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( 3,6 00 , 2000 ) ; ( 4, 000 , 2001 ) ; ( 4,7 00 , 2003 ) ; ( 6, 000 , 2006 )

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

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Predict when the population will hit 12,000.

2027

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What is the correlation coefficient for this model to three decimal places of accuracy?

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According to the model, what is the population in 2014?

7,660

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Chapter practice test

Determine whether the following algebraic equation can be written as a linear function. 2 x + 3 y = 7

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Determine whether the following function is increasing or decreasing. f ( x ) = 2 x + 5

Decreasing

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Determine whether the following function is increasing or decreasing. f ( x ) = 7 x + 9

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Find a linear equation that passes through (5, 1) and (3, –9), if possible.

y = 5 x 24

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Find a linear equation, that has an x intercept at (–4, 0) and a y -intercept at (0, –6), if possible.

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Find the slope of the line in [link] .

This image is a graph of a decreasing linear function on an x, y coordinate plane. The x and y-axis range from -6 to 6. The line passes through the points (0,2) and (1,0).

m = 2

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Write an equation for line in [link] .

This image is a graph showing a decreasing linear function on an x, y coordinate plane. The x and y axis range from -6 to 6. The line passes through the points (0,-1) and (-.5,0).
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Does [link] represent a linear function? If so, find a linear equation that models the data.

x –6 0 2 4
g ( x ) 14 32 38 44

Yes, y = 3 x + 32

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Does [link] represent a linear function? If so, find a linear equation that models the data.

x 1 3 7 11
g ( x ) 4 9 19 12
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At 6 am, an online company has sold 120 items that day. If the company sells an average of 30 items per hour for the remainder of the day, write an expression to represent the number of items that were sold n after 6 am.

y = 30 x + 120

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For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular.

y = 3 4 x 9 4 x 3 y = 8

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2 x + y = 3 3 x + 3 2 y = 5

Neither

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Find the x - and y -intercepts of the equation 2 x + 7 y = 14.

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Given below are descriptions of two lines. Find the slopes of Line 1 and Line 2. Is the pair of lines parallel, perpendicular, or neither?

Line 1: Passes through ( −2 , −6 ) and ( 3 , 14 )

Line 2: Passes through ( 2 , 6 ) and ( 4 , 14 )

Line 1: m = 4 ; Line 2: m = 4 ; parallel

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Write an equation for a line perpendicular to f ( x ) = 4 x + 3 and passing through the point ( 8 , 10 ) .

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Sketch a line with a y -intercept of ( 0 , 5 ) and slope 5 2 .


This image is a graph showing a decreasing linear function on an x, y coordinate plane. The x and y-axis range from -6 to 6. The line passes through the points (0,5) and (2,0) and a slope of: -5/2.

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Graph of the linear function f ( x ) = x + 6.

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For the two linear functions, find the point of intersection: x = y + 2 2 x 3 y = 1 .

( 7 , 5 )

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A car rental company offers two plans for renting a car.

Plan A: $25 per day and $0.10 per mile

Plan B: $40 per day with free unlimited mileage

How many miles would you need to drive for plan B to save you money?

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Find the area of a triangle bounded by the y axis, the line f ( x ) = 12 4 x , and the line perpendicular to f that passes through the origin.

16.94 square units

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A town’s population increases at a constant rate. In 2010 the population was 65,000. By 2012 the population had increased to 90,000. Assuming this trend continues, predict the population in 2018.

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The number of people afflicted with the common cold in the winter months dropped steadily by 25 each year since 2002 until 2012. In 2002, 8,040 people were inflicted. Find the linear function that models the number of people afflicted with the common cold C as a function of the year, t . When will less than 6,000 people be afflicted?

2083

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For the following exercises, use the graph in [link] , showing the profit, y , in thousands of dollars, of a company in a given year, x , where x represents years since 1980.

This image is a graph showing the company's profit from 1985 at around $15,000 to 2010 at about $32,500.  The x-axis goes from 0 to 30 in intervals of 5 and the y-axis goes from 0 to 35,000 in intervals of 5,000.

Find the linear function y , where y depends on x , the number of years since 1980.

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Find and interpret the y -intercept.

( 0 , 10 , 625 ) ; In 1980, the profit was $10,625,000.

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In 2004, a school population was 1250. By 2012 the population had dropped to 875. Assume the population is changing linearly.

