Name: Period - Hazleton Area School District / Overvie · 5.7 Scatter Plots and trend Lines ... 12-3 Practice Form G ... 23. 12.1, 13.6, 10, 9.7, 13.2, 14; divide by 0.5 24. 3.2,

1

ALGEBRA 1 KEYSTONE

STUDENT WORKBOOK 4

TOPIC 8-10

STUDY ISLAND TOPICS

Name: _______________________________ Period ____

TOPIC 8 Data Analysis PURLE GREEN RED QUIZ

12.3 Measures of Central Tendency and Dispersion

12.2 Frequency and Histograms

12.4 Box and Whisker Plot

12.5 Samples and Surveys

5.7 Scatter Plots and trend Lines

12.7 Theoretical and Experimental Probability

12.8 Prob of Compound Events

TOPIC 9 Inequalities PURLE GREEN RED QUIZ

3.1 Inequalities and Their Graphs

3.2 Solve Inequalities Add and Sub

3.3 Solve Inequalities Mult and Div

3.4 Solving Multi Step Inequalities

3.5 Working with Sets

3.6 Compound Inequalities

3.7 Absolute Value EQ and Inequalities

3.8 Unions and Intersections

TOPIC 10 Linear Inequalities PURLE GREEN RED QUIZ

6.5 Linear Inequalities

6.6 Systems of Linear Inequalities

PA CORE 8: SCATTER PLOTS BEST FIT LINEAR MODELS TWO WAY TABLES KEYSTONE: LINEAR INEQUALITIES SYSTEMS OF LINEAR INEQUALITIES

Find the mean, median, and mode of each data set. Explain which measure of

central tendency best describes the data.

1. touchdowns scored:

1 3 4 4 3

3. average speed (mi/hr):

36 59 47 56 67

5. daily high temperature (˚F):

74 69 78 80 92

2. distance from school (mi):

0.5 3.9 4.1 5 3

4. price per pound:

$30 $8 $2 $5 $6

6. number of volunteers:

24 22 35 19 35

Find the value of x such that the data set has the given mean.

7. 11, 12, 5, 3, x; mean 7.4 8. 55, 60, 35, 90, x; mean 51

9. 6.5, 4.3, 9.8, 2.2, x; mean 4.8 10. 100, 112, 98, 235, x; mean 127

11. 1.2, 3.4, 6.7, 5.9, x; mean 4.0 12. 34, 56, 45, 29, x; mean 40

13. One golfer’s scores for the season are 88, 90, 86, 89, 96, and 85. Another

golfer’s scores are 91, 86, 88, 84, 90, and 83. What are the range and mean

of each golfer’s scores? Use your results to compare the golfers’ skills.

Find the range and mean of each data set. Use your results to compare the two data

sets.

14. Set A: 5 4 7 2 8

Set B: 3 8 9 2 0

15. Set C: 1.2 6.4 2.1 10 11.3

Set D: 8.2 0 3.1 6.2 9

16. Set E: 12 12 0 8 Set F: 1 15 10 2

17. Set G: 22.4 20 33.5 21.3 Set H: 6.2 15 50.4 28

18. The heights of a painter’s ladders are 12 ft, 8 ft, 4 ft, 3 ft, and 6 ft. What are the

mean, median, mode, and range of the ladder heights?

Name Class Date

Practice Form G

12-3 Measures of Central Tendency and Dispersion

2

Find the mean, median, mode, and range of each data set after you perform the

given operation on each data value.

19. 4, 7, 5, 9, 5, 6; add 1 20. 23, 21, 17, 15, 12, 11; subtract 3

21. 1.1, 2.6, 5.6, 5, 6.7, 6; add 4.1 22. 5, 2, 8, 6, 11, 1; divide by 2

23. 12.1, 13.6, 10, 9.7, 13.2, 14; divide by 0.5 24. 3.2, 4.4, 6, 7.8, 3, 2; subtract −4

25. The lengths of Ana’s last six phone calls were 3 min, 19 min, 2 min, 44 min,

120 min, and 4 min. Greg’s last six phone calls were 5 min, 12 min, 4 min,

80 min, 76 min, and 15 min. Find the mean, median, mode, and range of

Ana’s calls and Greg’s calls. Use your results to compare each person’s

phone call habits.

26. The table shows a basketball player’s scores in five games.

How many points must the basketball player score in the

next game to achieve an average of 13 points per game?

27. You and a friend weigh your loaded backpack every day

for a week. The results are shown in the table. Find the

mean, median, mode, and range of the weights of your

backpack and your friend’s backpack. Use your results to

compare the backpack weights.

28. Over six months, a family’s electric bills averaged $55 per month. The bills for the

first five months were $57.60, $60, $53.25, $50.75, and $54.05. What was the

electric bill in the sixth month? Find the median, mode, and range of the six electric

bills.

Name Class Date

Practice (continued) Form G

12-3 Measures of Central Tendency and Dispersion

3

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Pre-Algebra

Center and Spread of Data

Name___________________________________

Date________________ Period____

-1-

Find the mode, median, mean, range, lower quartile, upper quartile, interquartile range, and meanabsolute deviation for each data set.

1)

6.5 7 7.5 8 8 8 9

10 10.5

Shoe Size 2)

2 3 3 3 4 4 6 7

12 18 19

Hits in a Round of Hacky Sack

3)

Movie # Awards Movie # Awards Movie # Awards

The Greatest Show on Earth 2 No Country for Old Men 4 Mrs. Miniver 6

Gentleman's Agreement 3 Unforgiven 4 Lawrence of Arabia 7

The Great Ziegfeld 3 It Happened One Night 5 On the Waterfront 8

The King's Speech 4 Forrest Gump 6

Academy Awards

4)

Plant Days Plant Days Plant Days Plant Days Plant Days

Bok Choi 45 Swiss Chard 60 Sugar Baby Watermelon 75 Honeydew 80 Rutabaga 90

Okra 55 Bell Pepper 75 Cantaloupe 80 Beefsteak Tomato 80 Tomatillo 100

Average Time to Maturity

4

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Worksheet by Kuta Software LLC-2-

5)

199

6

199

7

199

8

199

9

200

0

200

1

200

2

200

3

200

4

200

5

200

6

200

7

200

8

200

9

201

0

Lau

nche

s

Year

European Spacecraft Launches 6)

$15

,00

0$2

5,0

00

$35

,00

0$4

5,0

00

$55

,00

0$6

5,0

00

$75

,00

0$8

5,0

00

$95

,00

0$1

05,0

00

$115

,00

0$1

25,0

00

$135

,00

0$1

45,0

00

$155

,00

0$1

65,0

00

$175

,00

0

Tax

Rat

e (%

)

Income

Federal Income Tax

7)

Goals Frequency

Goals in a Hockey Game 8)

Stem Leaf

Key: | = 24,200

Mountain Heights (ft)

9)

Age

US Senators When Assuming Office

5

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Kuta Software - Infinite Algebra 1

Center and Spread of Data

Name___________________________________

Date________________ Period____

-1-

Find the mode, median, mean, lower quartile, upper quartile, interquartile range, and populationstandard deviation for each data set.

