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4 years ago

Which statement defines a function correctly

Mathematics

1 answer:

Brut [27]4 years ago

5 0

Answer:

A function gives for each element of the domain only one element of the range.

Step-by-step explanation:

We have to choose from the statements in the options that define a function correctly.

From my point of view the statement that a function gives for each element of the domain only one element of the range, defines a function properly.

Geometrically it represents that if we draw a vertical line in the graph of the function that intersects the graph at more than one points then this is not a function, this is only a relation. (Answer)

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Gretchen earns extra money mowing lawns on the weekend. She mows 3 lawns per hour and earns $12.00 per lawn. How much does Gretc

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This is the measure of one unit against another unit. An example of this is speed which is the rate of distance covered to time.

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An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by th

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Answer:

a) A sample size of 5615 is needed.

b) 0.012

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

99.5% confidence level

So $\alpha = 0.005$ , z is the value of Z that has a pvalue of $1 - \frac{0.005}{2} = 0.9975$ , so $Z = 2.81$ .

(a) Past studies suggest that this proportion will be about 0.2. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.015.

This is n for which M = 0.015.

We have that $\pi = 0.2$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.015 = 2.81\sqrt{\frac{0.2*0.8}{n}}$

$0.015\sqrt{n} = 2.81\sqrt{0.2*0.8}$

$\sqrt{n} = \frac{2.81\sqrt{0.2*0.8}}{0.015}$

$(\sqrt{n})^{2} = (\frac{2.81\sqrt{0.2*0.8}}{0.015})^{2}$

$n = 5615$

A sample size of 5615 is needed.

(b) Using the sample size above, when the sample is actually contacted, 12% of the sample say they are not satisfied. What is the margin of the error of the confidence interval?

Now $\pi = 0.12, n = 5615$ .

We have to find M.

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$M = 2.81\sqrt{\frac{0.12*0.88}{5615}}$

$M = 0.012$

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