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garri49 [273]
3 years ago
9

If a gardener fences in the total rectangular area shown in the illustration instead of just the square area, he will need twice

as much fencing to enclose the garden. How much fencing will he need?

Mathematics
1 answer:
Norma-Jean [14]3 years ago
5 0

Answer:

He needs 5x+56 ft

Step-by-step explanation:

To find how much of fencing he needs , we find the perimeter of the given figure

All sides are equal in a square

To find perimeter of the square we add all the sides

4 sides we have for the square

one side is x, so perimeter of square = x+x+x+x= 4x

Now we find perimeter of rectangle

Opposite sides of rectangle are equal

Here for rectangle we consider only three sides

because fourth side is common for rectangle and square

So perimeter of the rectangle (with 3 sides) = 28 +x+ 28 = 56+x

Total fencing = perimeter of square + perimeter of rectangle

4x + 56 + x= 5x+56


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Hence, \$9000 \cdot (100\% - 90\%)

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Answer:

The new sample size required in order to have the same confidence 95% and reduce the margin of erro to $60 is:

n=28

Step-by-step explanation:

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Assuming the X follows a normal distribution  

X \sim N(\mu, \sigma=160)  

And the distribution for \bar X is:

\bar X \sim N(\mu, \frac{160}{\sqrt{n}})  

We know that the margin of error for a confidence interval is given by:  

Me=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)  

The next step would be find the value of \z_{\alpha/2}, \alpha=1-0.95=0.05 and \alpha/2=0.025  

Using the normal standard table, excel or a calculator we see that:  

z_{\alpha/2}=\pm 1.96  

If we solve for n from formula (1) we got:  

\sqrt{n}=\frac{z_{\alpha/2} \sigma}{Me}  

n=(\frac{z_{\alpha/2} \sigma}{Me})^2  

And we have everything to replace into the formula:  

n=(\frac{1.96(160)}{78.4})^2 =16  

And this value agrees with the sample size given.

For the case of the problem we ar einterested on Me= $60, and we need to find the new sample size required to mantain the confidence level at 95%. We know that n is given by this formula:

n=(\frac{z_{\alpha/2} \sigma}{Me})^2  

And now we can replace the new value of Me and see what we got, like this:

n=(\frac{1.96*160}{60})^2 =27.32

And if we round up the answer we see that the value of n to ensure the margin of error required Me=\pm 60 $ is n=28.    

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3 years ago
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