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2 years ago

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Peter uses the equation y = StartFraction 13 over 4 EndFraction x to model the number of miles that he has walked in x hours. Wh

ich statement is true about the proportional relationship that is modeled by Peter’s equation?

1 answer:

Umnica [9.8K]2 years ago

8 0

The true statement is Peter walks at a rate of 13 over 4 miles per hour.

<h3>What is the true statement?
</h3>

Direct variation is when two variables move in the same direction. If one variable increases, the other variable increases. When the hour Peter walks increases, the distance he walks also increases.

Here are the options:

Peter walks at a rate of StartFraction 4 over 13 EndFraction miles per hour.

Peter walks at a rate of 4 miles per hour.

Peter walks at a rate of StartFraction 13 over 4 EndFraction miles per hour.

Peter walks at a rate of 13 miles per hour.

To learn more about direct variation, please check: brainly.com/question/27573249

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Step-by-step explanation:

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To solve this problem you must apply the proccedure shown below:

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$FV=(PV)(e^{it})$

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An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining.

jeka94

Answer:

The point estimate is 5,617.

The margin of error of a confidence interval for the difference between the two population means is 454.18386 .

The 98% confidence interval for the difference between the two population means is (5163, 6071).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Compound 1:

127 brakes, average brake life of 42,814 miles, population standard deviation of 1819 miles. This means that:

$\mu_1 = 42814$

$s_1 = \frac{1819}{\sqrt{127}} = 161.41$

Compound 2:

163 brakes, average brake life of 37,197 miles, population standard deviation of 1401 miles. This means that:

$\mu_2 = 37197$

$s_2 = \frac{1401}{\sqrt{163}} = 109.73$

Distribution of the difference:

$\mu = \mu_1 - \mu_2 = 42814 - 37197 = 5617$

The point estimate is 5,617.

$s = \sqrt{s_1^2 + s_2^2} = \sqrt{161.41^2 + 109.73^2} = 195.18$

Confidence interval

The confidence interval is:

$\mu \pm zs$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = zs$

98% confidence level

So $\alpha = 0.02$ , z is the value of Z that has a p-value of $1 - \frac{0.02}{2} = 0.99$ , so $Z = 2.327$ .

Margin of error:

$M = zs = 195.18*2.327 = 454.18386
$

The margin of error of a confidence interval for the difference between the two population means is 454.18386 .

For the confidence interval, as we round to the nearest whole number, we round it 454. So

The lower bound of the interval is:

$\mu - zs = \mu - M = 5617 - 454 = 5163$

The upper bound of the interval is:

$\mu + zs = \mu + M = 5617 + 454 = 6071$

The 98% confidence interval for the difference between the two population means is (5163, 6071).

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