Jake wanted to measure the height of the great sphinx of giza. he placed a mirror on the ground and then walked backwards until he was able to see the top of the statue in the mirror. if his eyes were 5.5 feet above the ground, how tall is the statue, to the nearest foot? . a. 65 ft . b. 87 ft . c. 103 ft . d. 137 ft.

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =

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 mean average cost of standard room per night at a hostel is ? 20.60. therefore, how much does a standard room cost per night at night-time rest days?