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x y
900 70
988 80
1000 82
1010 84
1200 105
1205 108

y = 0. 121 x 38.841 , r = 0.998

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Extensions

Graph f ( x ) = 0.5 x + 10 . Pick a set of 5 ordered pairs using inputs x = −2 ,  1 ,  5 ,  6 ,  9 and use linear regression to verify that the function is a good fit for the data.

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Graph f ( x ) = 2 x 10 . Pick a set of 5 ordered pairs using inputs x = −2 ,  1 ,  5 ,  6 ,  9 and use linear regression to verify the function.

( −2 , −6 ) , ( 1 , −12 ) , ( 5 , −2 0 ) , ( 6 , −22 ) , ( 9 , −28 ) ; y = −2 x −10

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For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year span. The following ordered pairs shows dollars and the number of units sold in hundreds and the profit in thousands of over the ten-year span, (number of units sold, profit) for specific recorded years:

( 46 ,  1 , 6 00 ) ,   ( 48 ,  1 , 55 0 ) ,   ( 5 0 ,  1 , 5 0 5 ) ,   ( 52 ,  1 , 54 0 ) ,   ( 54 ,  1 , 495 ) .

Use linear regression to determine a function P where the profit in thousands of dollars depends on the number of units sold in hundreds.

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Find to the nearest tenth and interpret the x -intercept.

( 189 . 8 , 0 )   If 18,980 units are sold, the company will have a profit of zero dollars.

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Find to the nearest tenth and interpret the y -intercept.

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Real-world applications

For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span. The following ordered pairs shows the population and the year over the ten-year span, (population, year) for specific recorded years:

(2500, 2000), (2650, 2001), (3000, 2003), (3500, 2006), (4200, 2010)

Use linear regression to determine a function y , where the year depends on the population. Round to three decimal places of accuracy.

y = 0.00587 x + 1985 .4 1

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Predict when the population will hit 8,000.

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For the following exercises, consider this scenario: The profit of a company increased steadily over a ten-year span. The following ordered pairs show the number of units sold in hundreds and the profit in thousands of over the ten year span, (number of units sold, profit) for specific recorded years:

( 46 ,  25 0 ) ,   ( 48 ,  3 0 5 ) ,   ( 5 0 ,  35 0 ) ,   ( 52 ,  39 0 ) ,   ( 54 ,  41 0 ) .

Use linear regression to determine a function y , where the profit in thousands of dollars depends on the number of units sold in hundreds .

y = 2 0. 25 x 671 . 5

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Predict when the profit will exceed one million dollars.

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For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year span. The following ordered pairs show dollars and the number of units sold in hundreds and the profit in thousands of over the ten-year span (number of units sold, profit) for specific recorded years:

(46, 250), (48, 225), (50, 205), (52, 180), (54, 165) .

Use linear regression to determine a function y , where the profit in thousands of dollars depends on the number of units sold in hundreds .

y = 1 0. 75 x + 742 . 5 0

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Predict when the profit will dip below the $25,000 threshold.

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Chapter review exercises

Linear Functions

Determine whether the algebraic equation is linear. 2 x + 3 y = 7

Yes

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Determine whether the algebraic equation is linear. 6 x 2 y = 5

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Determine whether the function is increasing or decreasing.

f ( x ) = 7 x 2

Increasing.

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Questions & Answers

Discuss the differences between taste and flavor, including how other sensory inputs contribute to our  perception of flavor.
John Reply
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
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omeprazole
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Nency Reply
Not really sure
Eli
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
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Oyindarmola Reply
Anatomy is the identification and description of the structures of living things
Kamara
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Oyerinde Reply
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Mohammed Reply
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
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Prince
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it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
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function of digestive
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the diagram of the lungs
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37 degrees selcius
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37°c
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36.5
Simon
37°c
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the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
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Wulku
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anaemia is the decrease in RBC count hemoglobin count and PVC count
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acid
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Organ Systems Of The Human Body (Continued) Organ Systems Of The Human Body (Continued)
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Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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