Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B. Triangle A B C is shown. Angle A C B is 90 degrees and angle A B C is 60 degrees. The length of side B C is a, the length of C A is b, and the length of hypotenuse A B is 500 meters. About how much farther is it to drive than to walk directly from building A to building B? Round to the nearest whole number. 183 meters 250 meters 366 meters 683 meters

Ineed to know the answer to this algebra question.

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.

Does the construction demonstrate how to copy an angle correctly using technology a) yes the distance between points a and f was used to create circle h b) yes the distance between points f and g was used to create circle h c) no the distance between points a and f was used to create circle h d) no the distance between points f and g was used to create circle h