12 The attendance for the last 4 years at a county fair is shown in the table.
County Fair Attendance
Attendance
Year
1
2
9,278
10,365
12,128
13,304
3
4
This year, the first 20% of people attending the fair will receive a raffle ticket. Of the people who receive raffle tickets,
will receive a small prize.
• Based on the data in the table, determine a reasonable estimate of the number of people who will attend this year's fair.
Explain how you found your estimate.
• Use your estimate to find the approximate number of people who will receive a small prize at this year's fair.
• Show your work or provide an explanation of how you found the approximate number of people who will receive a small
prize at the year's fair.
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The height of a triangle is 4 in. greater than twice its base. the area of the triangle is no more than 168 in.^2. which inequalitycan be used to find the possible lengths, x, of the base of the triangle?

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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.