Sophee left her house on her bike and traveled 3 kilometers north, 5 kilometers east, 3 meters south, then 5 kilometers west, arriving home in time for dinner. which of the following statements about her distance and displacement is correct?

(a.) her distance is 16 kilometers, and her displacement is 16 kilometers.

(b.) her distance traveled is 16 kilometers, and her displacement is 0 kilometers.

(c.) her distance traveled is 0 kilometers, and her displacement is 16 kilometers.

Find the area of the unshaded square

Pls never taught i’m really confused and i rlly need

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.