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4 years ago

What is the area of a trapezoid that has the bases of 1 1/4ft and 14 inches and a height of 3 inches.

Mathematics

1 answer:

Rom4ik [11]4 years ago

5 0

The area of the trapezoid is 43.5 inches²

Step-by-step explanation:

The formula of the area of a trapezoid is $A=\frac{1}{2}(b_{1}+b_{2})h$ , where:

$b_{1}$ and $b_{2}$ are the two parallel bases
h is its height

∵ $b_{1}$ = $1\frac{1}{4}$ feet

∵ $b_{2}$ = 14 inches

∵ h = 3 inches

- Change the length of $b_{1}$ from feet to inches

∵ 1 foot = 12 inches

∴ $1\frac{1}{4}$ feet = $1\frac{1}{4}$ × 12 = 15 inches

∴ $b_{1}$ = 15 inches

Substitute the values of $b_{1}$ , $b_{2}$ and h in the

formula of the area

∴ $A=\frac{1}{2}(15+14)(3)$

∴ A = 43.5 inches²

The area of the trapezoid is 43.5 inches²

Learn more:

You can learn more about the area of figures in brainly.com/question/12919591

#LearnwithBrainly

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$182.167-2.03\frac{114.05}{\sqrt{36}}=143.580$

$182.167+2.03\frac{114.05}{\sqrt{36}}=220.754$

So on this case the 95% confidence interval would be given by (143.580;220.754)

Step-by-step explanation:

Assuming the following dataset:

77, 349,417,349, 167 , 225, 265, 360,205

145,335,40,139, 177,108, 163, 202, 22

123,439, 125,135, 86,43, 217,49, 156

119,178, 151, 61, 350, 312, 91, 89,89

We can calculate the sample mean with the followinf formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}= 182.167$

And the sample deviation with:

$s = \sqrt{\frac{\sum_{i=1}^n (X_i-\bar X)^2}{n-1}}=114.05$

The sample size on this case is n =36.

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".

$\bar X=182.167$ represent the sample mean

$\mu$ population mean (variable of interest)

s=114.05 represent the sample standard deviation

n=36 represent the sample size

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

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

The point estimate of the population mean is $\hat \mu = \bar X =182.167$

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

$df=n-1=36-1=35$

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(0.025,35)".And we see that $t_{\alpha/2}=2.03$

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

$182.167-2.03\frac{114.05}{\sqrt{36}}=143.580$

$182.167+2.03\frac{114.05}{\sqrt{36}}=220.754$

So on this case the 95% confidence interval would be given by (143.580;220.754)

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