1 1
2
3
4
5
6
7
8
9
2
4
6
8
10
12
14
18
15
3
Tolo
9
12
15
18
27
4
12
16
20
36
21
28
35
24
30
5
10
oN.
15
25
40
45
6
12
18
20
24
28
30
54
42
49
7
14
35
36
42
48
48
56
64
21
24
27
63
72
8
16
32
40
8
56
63
9
18
36
45
54
81
Which ratio is equivalent to the ratio 18:24?
0 15:20
O 20:15
O 30:36
36:30
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The frequency table shows the results of a survey comparing the number of beach towels sold for full price and at a discount during each of the three summer months. the store owner converts the frequency table to a conditional relative frequency table by row. which value should he use for x? round to the nearest hundredth. 0.89 0.90 0.92 0.96

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.

During each minute of a comedy show, carlin laughs 55 times. carlin watches 33 comedy shows every day, and each show is 40 minutes long. how many times does carlin laugh every day due to the comedy shows?