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11 months ago

<2 and _ are vertical angles. <2 and _ or ___ are a linear pair help me pls.

Mathematics

1 answer:

Lena [83]11 months ago

7 0

It should be noted that angle 2 and angle 1 are vertical angles and angle 2 and angle 5 are linear pair.

<h3>How to illustrate the information?</h3>

When two lines cross at a point, vertical angles are created. They are always on an equal footing. In other words, four angles are created anytime two lines cross or intersect. It is evident that two opposed angles are equal and are referred to as vertical angles.

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as additional angles.

Therefore, it should be noted that angle 2 and angle 1 are vertical angles and angle 2 and angle 5 are linear pair.

Learn more about vertical angle on:

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Answer:

a) $y=0.00991 x +1.042$

b) $r^2 = 0.7503^2 = 0.563$

c) $r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503$

Step-by-step explanation:

Data given

x: 500, 700, 750, 590 , 540, 650, 480

y: 7.00, 7.50 , 9.00, 6.5, 7.50 , 7.0, 4.50

Part a

We want to create a linear model like this :

$y = mx +b$

Wehre

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

And:

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

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

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=2595100-\frac{4210^2}{7}=63085.714$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=30095-\frac{4210*49}{7}=625$

And the slope would be:

$m=\frac{625}{63085.714}=0.00991$

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

$\bar x= \frac{\sum x_i}{n}=\frac{4210}{7}=601.429$

$\bar y= \frac{\sum y_i}{n}=\frac{49}{7}=7$

And we can find the intercept using this:

$b=\bar y -m \bar x=7-(0.00991*601.429)=1.042$

And the line would be:

$y=0.00991 x +1.042$

Part b

The correlation coefficient is given by:

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

For our case we have this:

n=7 $\sum x = 4210, \sum y = 49, \sum xy = 30095, \sum x^2 =2595100, \sum y^2 =354$

$r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503$

The determination coefficient is given by:

$r^2 = 0.7503^2 = 0.563$

Part c

$r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503$

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Step-by-step explanation:

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<2 and ___ are vertical angles. <2 and ___ or ___ are a linear pair help me pls.

<2 and _ are vertical angles. <2 and _ or ___ are a linear pair help me pls.