50 POINTS EACH Please use your own answers Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2x and y = 4x−2 intersect are the solutions of the equation 2x = 4x−2. (4 points)

Part B: Make tables to find the solution to 2x = 4x−2. Take the integer values of x between −4 and 4. (4 points)

Part C: How can you solve the equation 2x = 4x−2 graphically? (2 points)

(10 points)

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.

Which is an accurate comparison of the two data sets? the commute to work is typically shorter and more consistent than the commute home. the commute to work is typically shorter but less consistent than the commute home. the commute to work is typically longer and less consistent than the commute home. the commute to work is typically longer but more consistent than the commute home.

Michael and imani go out to eat for lunch if their food and beverages cost 25.30 and there is an 8% meals tax how much is the bill