1)

37 42 48 51 52 53 54

54 55

Test Scores 2)

62 64 69 70 70 71 72

73 74 75 77

Mens Heights (Inches)

3)

Senator Age Senator Age Senator Age Senator Age Senator Age

Patrick Leahy 34 Carl Levin 44 Tammy Baldwin 50 John Barrasso 54 Mike Johanns 58

Mark Pryor 39 Rand Paul 47 Barbara Boxer 52 Kay Hagan 55 John Boozman 60

Brian Schatz 40 John Cornyn 50 Claire McCaskill 53 Jerry Moran 56 Jim Risch 65

John Thune 43

Age Assumed Office

4)

State Percent State Percent State Percent State Percent

Colorado 2.9 New Mexico 5.125 Maryland 6 Washington 6.5

Louisiana 4 Maine 5.5 South Carolina 6 Indiana 7

Wyoming 4 Florida 6 Kansas 6.15 New Jersey 7

Oklahoma 4.5 Idaho 6 Massachusetts 6.25 Rhode Island 7

North Dakota 5

Sales Tax

6

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5)

Births/woman

Birth Rate by Country 6)

# Words Frequency

Length of Book Titles

7)

Goa

ls

Game

Goals in a Hockey Game 8)

Stem Leaf

Key: | = 1,800

Boiling Point (°C)

9)

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

Cos

t (¢)

Year

Cost of Electricity, per kWh 10)

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

Lau

nche

s

Year

European Spacecraft Launches

7

Use the data to make a frequency table.

1. runs per game: 5 4 3 6 1 9 3 4 2 2 0 7 5 1 6

2. weight (lb): 10 12 6 15 21 11 12 9 11 8 8 13 10 17

Use the data to make a histogram.

3. number of pages: 452 409 355 378 390 367 375 514 389 438 311 411 376

4. price per yard: $9 $5 $6 $4 $8 $9 $12 $7 $10 $4 $5 $6 $6 $7

Tell whether each histogram is uniform, symmetric, or skewed.

5. 6.

7. 8.

Name Class Date

Practice Form G

12-2 Frequency and Histograms

8

Use the data to make a cumulative frequency table.

9. call length (min): 3 5 12 39 12 3 15 23 124 2 1 1 7 19 11 6

10. package weight (kg): 1.25 3.78 2.2 12.78 3.15 4.98 3.45 9.1 1.39

Use the snowfall amounts, in inches, below.

10 2.5 1.5 3 6 8.5 9 12 2 0.5 1 3.25 5 6.5 10.5 4.5 8 8.5

11. What is a histogram of the data

that uses intervals of 2?

12. What is a histogram of the data that uses

intervals of 4?

The amount of gasoline that 80 drivers bought to fill their cars’ gas tanks is shown.

13. Which interval represents the greatest number of drivers?

14. How many drivers bought more than 12 gallons?

15. How many drivers bought 9 gallons or less?

Name Class Date


12-2 Frequency and Histograms

9

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Visualizing Data

Name___________________________________

Date________________ Period____

-1-

Draw a dot plot for each data set.

1)

4 4 4 4 5 5 5 6

6 7 7 7 7 7 7 7

7

Games per World Series

2)

Senator Age Senator Age Senator Age Senator Age Senator Age

Mary Landrieu 41 Jon Tester 50 Mike Enzi 52 Barbara Boxer 52 Lamar Alexander 62

Mike Crapo 47 Tim Johnson 50 Dick Durbin 52 Sherrod Brown 54 Richard Blumenthal 64

John Cornyn 50 Jeff Sessions 50 Bob Menendez 52 John Barrasso 54 Angus King 68

Age Assumed Office

Draw a stem-and-leaf plot for each data set.

3)

9.2 15.6 15.8 22.4 26.4

34 34.4 34.8 38.8 39.6

45.2 50.4 51.6 55.6 55.6

56.6 69.2

Annual Precipitation (Inches)

10

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4)

Country US $ Country US $ Country US $ Country US $

Central African Rep. 604 Uzbekistan 5,167 Maldives 11,654 Chile 21,911

Djibouti 2,998 Rep. of Congo 5,867 South Africa 12,504 Japan 36,315

Yemen 3,958 Mongolia 9,433 Botswana 15,675 Belgium 40,338

Laos 4,812 Grenada 11,498 Gabon 19,260 United Arab Emirates 58,042

Per Capita Income

Draw a box-and-whisker plot for each data set.

5)

37 38 39 44 44 45 46

47 47 47 47 48 51 52

52 53 54

Test Scores 6)

State Years State Years

Arkansas 74.2 Wisconsin 79.8

New Mexico 77.7 Washington 80.3

Alabama 78.1 Colorado 80.9

Louisiana 78.2 Indiana 81.3

Wyoming 78.4 Nevada 81.3

Kansas 78.6 Pennsylvania 81.6

Maine 79.1 Florida 81.7

Hawaii 79.7 Massachusetts 83.8

Life Expectancy

11

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Visualizing Data

Name___________________________________

Date________________ Period____

-1-

Draw a dot plot for each data set.

1)

2 3 4 5 5 5 5 6

6 7 7 7 7 8 13

Hits in a Round of Hacky Sack 2)

7 4 6 7 9 7 6 7

6 8 7 7 6 7 6 5

Hours Slept

Draw a stem-and-leaf plot for each data set.

3)

Name Age Name Age Name Age

Rudolf Ludwig Mössbauer 32 Stanley Ben Prusiner 55 Robert Merton Solow 63

Wolfgang Ketterle 44 Torsten Nils Wiesel 57 Stanley Cohen 64

Joseph Leonard Goldstein 45 Richard Axel 58 Peter Mansfield 70

Aung San Suu Kyi 46 Robert Coleman Richards 59 Vernon Lomax Smith 75

Kenneth Joseph Arrow 51 James Alexander Mirrlees 60 Richard Fred Heck 79

Barry James Marshall 54

Nobel Laureates

4)

City Population City Population City Population City Population

Boston 617,594 Seattle 608,660 Irving 216,290 Washington DC 601,723

Gilbert 208,453 Richmond 204,214 Santa Ana 324,528 Columbus 787,033

Stockton 291,707 Scottsdale 217,385 Fort Worth 741,206 Aurora 325,078

Austin 790,390 Portland 583,776 San Francisco 805,235

Large US Cities

Draw a box-and-whisker plot for each data set.

