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alexandr1967 [171]
2 years ago
10

The equation to convert from degrees Celsius to degrees Fahrenheit is F=1.8C+32, whereas a simpler estimate for this conversion

is F=2C+30. By solving each of these equations for C, we can convert from degrees Fahrenheit to degrees Celsius.
Mathematics
1 answer:
anygoal [31]2 years ago
7 0

Answer:

The answer to your question is  Equation 1  C = (F -32)/1.8

                                                      Equation 2   C = (F - 30)/2

Step-by-step explanation:

Data

Equation 1   F = 1.8C + 32

Equation 2  F = 2C + 30

Solve both equations for C

Equation 1

- Substract 32 in both sides

                  F - 32 = 1.8C + 32 - 32

- Simplify

                  F - 32 = 1.8C

- Divide both sides by 1.8

                  C = (F -32)/1.8

Equation 2

                   F = 2C + 30

- Substract 30 in both sides

                  F - 30 = 2C + 30 - 30

- Simplify

                  F - 30 = 2C

- Divide both sides by 2

                  C = (F - 30)/2

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An automobile dealer wants to see if there is a relationship between monthly sales and the interest rate. A random sample of 4 m
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Answer:

a) y=-6.254 x +75.064  

b) r =-0.932

The % of variation is given by the determination coefficient given by r^2 and on this case -0.932^2 =0.8687, so then the % of variation explained by the linear model is 86.87%.

Step-by-step explanation:

Assuming the following dataset:

Monthly Sales (Y)     Interest Rate (X)

       22                               9.2

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Part a

And we want a linear model on this way y=mx+b, where m represent the slope and b the intercept. In order to find the slope we have this 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}  

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}=278.65-\frac{32.5^2}{4}=14.5875  

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=696.9-\frac{32.5*97}{4}=-91.225  

And the slope would be:  

m=\frac{-91.225}{14.5875}=-6.254  

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

\bar x= \frac{\sum x_i}{n}=\frac{32.5}{4}=8.125  

\bar y= \frac{\sum y_i}{n}=\frac{97}{4}=24.25  

And we can find the intercept using this:  

b=\bar y -m \bar x=24.25-(-6.254*8.125)=75.064  

So the line would be given by:  

y=-6.254 x +75.064  

Part b

For this case we need to calculate the correlation coefficient 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]}}  

r=\frac{4(696.9)-(32.5)(97)}{\sqrt{[4(278.65) -(32.5)^2][4(3009) -(97)^2]}}=-0.937  

So then the correlation coefficient would be r =-0.932

The % of variation is given by the determination coefficient given by r^2 and on this case -0.932^2 =0.8687, so then the % of variation explained by the linear model is 86.87%.

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