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3 years ago

The total fencing around a square field is 80 yards. The field has an area of how many square yards?

2 answers:

7 0

The side length of the square is 1/4 of its perimeter, so is 20 yards. The area of the square is the square of its side length, so is (20 yd)² = 400 yd².

Karolina [17]3 years ago

4 0

ANSWER

The field has an area of
$400 \: square \: yards$

EXPLANATION

The total fencing around a square field gives the total distance around the square field.

The total fencing around the field being
$80$
yards means, the perimeter is 80 yards.

Recall that the perimeter of a square is given by the formula,

$perimeter = 4l$

This implies that,

$80 = 4l$

We divide both sides by 4 to get,

$\frac{80}{4} = l$

This implies that
$l = 20 \: units$

We now obtain the area of the square by using the formula,

$A rea= {l}^{2}$
$A rea= {(20)}^{2} = 400 \: \: square \: \: yards$

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Suppose a baker claims that the average bread height is more than 15cm. Several of this customers do not believe him. To persuad

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Answer:

$17-2.262\frac{1.9}{\sqrt{10}}=15.641$

$17+2.262\frac{1.9}{\sqrt{10}}=18.359$

So on this case the 95% confidence interval would be given by (15.641;18.359)

And since the lower limit for the confidence interval is higher than 15 we can conclude that at 5% of significance the true mean is higher than 15 cm

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

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".

$\bar X=17$ represent the sample mean

$\mu$ population mean (variable of interest)

s=1.9 represent the sample standard deviation

n=10 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=10-1=9$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,9)".And we see that $t_{\alpha/2}=2.262$