  1. How much did the population drop between the year 2004 and 2012?
  2. What is the average population decline per year?
  3. Find an equation for the population, P , of the school t years after 2004.
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Draw a scatter plot for the data provided in [link] . Then determine whether the data appears to be linearly related.

0 2 4 6 8 10
–450 –200 10 265 500 755


Scatterplot with a collection of points: (0,-450); (2,-200); (4,10); (6,265); (8,500) and (10,755). The data appears linear.

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Draw a best-fit line for the plotted data.

Scatterplot with domain from 2 to 10 and range from 20 from 33.  The points plotted are (2,20); (4,23); (6,26); (8,26); and (10,32).
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For the following exercises, use [link] , which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year.

Year 2000 2002 2005 2007 2010
Percent Graduates 8.5 8.0 7.2 6.7 6.4

Determine whether the trend appears linear. If so, and assuming the trend continues, find a linear regression model to predict the percent of unemployed in a given year to three decimal places.


Scatterplot with a collection of points: (2000,8.5); (2002,8); (2005,7.2); (2007,6.7); and (2010,6.4). The data appears linear

y = 0.219 x + 445.990

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In what year will the percentage drop below 4%?

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Based on the set of data given in [link] , calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracy.

x 16 18 20 24 26
y 106 110 115 120 125

y = 1.820 x + 77.349 , r = 0.986

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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 (in hundreds) and the year over the ten-year span, (population, year) for specific recorded years:

( 4 , 500 , 2000 ) ; ( 4 , 700 , 2001 ) ; ( 5 , 200 , 2003 ) ; ( 5 , 800 , 2006 )

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

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Predict when the population will hit 20,000.

2070

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What is the correlation coefficient for this model?

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Questions & Answers

can you solve it step b step
Ching Reply
what is linear equation with one unknown 2x+5=3
Joan Reply
-4
Joel
x=-4
Joel
x=-1
Joan
I was wrong. I didn't move all constants to the right of the equation.
Joel
x=-1
Cristian
Adityasuman x= - 1
Aditya
what is the VA Ha D R X int Y int of f(x) =x²+4x+4/x+2 f(x) =x³-1/x-1
Shadow Reply
can I get help with this?
Wayne
Are they two separate problems or are the two functions a system?
Wilson
Also, is the first x squared in "x+4x+4"
Wilson
x^2+4x+4?
Wilson
thank you
Wilson
Please see ***imgur.com/a/lpTpDZk for solutions
Wilson
f(x)=x square-root 2 +2x+1 how to solve this value
Marjun Reply
factor or use quadratic formula
Wilson
what is algebra
Ige Reply
The product of two is 32. Find a function that represents the sum of their squares.
Paul
if theta =30degree so COS2 theta = 1- 10 square theta upon 1 + tan squared theta
Martin Reply
how to compute this 1. g(1-x) 2. f(x-2) 3. g (-x-/5) 4. f (x)- g (x)
Yanah Reply
hi
John
hi
Grace
what sup friend
John
not much For functions, there are two conditions for a function to be the inverse function:   1--- g(f(x)) = x for all x in the domain of f     2---f(g(x)) = x for all x in the domain of g Notice in both cases you will get back to the  element that you started with, namely, x.
Grace
sin theta=3/4.prove that sec square theta barabar 1 + tan square theta by cosec square theta minus cos square theta
Umesh Reply
acha se dhek ke bata sin theta ke value
Ajay
sin theta ke ja gha sin square theta hoga
Ajay
I want to know trigonometry but I can't understand it anyone who can help
Siyabonga Reply
Yh
Idowu
which part of trig?
Nyemba
functions
Siyabonga
trigonometry
Ganapathi
differentiation doubhts
Ganapathi
hi
Ganapathi
hello
Brittany
Prove that 4sin50-3tan 50=1
Sudip Reply
False statement so you cannot prove it
Wilson
f(x)= 1 x    f(x)=1x  is shifted down 4 units and to the right 3 units.
Sebit Reply
f (x) = −3x + 5 and g (x) = x − 5 /−3
Sebit
what are real numbers
Marty Reply
I want to know partial fraction Decomposition.
Adama Reply
classes of function in mathematics
Yazidu Reply
divide y2_8y2+5y2/y2
Sumanth Reply
Practice Key Terms 5

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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