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2 years ago

9. If a person bikes 0.24 miles in 1 minute, how far can they bike in 45 minutes?

Mathematics

1 answer:

igomit [66]2 years ago

8 0

Answer:

9. 10.8 miles

10. Yes

Step-by-step explanation:

To solve number 9 I multipled 0.24 x 45 to find the distance the biker can bike in 45 minutes.

Number 10 is yes because the numbers continue proportionaly. If you work it out, you can see that each half gallon takes the car 16 miles. The distances went 16 miles for 1/2 gallon, 32 miles for 1 gallon, would go 48 miles for 1 1/2 gallons, and went 64 miles for 2 gallons.

Hope it helps!

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Answer:

95% Confidence interval for the variance:

$3.6511\leq \sigma^2\leq 34.5972$

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Step-by-step explanation:

We have to calculate a 95% confidence interval for the standard deviation σ and the variance σ².

The sample, of size n=8, has a standard deviation of s=2.89 miles.

Then, the variance of the sample is

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The confidence interval for the variance is:

$\dfrac{ (n - 1) s^2}{ \chi_{\alpha/2}^2} \leq \sigma^2 \leq \dfrac{ (n - 1) s^2}{\chi_{1-\alpha/2}^2}$

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$\chi_{0.025}=1.6899\\\\\chi_{0.975}=16.0128$

Then, the confidence interval can be calculated as:

$\dfrac{ (8 - 1) 8.3521}{ 16.0128} \leq \sigma^2 \leq \dfrac{ (8 - 1) 8.3521}{1.6899}\\\\\\3.6511\leq \sigma^2\leq 34.5972$

If we calculate the square root for each bound we will have the confidence interval for the standard deviation:

$\sqrt{3.6511}\leq \sigma\leq \sqrt{34.5972}\\\\\\1.9108\leq \sigma \leq 5.8819$

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