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3 months ago

The table shows ordered pairs of the function y = 16 + 0.5x .

Mathematics

1 answer:

Leona [12.6K]3 months ago

4 0

Answer: The unknown values x and y correspond to 8 and 20, specifically;

(x, y) = (8, 20)

Step-by-step explanation: The equation y = 16 + 0.5x represents a linear relationship that can be illustrated with a graph. This indicates that values for x and y can be located at various points on the line.

The ordered pairs signify that for each x value, there exists a matching y value.

The values listed in a two-column format for x and y all fulfill the equation y = 16 + 0.5x. Observing the first example, the pair (-4, 14) is presented.

This reveals that when x is -4, y will be 14.

Where y = 16 + 0.5x

y = 16 + 0.5(-4)

y = 16 - 2

y = 14

Thus, the first pair, similar to the other pairs, satisfies the equation.

Consequently, by reviewing the options provided, we can deduce which one fulfills the equation.

(option 1) If x = 0

y = 16 + 0.5(0)

y = 16 + 0

y = 16

(0, 16)

(option 2) If x = 5

y = 16 + 0.5(5)

y = 16 + 2.5

y = 18.5

(5, 18.5)

(option 3) If x = 8

y = 16 + 0.5(8)

y = 16 + 4

y = 20

(8, 20)

Our calculations confirm that the third option (8, 20) is the correct ordered pair for x and y.

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Let's explore this step-by-step:

Greetings!

Here are the variables

X: daily cost of hotel rooms

Y: expenses for entertainment

Refer to the second attachment for the scatter plot.

The population regression equation can be expressed as E(Yi)= α + βXi

To find the y-intercept and the slope of the regression line, apply the following formulas:

a= Y[bar]-bX[bar] $b= \frac{sum XY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} }$

In this scenario, n= 9; ∑X= 945; ∑X²= 103325; ∑Y= 1134; ∑Y²= 148804; ∑XY= 123307

Calculating X[bar]= ∑X/n= 945/9= 105

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Thus, it follows that a= 126 - 1.03*105= 17.49 $b= \frac{123307-\frac{945*1134}{9} }{103325-\frac{(945)^2}{9} }= 1.03$

The regression equation is then given by ^Y= 17.49 + 1.03Xi

Slope interpretation: For each unit increase in the daily hotel rate, the expected average spending on entertainment rises by $1.03.

Given that the room rate in Chicago is $128 (X), we can predict the entertainment expenditure (Y) using the estimated regression line:

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I trust this will assist you!

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