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2 years ago

7

Mathematics

1 answer:

Vinvika [58]2 years ago

5 0

Answer:

126 square units

Step-by-step explanation:

Area of section 1 is 8 square units which is triangle and,

Area of triangle is = $\frac{1}{2}\times b\times h$

b= 2 units and height =8 units

So,

Area of section 1 = $\frac{1}{2}\times 2\times 8=8 \quad\text{ square units}$

Same Area is of section 2 which is also a triangle and has same base and height.

So,

Area of Section 2 = $\frac{1}{2}\times 2\times 8=8 \quad\text{ square units}$

Now the Area of section 3 which is square with side of 10 units

So,

Area of section 3 = $a^{2} =10\times10=100\quad \text{square units}$

Total Area of Trapezoid = $8+8+100=126 \quad \text{square units}$

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Answer:

a) Figure attached

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c) The correlation coefficient would be r =0.47719

d) $y=1.31 x +98.57=1.31*21 + 98.57 =126.08$

Step-by-step explanation:

(a) Draw a scatter diagram for the data.

See the figure attached

(b) Find x, y, b, and the equation of the least-squares line. (Round your answers to three decimal places.) x =__ y =__ b =__ y =__ + __x

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

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$m=\frac{193.143}{147.429}=1.31$

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

$\bar x= \frac{\sum x_i}{n}=\frac{300}{14}=21.429$

$\bar y= \frac{\sum y_i}{n}=\frac{1773}{14}=126.643$

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$b=\bar y -m \bar x=126.643-(1.31*21.429)=98.571$

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$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

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The % of variation is given by the determination coefficient given by $r^2$ and on this case $0.47719^2 =0.2277$ , so then the % of variation explaines is 22.8%.

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