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Scrat [10]
3 years ago
14

11 relaxing after work. the 2010 general social survey asked the question: "after an average work day, about how many hours do y

ou have to relax or pursue activities that you enjoy?" to a random sample of 1,155 americans.41 a 95% confidence interval for the mean number of hours spent relaxing or pursuing activities they enjoy was (1.38, 1.92). (a) interpret this interval in context of the d
Mathematics
1 answer:
Bogdan [553]3 years ago
3 0
A confidence interval tells us how many percents we are confident about the range of a parameter. In this problem, <span>a 95% confidence interval for the mean number of hours spent relaxing or pursuing activities they enjoy was (1.38, 1.92). That means we're 95% confident that the Americans spend from 1.38 hours to 1.92 hours per day on average relaxing or pursuing activities they enjoy. In other words, 95% of the samples of the same size would have a mean number of hours relaxing or pursuing activities they enjoy between 1.38 to 1.92.</span>
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How many subsets of {1, 2, 3, 4, 6, 8, 10, 15} are there for which the sum of the elements is 15?
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Answer:

512

Step-by-step explanation:

Suppose we ask how many subsets of {1,2,3,4,5} add up to a number ≥8. The crucial idea is that we partition the set into two parts; these two parts are called complements of each other. Obviously, the sum of the two parts must add up to 15. Exactly one of those parts is therefore ≥8. There must be at least one such part, because of the pigeonhole principle (specifically, two 7's are sufficient only to add up to 14). And if one part has sum ≥8, the other part—its complement—must have sum ≤15−8=7

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For instance, if I divide the set into parts {1,2,4}

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Once one makes that observation, the rest of the proof is straightforward. There are 25=32

different subsets of this set (including itself and the empty set). For each one, either its sum, or its complement's sum (but not both), must be ≥8. Since exactly half of the subsets have sum ≥8, the number of such subsets is 32/2, or 16.

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2 years ago
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Alika [10]

 

Distance from a point to a line (Coordinate Geometry)

Method 1: When the line is vertical or horizontal , the distance from a point to a vertical or horizontal line can be found by the simple difference of coordinates . Finding the distance from a point to a line is easy if the line is vertical or horizontal. We simply find the difference between the appropriate coordinates of the point and the line. In fact, for vertical lines, this is the only way to do it, since the other methods require the slope of the line, which is undefined for evrtical lines.

Method 2: (If you're looking for an equation) Distance = | Px - Lx |

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