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3 years ago

Please answer it correctly and please show work please help me I need it

Mathematics

1 answer:

tamaranim1 [39]3 years ago

4 0

Answer:

the equation is

y = 0.75x

And, the constant of proportionality is 0.75

Step-by-step explanation:

The computation is shown below:

Given that

4y = 3x

And,

12y = 9x

Here the equation that represent proportional relationship is

4y = 3x

Divide both sides by 4

y = 3x ÷ 4

Now

12y = 9x

divides both sides by 12

y = 9 ÷ 12x

y = 3 ÷ 4x

y = 0.75x

so the equation is

y = 0.75x

And, the constant of proportionality is 0.75

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Darren wants to estimate the mean age in a population of trees. He'll sample nnn trees and build a 90\%90%90, percent confidence

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Using the z-distribution, as we have the standard deviation for the population, it is found that the smallest sample size required to obtain the desired margin of error is of 77.

<h3>What is a z-distribution confidence interval?</h3>

The confidence interval is:

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In which:

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n is the sample size.

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The margin of error is given by:

$M = z\frac{\sigma}{\sqrt{n}}$

In this problem, we have that the parameters are given as follows:

$M = 3, z = 1.645, \sigma = 16$ .

Hence, solving for n, we find the sample size.

$M = z\frac{\sigma}{\sqrt{n}}$

$3 = 1.645\frac{16}{\sqrt{n}}$

$3\sqrt{n} = 1.645 \times 16$

$\sqrt{n} = \frac{1.645 \times 16}{3}$

$(\sqrt{n})^2 = \left(\frac{1.645 \times 16}{3}\right)^2$

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Rounding up, the smallest sample size required to obtain the desired margin of error is of 77.

More can be learned about the z-distribution at brainly.com/question/25890103

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