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koban [17]
2 years ago
7

The triangular-shaped bases of a prism are 24 cm in length and have a height of 35 cm. Each side is 37 cm. The height of the pri

sm is 29 cm. What is the surface area of the triangular prism?
A) 2192 cm2
B) 2312 cm2
C) 3220 cm2
D) 3682 cm2
Mathematics
1 answer:
Savatey [412]2 years ago
3 0

Answer:

The surface area of Triangular base Prism = 3682 cm²

Step-by-step explanation:

Given in question as :

For a Triangular base prism ,

The base of  prism (b) = 24 cm

The height of prism (l) = 29 cm

Each side length (s) = 37 cm

The height of base triangle ( h ) = 35 cm

Hence , we know that The surface area of Triangular base prism is

 = (b×h) + (2×l×s) + (l×b)

 = (24×35) + (2×29×37) + (29×24)

 = (840) + (2146) + (696)

 = 3682  cm²

Hence The surface area of Triangular base Prism is 3682 cm²  Answer

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Answer:

a) y=-0.317 x +46.02

b) Figure attached

c) S^2=\hat \sigma^2=MSE=\frac{190.33}{10}=19.03

Step-by-step explanation:

We assume that th data is this one:

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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 = 30+30+30+50+50+50+70+70+70+90+90+90=720

\sum_{i=1}^n y_i =38+43+29+32+26+33+19+27+23+14+19+21=324

\sum_{i=1}^n x^2_i =30^2+30^2+30^2+50^2+50^2+50^2+70^2+70^2+70^2+90^2+90^2+90^2=49200

\sum_{i=1}^n y^2_i =38^2+43^2+29^2+32^2+26^2+33^2+19^2+27^2+23^2+14^2+19^2+21^2=9540

\sum_{i=1}^n x_i y_i =30*38+30*43+30*29+50*32+50*26+50*33+70*19+70*27+70*23+90*14+90*19+90*21=17540

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}=49200-\frac{720^2}{12}=6000

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=17540-\frac{720*324}{12}{12}=-1900

And the slope would be:

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

\bar x= \frac{\sum x_i}{n}=\frac{720}{12}=60

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In oder to calculate S^2 we need to calculate the MSE, or the mean square error. And is given by this formula:

MSE=\frac{SSE}{df_{E}}

The degred of freedom for the error are given by:

df_{E}=n-2=12-2=10

We can calculate:

S_{y}=\sum_{i=1}^n y^2_i -\frac{(\sum_{i=1}^n y_i)^2}{n}=9540-\frac{324^2}{12}=792

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SSR=\frac{S^2_{xy}}{S_{xx}}=\frac{(-1900)^2}{6000}=601.67

We have that SST= SSR+SSE, and then SSE=SST-SSR= 792-601.67=190.33[/tex]

So then :

S^2=\hat \sigma^2=MSE=\frac{190.33}{10}=19.03

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