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2 years ago

What is the measure of ∠EGF? What is the measure of ∠CGF?

Mathematics

2 answers:

andrey2020 [161]2 years ago

4 0

measure of ∠EGF = 1/2( 180 - 50)
= 1/2(130)
= 65

the measure of ∠CGF = 180 - 65
= 115

Leni [432]2 years ago

3 0

Hello!

This is an isosceles triangle, which means its base angles are congruent. Interior angles of triangle add to equal 180 degrees, so you can make an equation to solve for the measure of the base angles. I'll call the base angles x.

180 = 50 + 2x
130 = 2x
65 = x

That gives you m∠EGF and m∠FGE (65°).

To find m∠CGF, you must know that it and ∠EGF are supplementary (they add to equal 180 degrees). Make another equation setting them to equal 180 using m∠EGF (65°):

180 = 65 + x
115 = x

Answer:
m∠EGF = 65°
m∠CGF = 115°

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At a recent county fair, you observed that at one stand people's weight was forecasted, and were surprised by the accuracy (with

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Answer:

a)Slope: $\hat \beta_1 =\frac{7625.9}{1248.9}=6.106$

Intercept: $\hat \beta_o = 157.955 -6.106 (69.686)=-267.548$

b) $r=\frac{7625.9}{\sqrt{[1248.9][94228.8]}}=0.657$

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Step-by-step explanation:

Data given and definitions

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

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n=110, $\sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9 , sum y^2_i=\sum(y-\bar y)^2 =94228.8$

$\sum Y_i =17375 , \sum X_i = 7665.5$

Part a

The slope is given by this formula:

$\hat \beta_1 =\frac{\sum (x-\bar x) (y-\bar y)}{\sum (x-\bar x )^2}$

If we replace we got:

$\hat \beta_1 =\frac{7625.9}{1248.9}=6.106$

We can find the intercept with the following formula

$\hat \beta_o = \bar y -\hat \beta_1 \bar x$

We can find the average for x and y like this:

$\bar X=7665.5/110 =69.686, \bar y= 17375/110=157.955$

And replacing we got:

$\hat \beta_o = 157.955 -6.106 (69.686)=-267.548$

Part b

In order to calculate the correlation coefficient we can use this formula:

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

For our case we have this:

n=110, $\sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9 , sum y^2_i=\sum(y-\bar y)^2 =94228.8$

So we can find the correlation coefficient replacing like this:

$r=\frac{7625.9}{\sqrt{[1248.9][94228.8]}}=0.657$

And the determination coeffecient is $r^2 = 0.657^2 =0.432$

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