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3 years ago

richie has a rug in his bedroom with a perimeter of 42 feet. the length of the rug is 12 feet what is the width of the rug

Mathematics

1 answer:

Usimov [2.4K]3 years ago

8 0

The width of the rug is 9 feet.

Step-by-step explanation:

Perimeter of rug = 42 feet

Lengths are same in square and rectangle shapes; therefore;

Length of rug = 12 feet

Width of rug = w

Perimeter = Length + Length + Width + Width

Perimeter = $12+12+w+w$

$42=24+2w\\42-24=2w\\18=2w\\2w=18$

Dividing both sides by 2

$\frac{2w}{2}=\frac{18}{2}\\w=9$

The width of the rug is 9 feet.

Keywords: perimeter, division

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$652.6-2.01\frac{311.7}{\sqrt{50}}=563.997$

$652.6+2.01\frac{311.7}{\sqrt{50}}=741.203$

So on this case the 95% confidence interval would be given by (563.997;741.203)

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".

$\bar X=652.6$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=311.7 represent the sample standard deviation

n=50 represent the sample size

Soltuion to the problem

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:

$df=n-1=50-1=49$

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(0.025,49)".And we see that $t_{\alpha/2}=2.01$

Now we have everything in order to replace into formula (1):

$652.6-2.01\frac{311.7}{\sqrt{50}}=563.997$

$652.6+2.01\frac{311.7}{\sqrt{50}}=741.203$

So on this case the 95% confidence interval would be given by (563.997;741.203)

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