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snow_tiger [21]
3 years ago
12

The volume of a rectangular prism is 2,058 cubic cm. The length of the prism is 3 times the width. The height is twice the width

. Find the width of the prism.
Mathematics
1 answer:
liraira [26]3 years ago
8 0
Let the width be w, length = 3w and height = 2w

Volume = length x width x height = w x 3w x 2w = 6w^3
6w^3 = 2,058
w^3 = 2,058/6 = 343
w = ∛343 = 7

width = 7 cm
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\chi^2 = \frac{(21-12)^2}{12}+\frac{(16-12)^2}{12}+\frac{(10-12)^2}{12}+\frac{(8-12)^2}{12}+\frac{(5-12)^2}{12}=13.833

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A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

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Method   Beverage   Nap   Walk   Snack   Other

Number       21             16       10         8         5

The total on this case is 60

We need to conduct a chi square test in order to check the following hypothesis:

H0: Drowsiness are equally distributed among office workers

H1: Drowsiness IS NOT equally distributed among office workers

The level of significance assumed for this case is \alpha=0.1

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\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}

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E_{Beverage} =\frac{60}{5}=12

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E_{Walk} =\frac{60}{5}=12

E_{Snack} =\frac{60}{5}=12

E_{Other} =\frac{60}{5}=12

And the expected values are given by:

Method   Beverage   Nap   Walk   Snack   Other

Number       12             12       12         12         12

And now we can calculate the statistic:

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Now we can calculate the degrees of freedom for the statistic given by:

df=(catgories-1)=(5-1)=4

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"=1-CHISQ.DIST(13.833,4,TRUE)"

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