Darryl has written 60 percent, or 12 pages, of his history report. Darryl wants to figure out how many pages he needs to write. Darryl’s work is shown below. Step 1: Write 60 percent as a ratio. StartFraction part Over whole EndFraction = StartFraction 60 Over 100 EndFraction Step 2: Write an equivalent ratio using the number of pages done so far. StartFraction 60 Over 100 EndFraction = StartFraction 12 Over question mark EndFraction Step 3: Rewrite as: 12 (100) divided by 60. Step 4: 120 divided by 60 = 2 What mistake did Darryl make? In Step 1, Darryl should have written the ratio as StartFraction 100 Over 60 EndFraction. In Step 2, Darryl should have put 12 in the denominator. In Step 3, Darryl should have multiplied 60 and 100. In Step 4, Darryl multiplied 12 and 100 incorrectly.

What is the range for 31,39,29,34,37,24,36,33,34,28

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.

From the top of a tree a bird looks down on a field mouse at an angle of depression of 50°. if the field mouse is 40 meters from the base of the tree, find the vertical distance from the ground to the bird's eyes.