5)

26 26.1 27.2 27.6 28.9

30.2 30.6 31.1 31.5 32.1

33.4 34 34 34 36.7

45

Minutes to Run 5km

12

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6)

President Age President Age President Age President Age

Calvin Coolidge 51 James Madison 57 Barack Obama 47 William McKinley 54

Lyndon B Johnson 55 Millard Fillmore 50 Chester A Arthur 51 James A Garfield 49

Gerald Ford 61 Zachary Taylor 64 Grover Cleveland 55 William Howard Taft 51

Theodore Roosevelt 42 James K Polk 49 Harry S Truman 60 Abraham Lincoln 52

Martin Van Buren 54

Age At Inauguration

Draw a histogram for each data set.

7)

Plant Days Plant Days Plant Days Plant Days Plant Days

Mesclun 40 Turnip 55 Romano Pole Bean 60 Sweet Potato 90 Tomatillo 100

Spinach 44 Swiss Chard 60 Yukon Gold Potato 65 Brussel Sprouts 90 Gooseneck Gourd 120

Endive 47 Kale 60 Cantaloupe 80 Celery 95 Pumpkin 120

Average Time to Maturity

8)

Animal Years Animal Years

Lion 35 Chinchilla 20

Cottontail 10 Bee (Queen) 5

Teal 20 Congo Eel 27

Macaw 50 Pheasant 18

Painted Turtle 11 Prarie Dog 10

Asian elephant 40 Nutria 15

Grouse 10 Flying Squirrel 14

Rhinoceros 40 Pionus Parrot 15

Average Lifespan

13

Find the minimum, first quartile, median, third quartile, and maximum of each

data set.

1. 220 150 200 180 320 330 300 2. 14 18 12 17 14 19 18

3. 33.2 45.1 22.3 76.7 41.9 39 32.2 4. 5 8 9 7 11 4 9 4

5. 1.4 0.2 2.3 1.0 0.8 2.4 0.9 2.1 6. 90 47 88 53 59 72 68 62 79

Make a box-and-whisker plot to represent each set of data.

7. snack prices: $0.99 $0.85 $1.05 $3.25 $1.49 $1.35 $2.79 $1.99

8. ticket buyers: 220 102 88 98 178 67 42 191 89

9. marathon race finishers: 3,869 3,981 3,764 3,786 4,310 3,993 3,258

10. winning times (min): 148 148 158 149 164 163 149 156

11. ticket prices: $25.50 $45 $24 $32.50 $32 $20 $38.50 $50 $45

12. head circumference (cm): 60.5 54.5 55 57.5 59 58.5 58.5 57 56.75 57

Name Class Date

Practice Form G

12-4 Box-and-Whisker Plots

14

13. Use the box-and-whisker plot below. What does it tell you about the test scores in each

class? Explain.

14. Of 200 golf scores during a city tournament, 32 are less than or equal to 90.

What is the percentile rank of a score of 90?

15. Of 25 dogs, 15 weigh more than 35 pounds. What is the percentile rank of a

dog that weighs 35 pounds?

16. The table shows how many votes each student who ran for class president

received. What is Li’s percentile rank?

17. Ten students earned the following scores on a test: 89, 90, 76, 78, 83, 88, 91,

93, 96, and 90. Which score has a percentile rank of 90? Which score has a

percentile rank of 10?

Make box-and-whisker plots to compare the data sets.

18. Test scores: 19. Monthly sales:

Andrew’s: 79 80 87 87 99 94 77 86 Kiera’s: 17 50 26 39 6 49 62 40 8

Dipak’s: 93 79 78 82 91 87 80 99 Paul’s: 18 47 32 28 12 49 60 28 15

Name Class Date


12-4

Box-and-Whisker Plots

15

Name: ___________________________ Period:_____ Date: __________ Score:__________ ID: A

1

Box and Whisker Worksheet

Make a box-and-whisker plot of the data.

1. 29, 34, 35, 36, 28, 32, 31, 24, 24, 27, 34

This box-and-whisker plot shows the ages of clerks in a supermarket.

2. Find the median age of the clerks.

3. Find the upper extreme of the data.

4. Find the range of the data.

5. Find the lower quartile of the data.

Use the box-and-whisker plot to answer the following question(s).

6. What is the median of the test scores of Class I?

7. What is the median of the test scores of Class II?

8. What is the difference of the median of the test scores of the two classes?

16

ID: A

2

9. Ms. Alison drew a box-and-whisker plot to represent her students' scores on a mid-term test.

Steve earned an 85 on the test. Describe how his score compares with those of his classmates.a. about 75% scored higher; about 25%

scored lowerc. about 25% scored higher; about 75%

scored lowerb. about 75% scored higher; about 50%

scored lowerd. about 50% scored higher; about 50%

scored lower

Use the following data to answer the following questions.

16, 22, 14, 12, 20, 19, 14, 11

10. Find the range.

11. Find the median.

12. What is the median of the data shown in the stem-and-leaf plot?

Evaluate the expression for the given values of the variables.

13. 2v � 3u, v 11, u 8

Evaluate the expression.

14. 24 y 6 u 2

15. �14 � 15

16. �6 � (�8)

17. �488

17

Name Class Date

5-7 Practice Form G

For each table, make a scatter plot of the data. Describe the type of correlation

the scatter plot shows.

1. 2.

Use the table below and a graphing calculator for Exercises 3 through 6.

3. Make a scatter plot of the data pairs (years since 1980, population).

4. Draw the line of best fit for the data.

5. Write an equation for the trend line.

6. According to the data, what will the estimated resident

population in Florida be in 2020?

Scatter Plots and Trend Lines

20

Name Class Date

5-7 Practice (continued) Form G

Use the table below and a graphing calculator for Exercises 7 through 10.

7. Make a scatter plot of the data pairs (years since 1999,

revenue).

8. Draw the line of best fit for the data.

9. Write an equation for the line of best fit.

10. According to the data, what will the estimated gross

revenue be in 2015?

In each situation, tell whether a correlation is likely. If it is, tell whether the

correlation reflects a causal relationship. Explain your reasoning.

11. the number of practice free throws you take and the number of free throws you

make in a game

12. the height of a mountain and the average elevation of the state it is in

13. the number of hours worked and an employee’s wages

14. a drop in the price of a barrel of oil and the amount of gasoline sold

15. Open-Ended Describe a real world situation that would show a strong

negative correlation. Explain your reasoning.

16. Writing Describe the difference between interpolation and extrapolation. Explain

how both could be useful.

17. Writing Describe how the slope of a line relates to a trend line. What does the y-

intercept represent?

