# The base of a pyramid covers an area of 13.0 acres (1 acre =43,560 ft^2) and has a height of 481 ft . Ifthe volume of a pyramid is given by the expression V =(1/3)bh, where b is the area of the base and his the height, find the volume of this pyramid in cubicmeters.

Question
The base of a pyramid covers an area of 13.0 acres (1 acre =43,560 $$\displaystyle{f}{t}^{{2}}$$) and has a height of 481 ft . Ifthe volume of a pyramid is given by the expression V =(1/3)bh, where b is the area of the base and his the height, find the volume of this pyramid in cubicmeters.

2020-12-25
$$\displaystyle{13}\ {a}{r}{c}{e}{s}\cdot{\frac{{{43560}\ {f}{t}^{{2}}}}{{{1}\ {a}{c}{r}{e}}}}={5.66}\times{10}^{{5}}\ {f}{t}^{{2}}$$
$$\displaystyle{5.66}\times{10}^{{5}}\ {f}{t}^{{2}}\cdot{\frac{{{0.0929}\ {m}^{{2}}}}{{{1}\ {f}{t}^{{2}}}}}={5.26}\times{10}^{{4}}\ {m}^{{2}}$$
$$\displaystyle{481}{f}{t}\cdot{\frac{{{0.3048}}}{{{1}{f}{t}}}}={147}{m}$$
$$\displaystyle{V}={\frac{{{\left({5.26}\times{10}^{{4}}{m}^{{2}}{\left({147}{m}\right)}\right\rbrace}{\left\lbrace{3}\right\rbrace}={2.58}\times{10}^{{6}}{m}^{{3}}}}{}}$$

### Relevant Questions

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Previous studies show that $$\sigma_1 = 19$$.
For Englewood (a suburb of Denver), a random sample of $$n_2 = 12$$ winter days gave a sample mean pollution index of $$x_2 = 37$$.
Previous studies show that $$\sigma_2 = 13$$.
Assume the pollution index is normally distributed in both Englewood and Denver.
(a) State the null and alternate hypotheses.
$$H_0:\mu_1=\mu_2.\mu_1>\mu_2$$
$$H_0:\mu_1<\mu_2.\mu_1=\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1<\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1\neq\mu_2$$
(b) What sampling distribution will you use? What assumptions are you making? NKS The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
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At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are not statistically significant.
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Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
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(Round your answers to two decimal places.)
lower limit
upper limit
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Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.

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