in meters)b. Write an expression in terms of t that represents the tortoise's distance from the starting line (in meters).c. Write an expression in terms of t that represents the number of meters the tortoise is ahead of the hare.

20 points 1. your friend, taylor, missed class today and needs some identifying solutions to systems. explain to taylor how to find the solution(s) of any system using its graph. 2. taylor graphs the system below on her graphing calculator and decides that f(x)=g(x) at x=0, x=1, and x=3. provide taylor some feedback that explains which part of her answer is incorrect and why it is incorrect. f(x)=2x+1 g(x)=2x^2+1

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 whose equation is 2x - 1 = 0 is