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3 days ago

Each state imposes its own excise tax on gasoline. Suppose, for example, that the state of Massachusetts imposes a state gasolin

e tax of $0.26 per gallon. Suppose further that an average of 1,022,000 gallons of gasoline per day were sold in Massachusetts in 2010.

Mathematics

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Match each pair of points to the equation of the line that is parallel to the line passing through the points.

Svet_ta [12734]

It's known that

When two lines are parallel, their slopes are identical.

The slope between any two points can be calculated using the following formula:

$m=\frac{y2-y1}{x2-x1}$

We will calculate the slope for each case to find the solution to the problem.

Case A) Point $B(5,2)\ C(7,-5)$

Determine the slope of BC

Insert the values into the formula:

$m=\frac{-5-2}{7-5}$

$m=\frac{-7}{2}$

$m=-3.5$

Thus,

The equation $y=-3.5x-15$ is parallel to the line that goes through the points $B(5,2)\ C(7,-5)$

Therefore,

the result for Part A) is

$B(5,2)\ C(7,-5)$ ------> $y=-3.5x-15$

Case B) Point $D(11,6)\ E(5,9)$

Calculate the slope of DE

Plug the values into the formula:

$m=\frac{9-6}{5-11}$

$m=\frac{3}{-6}$

$m=-0.5$

Thus,

The equation $y=-0.5x-3$ is parallel to the line that goes through the points $D(11,6)\ E(5,9)$

Therefore,

the result for Part B) is

$D(11,6)\ E(5,9)$ ------> $y=-0.5x-3$

Case C) Point $F(-7,12)\ G(3,-8)$

Determine the slope of FG

Insert the values into the formula:

$m=\frac{-8-12}{3+7}$

$m=\frac{-20}{10}$

$m=-2$

Thus,

Any linear equation with slope $m=-2$ will be parallel to the line through the points $F(-7,12)\ G(3,-8)$

Case D) Point $H(4,4)\ I(8,9)$

Calculate the slope of HI

Substitute the values in the formula:

$m=\frac{9-4}{8-4}$

$m=\frac{5}{4}$

$m=1.25$

Thus,

The equation $y=1.25x+4$ is parallel to the line through the points $H(4,4)\ I(8,9)$

Therefore,

the result for Part D) is

$H(4,4)\ I(8,9)$ ------> $y=1.25x+4$

Case E) Point $J(7,2)\ K(-9,8)$

Determine the slope of JK

Insert the values into the formula:

$m=\frac{8-2}{-9-7}$

$m=\frac{6}{-16}$

$m=-0.375$

Thus,

Any linear equation characterized by slope $m=-0.375$ will be parallel to the line that runs through the points $J(7,2)\ K(-9,8)$

Case F) Point $L(5,-7)\ M(4,-12)$

Find the slope of LM

Substitute the values in the formula:

$m=\frac{-12+7}{4-5}$

$m=\frac{-5}{-1}$

$m=5$

Thus,

The equation $y=5x+19$ is parallel to the line connecting the points $L(5,-7)\ M(4,-12)$

Therefore,

the result for Part F) is

$L(5,-7)\ M(4,-12)$ ------> $y=5x+19$

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2 months ago

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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

Leona [12618]

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

Additionally, the coefficient of determination is $r^2 = 0.657^2 =0.432$

Step-by-step explanation:

Definitions and data provided

The correlation coefficient is a measure that quantifies the strength of the relationship between two variable movements, denoted as r and ranging between -1 and 1.

The sum of squares refers to the total of the squared deviations, where deviation is defined as the difference between each value and the grand mean.

When performing multiple regression, the aim is to analyze the relationship between multiple independent variables and one dependent variable.

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