Find the area of the regular 24-gon with radius 11 mm.
Amm2
(Do not round until the final answer. Then round to the nearest tenth as needed.)

What is the ratio for the surface areas of the cones shown below, given that they are similar and that the ratio of their radii and altitudes is 2: 1? submit

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.

Mrs. blake's bill at a restaurant is $42.75. she wants to leave the waiter an 18% tip. how much will she pay in all, including the tip?