Scatter Plots and Trend Lines

21

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Scatter Plots

Name___________________________________

Date________________ Period____

-1-

State if there appears to be a positive correlation, negative correlation, or no correlation. Whenthere is a correlation, identify the relationship as linear or nonlinear.

1)

2)

3)

4)

5)

6)

22

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-2-

Construct a scatter plot.

7) X Y X Y

300 1 1,800 3

800 1 3,400 3

1,100 2 4,700 4

1,600 2 6,000 4

1,700 2 8,500 6

8) X Y X Y X Y

0.1 7.5 0.4 3.3 0.6 1.8

0.1 7.6 0.6 1.4 0.9 1.5

0.3 4.5 0.6 1.7 1 1.7

0.4 3.2

Construct a scatter plot. Find the slope-intercept form of the equation of the line that best fits thedata.

9) X Y X Y X Y

10 700 40 300 70 100

10 800 60 200 80 100

30 400 70 100 100 200

30 500

10) X Y X Y X Y

1 20 5 70 7 80

2 40 6 80 9 80

3 50 7 80 10 80

4 60

23

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Scatter Plots

Name___________________________________

Date________________ Period____

State if there appears to be a positive correlation, negative correlation, or no correlation. Whenthere is a correlation, identify the relationship as linear, quadratic, or exponential.

1)

2)

3)

4)

Construct a scatter plot. State if there appears to be a positive correlation, negative correlation, orno correlation. When there is a correlation, identify the relationship as linear, quadratic, orexponential.

5) X Y X Y

1,000 1,300 5,000 2,500

2,000 1,500 7,000 3,600

3,000 2,000 7,000 3,700

3,000 2,000 9,000 4,200

4,000 2,400 10,000 5,200

6) X Y X Y

140 500 280 900

150 1,000 450 500

170 300 450 500

180 100 770 400

270 200 910 600

24

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Using Statistical Models

Name___________________________________

Date________________ Period____

-1-

1) The height and weight of adults can be related by the equation yx where x is height infeet and y is weight in pounds.

Wei

ght (

poun

ds)

Height (feet)

a) What does the slope of the line represent?

b) What does the y-intercept of this function represent?

2) The average amount of electricty consumed by a household in a day is strongly correlated to theaverage daily temperature for that day. This relationship is given by yx where x isthe temperature in °F and y is the amount of electricity consumed in kilowatt-hours (kWh).

Ele

ctri

city

(kW

h)

Temperature (°F)

a) What does the slope of the line represent?

b) What does the y-intercept of this function represent?

26

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-2-

3) The number of marriage licenses issued byClark County Nevada, the county where LasVegas is located, has been decreasing sincethe year 2000:

Year Marriage Licenses

2001 141,000

2006 127,000

2007 121,000

2010 111,000

2011 109,000

2012 104,000

This can be modeled by the equation yx where x is the yearand y is the number of marriage licensesissued.

Mar

riag

e L

icen

ses

Year

a) According to the model, how many marriage licenses were issued in 2004? Round your answerto the nearest hundred.

b) Using this model, how many marriages licenses would you expect to be issued in 2023? Roundyour answer to the nearest hundred.

c) According to the model, in what year did Clark County issue 140,000 marriage licenses? Disregard years before 1990. Round your answer to the nearest year.

4) With the help of scientists, farmers inCameroon have been able to produce moreand more grain per hectare each year. Hereare the crop yields for several years:

Year Yield (kg/hectare)

1962 656

1969 728

1974 846

1980 1,100

2000 1,480

2004 1,540

The crop yield can be described by theequation yx where x is theyear and y is the grain yield in kilograms perhectare (kg/ha).

Yie

ld (

kg/h

ecta

re)

Year

a) According to the model, what was the crop yield in 1988? Round your answer to the nearestwhole number.

b) Assuming that this trend continues, what crop yield is predicted for the year 2022 by the model? Round your answer to the nearest whole number.

c) The model indicates that a crop yield of 1300 kg/hectare was achieved in what year? Roundyour answer to the nearest year.

27

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Using Statistical Models

Name___________________________________

Date________________ Period____

1) The oyster population of the Chesapeake Bay has been in decline for over 100 years. This can be

expressed by the equation y x where x is the number of years since 1900 and y is theamount of oysters harvested in metric tons.

Oys

ters

(m

etri

c to

ns)

Years since 1900

What does the y-intercept of this function represent?

2) The Hurricane Hunters took the followingmeasurements from a hurricane over severaldays as it developed:

Air Pressure (kPa) Wind Speed (knots)

924 126

946 104

956 93.5

967 84.9

991 44.4

1,003 30.6

They found that the air pressure and windspeed are related in the following way: yx where x is the airpressure in millibars (kPa) and y is themaximum sustained wind speed in knots(nautical miles per hour).

Win

d S

peed

(kn

ots)

Air Pressure (kPa)

a) Using the model, what would be the wind speed of a hurricane with an air pressure of 980 kPa? Round your answer to the nearest knot.

b) According to the model, a hurricane with an air pressure of 891 kPa would have what windspeed? Round your answer to the nearest knot.

c) The model indicates that a wind speed of 110 knots is associated with what air pressure? Roundyour answer to the nearest millibar.

28

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3) The time for the fastest runner for their agein the Marine Corps Marathon is given forseveral ages:

Age Time (minutes)

17 196

30 149

35 149

47 174

50 173

55 182

This can be modeled by the equation yxx where x is the ageand y is the number of minutes taken.

Tim

e (m

inut

es)

Age (years)

a) Using this model, what would be the time for the fastest 41-year-old? Round your answer to thenearest hundredth.

b) According to the model, what would be the time for the fastest 83-year-old? Round your answerto the nearest hundredth.

c) What age(s) correspond to a time of 171 minutes? Round your answer(s) to the nearest tenth.

4) Economists have found that the amount ofcorruption in a country is correlated to theproductivity of that country. Productivity ismeasured by gross domestic product (GDP)per capita. Corruption is measured on ascale from 0 to 100 with 0 being highlycorrupt and 100 being least corrupt:

Corruption Score GDP Per Capita ($)

18 2,850

24 4,050

33 3,740

45 10,100

60 25,000

65 25,000

This can be modeled by the equation yx where x is the corruptionscore and y is GDP per capita in dollars.

GD

P P

er C

apit

a ($

)

Corruption Score

a) According to the model, what would be the GDP per capita of a country with a corruption scoreof 38? Round your answer to the nearest dollar.

b) Using this model, a country with a corruption score of 75 would have what GDP per capita? Round your answer to the nearest dollar.

c) A GDP per capita of $17,000 corresponds to what corruption score, according to the model? Round your answer to the nearest whole number.

