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professor190 [17]

3 years ago

5

Pete is building a fence around a rectangular field. In his design, the length of the field is 62 feet and the width is 25 feet.

The fence includes a gate that measures 9 feet in length.
After Pete builds the fence, he determines that he used 168 feet of fence material, not including the gate. What is the percent error of Pete's design measurements compared to the actual fence material used? Round your answer to the nearest hundredth of a percent.

A. 1.79%
B. 1.82%
C. 3.00%
D. 3.45%

1 answer:

julia-pushkina [17]3 years ago

6 0

Answer:

The percentage error is;

A. 1.79%

Step-by-step explanation:

The given parameters of the rectangular field are;

The length of the field = 62 feet

The width of the field = 25 feet

The width of the gate of the fencing = 9 feet

The actual length of fencing Pete used to fence the field, P₁ = 168 feet

The length of the fencing required in the design, 'P₂' is given as follows;

P₂ = 62 ft. + 62 ft. + 25 ft. + 25 ft. - 9 ft. = 165 ft.

The difference between the actual and design length of fence measurements = P₁ - P₂ = 168 ft. - 165 ft. = 3 ft.

The percentage error in the design measurements compared to the actual fence material used, % Error, is given as follows;

$\% \ Error = \dfrac{\left | Design \ length - Actual \ length \right | }{Actual \ length } \times 100$

Therefore;

$\% \ Error = \dfrac{\left | P_1 - P_2 \right | }{P_2 } \times 100= \dfrac{\left | 165 - 168 \right |}{168} \times 100 = 1.785 \overline {714285} \%$

∴ The percentage error of Pete's design measurements compared to the actual fence material used, % Error ≈ 1.79 %.

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Answer:

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$\sum_{i=1}^n y_i =611$

$\sum_{i=1}^n x^2_i =13970$

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With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=13970-\frac{334^2}{10}=2814.4$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=26584-\frac{334*611}{10}=6176.6$

And the slope would be:

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Nowe we can find the means for x and y like this:

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And we can find the intercept using this:

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So the line would be given by:

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Step-by-step explanation:

The data given on this case is:

x: 14,12,20,16,46,23,48,50,55,50

y: 24,24,28,30,80,30,90,85,120,110

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i = 334$

$\sum_{i=1}^n y_i =611$

$\sum_{i=1}^n x^2_i =13970$

$\sum_{i=1}^n y^2_i =51581$

$\sum_{i=1}^n x_i y_i =26584$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=13970-\frac{334^2}{10}=2814.4$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=26584-\frac{334*611}{10}=6176.6$

And the slope would be:

$m=\frac{6176.6}{2814.4}=2.195$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{334}{10}=33.4$

$\bar y= \frac{\sum y_i}{n}=\frac{611}{10}=61.1$

And we can find the intercept using this:

$b=\bar y -m \bar x=61.1-(2.195*33.4)=-12.213$

So the line would be given by:

$y=2.195 x -12.213$

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