Area and Perimeter Tools
For this item, any answers that are not whole numbers should be entered as a decimal, rounded to the thousandths place.
Daniel is creating a model of a stone tool from the Neolithic era. A diagram of one side of the tool is shown below.
B
А
6 in
T
1.3 in
ID
4.8 in
F
т
0.75 in
1
F
T G
1.2 in
I
H
9 in
Note: Image not drawn to scale.
Using the diagram, complete the sentences below.
The length of side Al is
inches
The length of side IH is
inches
The area of the visible side of the model is
square inches
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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.