29

You spin a spinner that has 15 equal-sized sections numbered 1 to 15. Find the

theoretical probability of landing on the given section(s) of the spinner.

1. P(15) 2. P(odd number) 3. P(even number)

4. P(not 5) 5. P(less than 5) 6. P(greater than 8)

7. P(multiple of 5) 8. P(less than 16) 9. P(prime number)

10. You roll a number cube. What is the probability that you will roll a number less

than 5?

11. The probability that a spinner will land on a red section is 1

6 . What is the

probability that the spinner will not land on a red section?

You choose a marble at random from a bag containing 2 red marbles, 4 green

marbles, and 3 blue marbles. Find the odds.

12. odds in favor of red 13. odds in favor of blue

14. odds against green 15. odds against red

16. odds in favor of green 17. odds against blue

18. You roll a number cube. What are the odds that you will roll an even number?

Name Class Date

Practice Form G

12-7 Theoretical and Experimental Probability

32

One hundred twenty randomly selected students at

Roosevelt High School were asked to name their

favorite sport. The results are shown in the table. Find

the experimental probability that a student selected at

random makes the given response.

19. P(basketball)

20. P(soccer)

21. P(baseball)

22. P(football)

23. A meteorologist says that the probability of rain today is 35%. What is the

probability that it will not rain?

24. Hank usually makes 11 out of every 20 of his free throws. What is the

probability that he will miss his next free throw?

25. There are 250 freshmen at Central High School. You survey 50 randomly selected

freshmen and find that 35 plan to go to the school party on Friday. How many

freshmen are likely to be at the party?

26. The Widget Company randomly selects its widgets and checks for defects. If 5 of

the 300 selected widgets are defective, how many defective widgets would you

expect in the 1500 widgets manufactured today?

Name Class Date


12-7 Theoretical and Experimental Probability

33

You spin a spinner that has 12 equal-sized sections numbered 1 to 12. Find each

probability.

1. P(3 or 4) 2. P(even or 7)

3. P(even or odd) 4. P(multiple of 3 or odd)

5. P(odd or multiple of 5) 6. P(less than 5 or greater than 9)

7. P(even or less than 8) 8. P(multiple of 2 or multiple of 3)

9. P(odd or greater than 4) 10. P(multiple of 5 or multiple of 2)

11. Reasoning Why can you use P(A or B) = P(A) + P(B) − P(A and B) for

both mutually exclusive events and overlapping events?

You roll a red number cube and a blue number cube. Find each probability.

12. P(red 2 and blue 2) 13. P(red odd and blue even)

14. P(red greater than 2 and red 4) 15. P(red odd and blue less than 4)

16. P(red 1 or 2 and blue 5 or 6) 17. P(red 6 and blue even)

18. P(red greater than 4 and blue greater than 3)

Name Class Date

Practice Form G

12-8 Probability of Compound Events

34

19. The probability that Bob will make a free throw is 2

5. What is the

probability that Bob will make his next two free throws?

You choose a marble at random from a bag containing 3 blue marbles, 5 red

marbles, and 2 green marbles. You replace the marble and then choose again. Find

each probability.

20. P(both blue) 21. P(both red)

22. P(blue then green) 23. P(red then blue)

24. P(green then red) 25. P(both green)

You choose a tile at random from a bag containing 2 tiles with X, 6 tiles with Y,

and 4 tiles with Z. You pick a second tile without replacing the first. Find each

probability.

26. P(X then Y) 27. P(both Y)

28. P(Y then X) 29. P(Z then X)

30. P(both Z) 31. P(Y then Z)

32. There are 12 girls and 14 boys in math class. The teacher puts the names of

the students in a hat and randomly picks one name. Then the teacher picks

another name without replacing the first. What is the probability that both

students picked are boys?

Name Class Date


12-8 Probability of Compound Events

35

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Probability with Combinatorics

Name___________________________________

Date________________ Period____

-1-

Find the probability of each event.

1) Beth and Shayna each purchase one raffle

ticket. If a total of eleven raffle tickets are

sold and two winners will be selected, what

is the probability that both Beth and Shayna

win?

2) A meeting takes place between a diplomat

and fourteen government officials.

However, four of the officials are actually

spies. If the diplomat gives secret

information to ten of the attendees at

random, what is the probability that no

secret information was given to the spies?

3) A fair coin is flipped ten times. What is the

probability of the coin landing heads up

exactly six times?

4) A six-sided die is rolled six times. What is

the probability that the die will show an

even number exactly two times?

5) A test consists of nine true/false questions.

A student who forgot to study guesses

randomly on every question. What is the

probability that the student answers at least

two questions correctly?

6) A basketball player has a 50% chance of

making each free throw. What is the

probability that the player makes at least

eleven out of twelve free throws?

36

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7) A technician is launching fireworks near the

end of a show. Of the remaining fourteen

fireworks, nine are blue and five are red. If

she launches six of them in a random order,

what is the probability that exactly four of

them are blue ones?

8) A jar contains ten black buttons and six

brown buttons. If nine buttons are picked at

random, what is the probability that exactly

five of them are black?

9) You are dealt five cards from a standard and

shuffled deck of playing cards. Note that a

standard deck has 52 cards and four of those

are kings. What is the probability that you'll

have at most three kings in your hand?

10) A bag contains six real diamonds and five

fake diamonds. If six diamonds are picked

from the bag at random, what is the

probability that at most four of them are

real?

37

Name Class Date

3-1

Practice Form G

Write an inequality that represents each verbal expression.

1. v is greater 10.

2. b is less than or equal to 1.

3. the product of g and 2 is less than or equal to 6.

4. 2 more than k is greater than 3.

Determine whether each number is a solution of the given inequality.

5. 3y + 5 < 20 a. 2 b. 0 c. 5

6. 2m 4 ≥ 10 a. 1 b. 8 c. 10

7. 4x + 3 > 9 a. 0 b. 2 c. 4

8.

34

2

n

a. 3 b. 2 c. 10

Graph each inequality.

9. y < 2 10. t ≥ 4

11. z > 3 12. v ≤ 15

13. 3 ≥ f 14.5

3c

Inequalities and Their Graphs

38

Name Class Date

3-1


Write an inequality for each graph.

15. 16

17. 18.

Define a variable and write an inequality to model each situation.

19. The school auditorium can seat at most 1200 people.

20. For a certain swim meet, a competitor must swim faster than 23 seconds to

qualify.

21. For a touch-typing test, a student must type at least 65 wpm to receive an “A .”

Write each inequality in words.

22. n < 3 23. b > 0 24. 5 ≤ x

25. z ≥ 3.14 26. 4 < q 27. 18 ≥ m

28. A local pizzeria offered a special. Two pizzas cost $14.99. A group of students

spent less than $75. They purchased three pitchers of soda for $12.99. How many

pizzas could the group purchase?

