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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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
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John Reply
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Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
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emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
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Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
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Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
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hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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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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