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Amiraneli [1.4K]
2 years ago
13

In the trapezoid at the right, BE= 2x-8, DE= x-4, and AC= x+2

Mathematics
1 answer:
Marta_Voda [28]2 years ago
5 0

Answer:

A.  x = 5 (Equation below)

B. AC = 9 | BD = 9

Step-by-step explanation:

A. Since we know the diagonals of an isosceles trapezoid are congruent, we know that the two bottom parts of the diagonal BD (2x - 8 and x - 4) are congruent to the diagonal AC (x + 2) . This means you can just equal them together and get the value of x:

2x - 8 + x - 4 = x + 2

3x - 12 = x + 2

3x = x + 14

2x = 14

x = 7

B. Just plug in 5 for x:

AC = x + 2 = 7 + 2 = 9

BD = 2x - 8 + x -4 = 3x - 12 = 21 - 12 = 9

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It takes 40 cents worth of meat to make sandwiches. What is the cost of the meat for 20 sandwiches?
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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  

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

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.  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"    

When we conduct a multiple regression we want to know about the relationship between several independent or predictor variables and a dependent or criterion variable.  

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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