29. A student needs at least seven hours of sleep each night. The student goes to bed

at 11:00 p.m. and wakes up before 6:30 a.m. Is the student getting enough sleep?

Write an inequality for the number of hours of sleep the student gets each night.

Inequalities and Their Graphs

39

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Kuta Software - Infinite Pre-Algebra Name___________________________________

Period____Date________________Inequalities and Their Graphs

Draw a graph for each inequality.

1)

x

2)

m

3)

x

4)

m

5)

a

6)

x

7)

b

8)

x

9)

r

10)

n

11)

n

12)

x

13)

n

14)

k

-1-

40

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15)

p

16)

n

17)

x

18)

n

19)

n

20)

v

Write an inequality for each graph.

21)

22)

23)

24)

25)

26)

27)

28)

-2-

41

Name Class Date

3-2

Practice Form G

State what number you would add to or subtract from each side of the

inequality to solve the inequality.

1. x 4 < 0

2.

73 5

5

3. 6.8 ≤ m 4.2

4. x + 3 ≥ 0

5.

52

4S

6. 3.8 > m + 4.2

Solve each inequality. Graph and check your solutions.

7. y 2 < 7 8. v + 6 > 5

9. 12 ≥ c 2 10. 8 ≤ f + 4

11. 4.3 ≥ 2.4 + s 12. 22.5 < n 0.9

13.4 6

C7 7

14.1 1

1 12 2

p

Solving Inequalities Using Addition or Subtraction

42

Name Class Date

3-2


Solve each inequality. Justify each step.

15. y 4 + 2y > 11

16.

1 21

7 7d

17.

2 70

3 9v

18. 2p 4 + 3p > 10

19. 4y + 2 3y ≤ 8 20. 5m 4m + 4 > 12

21. The goal of a toy drive is to donate more than 1000 toys. The toy drive already

has collected 300 toys. How many more toys does the toy drive need to meet its

goal? Write and solve an inequality to find the number of toys needed.

22. A family earns $1800 a month. The family’s expenses are at least $1250. Write

and solve an inequality to find the possible amounts the family can save each

month.

23. To go to the next level in a certain video game, you must score at least

50 points. You currently have 40 points. You fall into a trap and lose 5 points.

What inequality shows the points you must earn to go to the next level?

Solving Inequalities Using Addition or Subtraction

43

Name Class Date

3-3

Practice Form G

Solve each inequality. Graph and check your solution.

1.1

3

x

2.1

4

w

3.4

2

p

4.

21

3y

5.

26

3x

6

21

3k

.

7. 3m > 6 8. 3t < 12

9. 18 ≥ 6c 10. 3w < 21

11. 9z > 36 12. 108 ≥ 9d

Solving Inequalities Using Multiplication or Division

44

Name Class Date

3-3


Solve each inequality. Graph and check your solution.

13. 2.5 > 5p

14.1

6

t

15.

24

3n

16. 27u ≥ 3

17. Writing On a certain marathon course, a runner reaches a big hill that is at least 10

miles into the race. If a total marathon is 26.2 miles, how can you find the number of

miles the runner still has to go?

18. You wonder if you can save money by using your cell phone for all long distance

calls. Long distance calls cost $.05 per minute on your cell phone. The basic plan for

your cell phone is $29.99 each month. The cost of regular phone service with

unlimited long distance is $39.99. Define a variable and write an inequality that will

help you find the number of long-distance call minutes you may make and still save

money.

19. The unit cost for a piece of fabric is $4.99 per yard. You have $30 to spend

on material. How many feet of material could you buy? Define a variable and write an

inequality to solve this problem.

Solving Inequalities Using Multiplication or Division

45

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Kuta Software - Infinite Algebra 1 Name___________________________________

Period____Date________________Two-Step Inequalities

Solve each inequality and graph its solution.

1)

x

2)

m

3)

(

p)

4)

(

x)

5)

b

6)

(

n)

7)

n

8)

(

r)

9)

x

10)

(

p)

11)

x

12)

a

-1-

46

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13)

v

14)

(

n)

15)

n

16)

(

k)

17)

n

18)

x

19)

n

20)

b

21)

(

v)

22)

r

23)

x

24)

m

-2-

47

Name Class Date

3-4

Practice Form G

Solve each inequality. Check your solutions.

1. 3f + 9 < 21 2. 4n 3 ≥ 105

3. 33y 3 ≤ 8 4. 2 + 2p > 17

5. 12 > 60 6r 6. 5 ≤ 11 + 4j

Solve each inequality.

7. 2(k + 4) 3k ≤ 14 8. 3(4c 5) 2c > 0

9. 15(j 3) + 3j < 45 10. 22 ≥ 5(2y + 3) 3y

11. 53 > 3(3z + 3) + 3z 12. 20(d 4) + 4d ≤ 8

13. x + 2 < 3x 6 14. 3v 12 > 5v + 10

Solve each inequality, if possible. If the inequality has no solution, write no

solution. If the solutions are all real numbers, write all real numbers.

15. 6w + 5 > 2(3w + 3) 16. 5r + 15 ≥ 5(r 2)

17. 2(6 + s) < 16 + 2s 18. 9 2x < 7 + 2(x 3)

19. 2(n 3) ≤ 13 + 2n 20. 3(w + 3) < 9 3w

Solving Multi-Step Inequalities

48

Name Class Date

3-4


21. A grandmother says her grandson is two years older than her granddaughter and that

together, they are at least 12 years old. How old are her grandson and granddaughter?

22. A family decides to rent a boat for the day while on vacation. The boat’s rental

rate is $500 for the first two hours and $50 for each additional half hour. Suppose

the family can spend $700 for the boat. What inequality represents the number of

hours for which they can rent the boat?

23. Writing Suppose a friend is having difficulty solving 1.75(q 5) > 3(q + 2.5).

Explain how to solve the inequality, showing all the necessary steps and identifying the

properties you would use.

24. Open-Ended Write two different inequalities that you can solve by adding 2 to

each side and then dividing each side by 12. Solve each inequality.

25. Reasoning a. Solve 3v 5 ≤ 2v + 10 by gathering the variable terms on the

left side and the constant terms on the right side of the inequality.

b. Solve 3v 5 ≤ 2v + 10 by gathering the constant terms on the left side

and the variable terms on the right side of the inequality.

c. Compare the results of parts (a) and (b).

d. Which method do you prefer? Explain.

