You are drawing a map of your school and want to make sure all the measurements are accurate. You decide to use a scale of 1 cm = 3 feet. In your drawing, the main hallway ends up being 12 cm long. The drawing is a little too big so you decide to change the scale to 1 cm = 4 feet.

Keeping the length in feet the same, how many centimeters long should the main hallway be in your new drawing?

What is the value of x when x + 7 = 21?

Two years ago a man was six times as old as his daughter. in 18 years he will be twice as old as his daughter. determine their present ages.

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.