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2 years ago

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The Scatter plot below shows the linear trend of the number of golf carts a company sold the month of February and a line of bes

t fit representing this trend.
IT IS A DIFFERENT QUESTION FROM REPAIRING GOLF CARTS PLEASE READ

A. Write a function that models the number of golf carts sold as a function of the number of days in the month of February

B. What is the meaning of the slope as a rate of change for this line of best fit.

1 answer:

Andrei [34K]2 years ago

4 0

Answer:

Part A) $y=-5.625x+90$

Part B) see the explanation

Step-by-step explanation:

Part A) Write a function that models the number of golf carts sold as a function of the number of days in the month of February

Let

x ----> the number of days

y ----> the number of golf carts sold

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem

The y-intercept is the point (0,90)

so

$b=90$

Find the slope m

The formula to calculate the slope between two points is equal to

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

take two points from the graph

(0,90) and (16,0)

substitute the values in the formula

$m=\frac{0-90}{16-0}$

$m=\frac{-90}{16}$

simplify

$m=-\frac{45}{8}$ ---> is negative because is a decreasing function

therefore

The linear equation is equal to

$y=-\frac{45}{8}x+90$

Part B) What is the meaning of the slope as a rate of change for this line of best fit

The slope is $m=-\frac{45}{8}\ golf\ carts\ sold/days$

That means ----> every 8 days 45 less cars are sold

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Find the correlation coefficient of the line of best fit for the points (-3,-40), (1,12), (5,72), (7,137). Explain how you guy y

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Answer:

r = 0.9825; good correlation.

Step-by-step explanation:

One formula for the correlation coefficient is

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

The calculation is not difficult, but it is tedious.

1. Calculate the intermediate numbers

We can display them in a table.

<u> </u><u>x</u> <u> y </u> <u> xy </u> <u> x² </u> <u> y² </u>

-3 -40 120 9 1600

1 12 12 1 144

5 72 360 25 5184

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Σ = 10 181 1451 84 25697

2. Calculate the correlation coefficient

$r = \dfrac{n\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2}-\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{4\times 1451 - 10\times 181}{\sqrt{[4\times 84 - 10^{2}][4\times25697 - 181^{2}]}}\\\\= \dfrac{5804 - 1810}{\sqrt{[336 - 100][102788 - 32761]}}\\\\= \dfrac{3994}{\sqrt{236\times70027}}\\\\= \dfrac{3994}{\sqrt{16526372}}\\\\= \dfrac{3994}{4065}\\\\= \mathbf{0.9825}$

The closer the value of r is to +1 or -1, the better the correlation is. The values of x and y are highly correlated.

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Answer:

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Step-by-step explanation:

A simple linear regression line is used to predict the value of the dependent variable from the independent variable.

The general form is:

$Y=\alpha +\beta X$

Dependent variables are those variables that are under study, i.e. they are being observed for any changes when the other variables in the model are changed.

The dependent variables are also known as response variables.

In this case the dependent variable is the average change in rent for a 1-bedroom apartment.

Independent variables are the variables that are being altered to see a proportionate change in the dependent variable. In a regression model there can be one or more than one independent variables.

The independent variables are also known as the predictor variables.

In this case the independent variable is the average income in a city.

So, for an increase of $5,000 in incomes the average change in rent can be determined by substituting the value of <em>X</em> as 5000 in the regression equation.

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$y = 3\cdot x^{2}-3\cdot x +2$

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Now, this system is now represented by means of a graphing tool and whose outcome is attached below. There are two solutions: (0, 2) and (1, 2)

ii) Let be $y=3\cdot x^{2}-3\cdot x -1$ , if $3\cdot x^{2}-3\cdot x +2 = x+1$ , which is equivalent to the following system of equations:

$y = 3\cdot x^{2}-3\cdot x +2$

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In order to find which table represents $g(x) = -2f(x)$ when $f(x) = x + 4$ , you can follow these steps:

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2. Substitute $x=2$ into the function $g(x)=-2x-8$ :

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3. Substitute $x=3$ into the function $g(x)=-2x-8$ :

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Notice that those ouput values (for $x=1,\ x=2$ and $x=3$ ) matches with the table provided in the third option. That table represents $g(x) = -2f(x)$ when $f(x) = x + 4$ :

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