Solving Multi-Step Inequalities

49

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Period____Date________________Solving Multi-Step Inequalities


1)

n

2)

x

x

3)

x

4)

n

n

5)

k

k

6)

p

7)

a

(

a)

8)

x

(

x)

-1-

50

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9)

(

n)

n

10)

(

b)

b

b

11)

n

(

n)

12)

(

p)

p

13)

x

(

x)

14)

n

(

n)

15)

(

b)

(

b)

16)

(

k)

(

k)

k

k

17)

(

x)

(

x)

x

x

18)

(

r)

r

r

(

r)

-2-

51

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Infinite Algebra 1 Name___________________________________

Period____Date________________Multi-Step Inequalities


1)

n

n

2)

x

x

3)

p

p

4)

k

k

5)

m

6)

(

x)

7)

(

n)

8)

(

b)

9)

(

r)

10)

(

r)

11)

x

x

x

x

12)

x

x

-1-

52

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13)

a

a

14)

v

v

15)

n

n

n

n

16)

x

x

(

x)

17)

n

(

n)

n

18)

(

p)

p

p

19)

k

(

k)

20)

x

(

x)

21)

(

k)

(

k)

22)

(

x)

(

x)

23)

(

x)

x

24)

(

n)

(

n)

-2-

53

Name Class Date

3-6 Practice Form G

Write a compound inequality that represents each phrase. Graph the solutions.

1. all real numbers that are less than 3 or greater than or equal to 5

2. The time a cake must bake is between 25 minutes and 30 minutes, inclusive.

Solve each compound inequality. Graph your solutions.

3. 5 < k 2 < 11 4. 4 y + 2 10

5. 6b 1 41 or 2b + 1 11 6. 5 m < 4 or 7m 35

7. 3 < 2p 3 12 8. 11

3 34

k

9. 3d + 3 1 or 5d + 2 12 10. 9 c < 2 or 3c 15

11. 4 y + 2 3(y 2) + 24 12. 5z + 3 < 7 or 2z 6 8

Write each interval as an inequality. Then graph the solutions.

13. (1, 10] 14. [3, 3]

15. (, 0] or (5, ) 16. [3, )

17. (, 4) 18. [25, 50)

Compound Inequalities

56

Name Class Date


Write each inequality or set in interval notation. Then graph the interval.

19. x < 2 20. x 0

21. x < 2 or x 1 22. 3 x < 4

Write a compound inequality that each graph could represent.

23. 24.

25. 26.

Solve each compound inequality. Justify each step.

27. 3r + 2 < 5 or 7r 10 60 28. 3 0.25v 2.5

29. 30.

31. The absorbency of a certain towel is considered normal if the towel is able

to hold between six and eight mL. The first checks for materials result in

absorbency measures of 6.2 mL and 7.2 mL. What possible values for the third

reading m will make the average absorbency normal?

32. A family is comparing different car seats. One car seat is designed for a child

up to and including 30 lb. Another car seat is designed for a child between 15

lb and 40 lb. A third car seat is designed for a child between 30 lb and 85 lb,

inclusive. Model these ranges on a number line. Represent each range of

weight using interval notation. Which car seats are appropriate for a 32-lb

child?

Compound Inequalities

3 5 32

2 6 4w

2 1 25 3or 41

2 3

y y

57

Name Class Date

3-7 Practice Form G

Solve each equation. Graph and check your solutions.

1. 2. 10 = |y|

3. |n| + 2 = 5 4. 4 = |s| 3

5. |x| 5 = 1 6. 7 |d| = 49

Solve each equation. If there is no solution, write no solution.

7. |r 9| = 3 8. |c + 3| = 15 9. 1 = |g + 3|

10. 11. 2|3d| = 4 12. 3|2w| = 6

13. 4|v 5| = 16 14. 3|d 4| = 12 15. |3f + 0.5| 1 = 7

Solve and graph each inequality.

16. |x| 1 17. |x| < 2

18. |x + 3| < 10 19. |y + 4| 12

20. |y 1| 8 21. |p 6| 5

22. |3c 4| 12 23. 2

2 43

t

Absolute Value Equations and Inequalities

2

3b

22

3m

58

Name Class Date


Solve each equation or inequality. If there is no solution, write no solution.

24. |d| + 3 = 33 25. 1.5|3p| = 4.5 26.

27. 28. 7|3y 4| 8 48 29. |t| 1.2 = 3.8

30. 1 |c + 4| = 3.6 31. 32. |9d| 6.3

Write an absolute value inequality that represents each set of numbers.

33. all real numbers less than 3 units from 0

34. all real numbers at most 6 units from 0

35. all real numbers more than 4 units from 6

36. all real numbers at least 3 units from 2

37. A child takes a nap averaging three hours and gets an average of 12 hours of

sleep at night. Nap time and night time sleep can each vary by 30 minutes.

What are the possible time lengths for the child’s nap and night time sleep?

38. In a sports poll, 53% of those surveyed believe their high school football team

will win the state championship. The poll shows a margin of error of 5

percentage points. Write and solve an absolute value inequality to find the least

and the greatest percent of people that think their team will win the state

championship.

Absolute Value Equations and Inequalities

1 3

5 15f

34

y

2 30

3 4d

59

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Period____Date________________Absolute Value Inequalities


1)

n

2)

p

3)

m

4)

x

5)

x

6)

m

7)

r

8)

n

9)

x

10)

x

11)

b

12)

v

13)

p

14)

x

-1-

60

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15)

a

16)

k

17)

m

18)

x

19)

r

20)

n

21)

b

22)

v

23)

a

24)

n

25)

x

26)

n

-2-

61

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Period____Date________________Absolute Value Equations

Solve each equation.

1)

6

m = 42 2)

−6

x = 30

3)

k − 10 = 34)

x

7 = 3

5)

7 +

p = 7 6)

−3

p = 15

7)

7

n = 568)

m

5 = 3

9)

−3

p = −12 10)

m + 2 = 11

11)

n + 1 = 212)

x

7 = 5

13)

a − 5

8 = 5

14)

4

n + 8 = 56

15)

7

m + 3 = 7316)

x

7 − 8 = −7

17)

−9 +

v

8 = 3

18)

−10

v + 2 = −70

62

Name Class Date

6-5

Practice Form G

Graph each linear inequality.

1. x ≥ 4 2. y < 2 3. 3x y 6

4. 4x + 5y < 3 5. 3x + 2y > 6 6. y < x

7. 3x 5y > 6 8.

9

yx 9. 4 3

4

xy

10. Error Analysis A student graphed y ≤ 4x + 3 as

shown. Describe and correct the student’s error.

11. Writing How do you decide which half-plane to shade

when graphing an inequality? Explain.

Linear Inequalities

65

Name Class Date

6-5

Practice (continued)Form G

Determine whether the ordered pair is a solution of the linear inequality.

12. 7x + 2y > 5, (1, 1) 13. x y ≤ 3, (2, 1)

14. y + 2x > 5, (4, 1) 15. x + 4y ≤ 2, (8, 2)

16. y < x + 4, (9, 5) 17. y < 3x + 2, (3, 10)

18. 1

3,(9,12)2

x y 19. 0.3x 2.4y > 0.9, (8, 0.5)

Write an inequality that represents each graph.

20.

21.

22. You and some friends have $30. You want to order large

pizzas (p) that are $9 each and drinks (d) that cost $1 each.

Write and graph an inequality that shows how many pizzas

and drinks can you order.?

23. Tickets to a play cost $5 at the door and $4 in advance. The

theatre club wants to raise at least $400 from the play. Write

and graph an inequality for the number of tickets the theatre

club needs to sell. If the club sells 40 tickets in advance, how

many do they need to sell at the door to reach their goal?

24. Reasoning Two students did a problem as above, but one

used x for the first variable and y for the second variable and the other student

used x for the second variable and y for the first variable. How did their

answers differ and which one, if either, was incorrect?

Linear Inequalities

66

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Period____Date________________Graphing Linear Inequalities

Sketch the graph of each linear inequality.

1)

y

x

x

y

2)

y

x

x

y

3)

y

x

x

y

4)

x

x

y

-1-

67

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5)

y

x

x

y

6)

y

x

x

y

7)

x

y

x

y

8)

x

y

x

y

-2-

68

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Period____Date________________Graphing Linear Inequalities

Sketch the graph of each linear inequality.

1)

y

x

2)

y

x

3)

x

4)

y

x

5)

y

x

6)

y

x

-1-

69

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7)

x

y

8)

x

y

9)

y

10)

x

y

11)

x

y

12)

x

y

Critical thinking questions:

13) Name one particular solution to # 14) Can you write a linear inequality whose solutioncontains only points with positive

x-valuesand positive

y-values? Why or why not?

-2-

70

Name Class Date

6-6

Practice Form G

Solve each system of inequalities by graphing.

1. 3x + y ≤ 1 2. 5x y ≤ 1 3. 4x + 3y ≤ 1

x y ≤ 3 x + 3y ≤ 2 2x y ≤ 2

4. Writing What is the difference between the solution of a system of linear

inequalities and the solution of a system of linear equations? Explain.

5. Open-Ended When can you say that there is no solution for a system of

linear inequalities? Explain your answer and show with a system and graph.

6. Error Analysis A student graphs the system below.

Describe and correct the student’s error.

x y ≥ 3

y < 2

x ≥ 1

Determine whether the ordered pair is a solution of the given system.

7. (0, 1); 8. (–2, 3); 9. (1, 4);

1 x ≥ 3y 2x + 3y > 2 2x + y > 3

3y 1 > 2x 3x + 5y > 1 –3x y ≤ 5

Systems of Linear Inequalities

71

Name Class Date

6-6


10. Mark is a student, and he can work for at most 20 hours a week.

He needs to earn at least $75 to cover his weekly expenses. His

dog-walking job pays $5 per hour and his job as a car wash

attendant pays $4 per hour. Write a system of inequalities to

model the situation, and graph the inequalities.

11. Britney wants to bake at most 10 loaves of bread for a bake sale.

She wants to make banana bread that sells for $1.25 each and

nut bread that sells for $1.50 each and make at least $24 in sales.

Write a system of inequalities for the given situation and graph

the inequalities.

12. Write a system of inequalities for the following graph.

Solve each system of inequalities by graphing.

13. 5x + 7y > 6 14. x + 4y 2 ≥ 0

x + 3y < 1 2x y + 1 > 2

15. 5 62

xy

3x + y > 2

Systems of Linear Inequalities

72

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Period____Date________________Systems of Inequalities

Sketch the solution to each system of inequalities.

1)

y

>

4

x

− 3

y

≥

−2

x

+ 3

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

2)

y

≥

−5

x

+ 3

y

> −2

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

3)

y

< 3

y

≤

−

x

+ 1

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

4)

y

≥

x

− 3

y

≥

−

x

− 1

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

-1-

73

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5)

x

≤ −3

5

x

+ 3

y

≥ −9

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

6)

4

x

− 3

y

< 9

x

+ 3

y

> 6

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

7)

x

+

y

> 2

2

x

−

y

> 1

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

8)

x

+

y

≥ 2

4

x

+

y

≥ −1

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

-2-

74

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9)

4

x

+ 3

y

> −6

x

− 3

y

≤ −9

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

10)

y

< −2

x

+

y

≥ 1

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

11)

3

x

+

y

≥ −3

x

+ 2

y

≤ 4

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

12)

x

+

y

≥ −3

x

+

y

≤ 3

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

Critical thinking questions:

13) State one solution to the system

y

<

2

x

− 1

y

≥

10 −

x

14) Write a system of inequalities whose solution

is the set of all points in quadrant I not including

the axes.

-3-

75

Honors Algebra II Linear Programming Word Problems Worksheet II 1) You need to buy some filing cabinets. You know that Cabinet X costs $10 per unit, requires six square feet of

floor space, and holds eight cubic feet of files. Cabinet Y costs $20 per unit, requires eight square feet of floor space, and holds twelve cubic feet of files. You have been given $140 for this purchase, though you don't have to spend that much. The office has room for no more than 72 square feet of cabinets. How many of which model should you buy, in order to maximize storage volume?

2) A snack bar cooks and sells hamburgers and hot dogs during football games. To stay in business, it must sell at

least 10 hamburgers but can not cook more than 40. It must also sell at least 30 hot dogs, but can not cook more than 70. The snack bar can not cook more than 90 items total. The profit on a hamburger is 33 cents, and the profit on a hot dog is 21 cents. Low many of each item should it sell to make the maximum profit?

76

3) In order to ensure optimal health (and thus accurate test results), a lab technician needs to feed the rabbits a daily diet containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates, and 4 g of protein. But the rabbits should be fed no more than five ounces of food a day. Rather than order rabbit food that is custom-blended, it is cheaper to order Food X and Food Y, and blend them for an optimal mix. Food X contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein per ounce, and costs $0.20 per ounce. Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per ounce, at a cost of $0.30 per ounce. What is the optimal blend of Food X and Food Y?

4) You are about to take a test that contains questions of type A worth 4 points and type B worth 7 points. You

must answer at least 4 of type A and 3 of type B, but time restricts answering more than 10 of either type. In total, you can answer no more than 18. How many of each type of question must you answer, assuming all of your answers are correct, to maximize your score? What is your maximum score?

77

Documents

Name: Period - Hazleton Area School District / Overvie · 5.7 Scatter Plots and trend Lines ... 12-3 Practice Form G ... 23. 12.1, 13.6, 10, 9.7, 13.2, 14; divide by 0.5 24. 3.2,