ALGEBRA 1 KEYSTONE STUDENT WORKBOOK 4 TOPIC 8-10 TOPIC 8 12.3 12.2 12.4 12.5 5.7 12.7 12.8 Data Analysis Measures of Central Tendency and Dispersion Frequency and Histograms Box and Whisker Plot Samples and Surveys Scatter Plots and trend Lines Theoretical and Experimental Probability Prob of Compound Events TOPIC 9 Inequalities 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 STUDY ISLAND TOPICS GREEN RED QUIZ PURLE GREEN RED QUIZ Inequalities and Their Graphs Solve Inequalities Add and Sub Solve Inequalities Mult and Div Solving Multi Step Inequalities Working with Sets Compound Inequalities Absolute Value EQ and Inequalities Unions and Intersections TOPIC 10 Linear Inequalities 6.5 6.6 PURLE PURLE GREEN RED QUIZ Linear Inequalities Systems of Linear Inequalities PA CORE 8: SCATTER PLOTS BEST FIT LINEAR MODELS KEYSTONE: LINEAR INEQUALITIES SYSTEMS OF LINEAR INEQUALITIES TWO WAY TABLES Name: _______________________________ Period ____ 1 Name Class Date Practice 12-3 Measures of Central Tendency and Dispersion Form G Find the mean, median, and mode of each data set. Explain which measure of central tendency best describes the data. 1. touchdowns scored: 2. distance from school (mi): 13443 0.5 3.9 4.1 5 3 3. average speed (mi/hr): 4. price per pound: 36 59 47 56 67 $30 $8 $2 $5 $6 5. daily high temperature (˚F): 6. number of volunteers: 74 69 78 80 92 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 10. 100, 112, 98, 235, x; mean 127 9. 6.5, 4.3, 9.8, 2.2, x; mean 4.8 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 15. Set C: 1.2 6.4 2.1 10 11.3 Set B: 3 8 9 2 0 Set D: 8.2 0 3.1 6.2 9 17. Set G: 22.4 20 33.5 21.3 16. Set E: 12 12 0 8 Set H: 6.2 15 50.4 28 Set F: 1 15 10 2 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? 2 Name Class Date Practice (continued) 12-3 Measures of Central Tendency and Dispersion Form G 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. 3 Kuta Software - Infinite Pre-Algebra Name___________________________________ Center and Spread of Data Date________________ Period____ Find the mode, median, mean, range, lower quartile, upper quartile, interquartile range, and mean absolute deviation for each data set. 1) Shoe Size 6.5 7 10 10.5 7.5 8 2) 8 8 3) Hits in a Round of Hacky Sack 9 2 3 3 12 18 19 3 4 4 6 7 Academy Awards Movie # Awards The Greatest Show on Earth 2 Gentleman's Agreement 3 The Great Ziegfeld 3 The King's Speech 4 4) Movie # Awards No Country for Old Men 4 Unforgiven 4 It Happened One Night 5 Forrest Gump 6 Movie # Awards Mrs. Miniver 6 Lawrence of Arabia 7 On the Waterfront 8 Average Time to Maturity Plant Bok Choi Okra Days 45 55 Plant Swiss Chard Bell Pepper Days 60 75 Plant Days Sugar Baby Watermelon Cantaloupe 75 80 Plant Days Honeydew Beefsteak Tomato 80 80 Plant Days Rutabaga 90 Tomatillo 100 4 -1©] K2[0\1V5W bKxuctua` \StovfQtUweaFrueY zLbLaCr.B U uAqlglJ XrSixgyhvtHst Srne[sLelruv[eudO.H a uMva^dSeW ewHiYtDhP FIynufyi`nMiJtKeK uPTree]-sABlCgWebbcrUaT. Worksheet by Kuta Software LLC 5) European Spacecraft Launches 6) Federal Income Tax Tax Rate (%) Launches $15,000 $25,000 $35,000 $45,000 $55,000 $65,000 $75,000 $85,000 $95,000 $105,000 $115,000 $125,000 $135,000 $145,000 $155,000 $165,000 $175,000 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Year Income 7) Goals in a Hockey Game Goals 8) Mountain Heights (ft) Stem Frequency Leaf Key: | = 24,200 US Senators When Assuming Office 9) Age 5 -2©J q2e0Q1Y5M cKIuLtyak nS_odfJtywsaargex wL^LDCg.` V OArlilc UrCipgfhbtXsY ZryeMsYeXrNvee[dH.A F PMNaTdted [wuift_hH tIxnwfvilnwittUeJ wPYrHes-_AElagSeWbBrvaY. Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 1 Name___________________________________ Center and Spread of Data Date________________ Period____ Find the mode, median, mean, lower quartile, upper quartile, interquartile range, and population standard deviation for each data set. 1) Test Scores 37 42 54 55 48 51 52 2) 53 54 3) Mens Heights (Inches) 62 64 69 70 73 74 75 77 70 71 72 Age Assumed Office Senator Age Patrick Leahy 34 Mark Pryor 39 Brian Schatz 40 John Thune 43 Senator Age Carl Levin 44 Rand Paul 47 John Cornyn 50 Senator Age Tammy Baldwin 50 Barbara Boxer 52 Claire McCaskill 53 Senator Age John Barrasso 54 Kay Hagan 55 Jerry Moran 56 Senator Age Mike Johanns 58 John Boozman 60 Jim Risch 65 Sales Tax 4) State Percent State Colorado Louisiana Wyoming 2.9 4 4 New Mexico Maine Florida Oklahoma North Dakota 4.5 5 Idaho Percent State Percent State 5.125 5.5 6 Maryland South Carolina Kansas 6 6 6.15 Washington Indiana New Jersey 6 Massachusetts 6.25 Rhode Island Percent 6.5 7 7 7 6 -1©T b2w0D1I5q sKHuUtpaC pSkoBfatowDaYrKer jLyLNCS.f W BAvlzlO GrHitgYhntbso hr]eYszeyrxv[eldy.Q g dMAaZdKez ]w`iBtXhC cIzn^fAiQnDiCtVee wAdlhgJeUbwrRat f1T. Worksheet by Kuta Software LLC 5) Birth Rate by Country 6) Length of Book Titles # Words Births/woman Goals in a Hockey Game Goals 7) 8) Frequency Boiling Point (°C) Stem Leaf Key: | = 1,800 Game 9) Cost of Electricity, per kWh 10) European Spacecraft Launches Launches 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 Cost (¢) Year Year 7 -2©V ^2h0i1`5X nKQuYtYa` DSqo`fHtVwaayrre` ZLrLNCj.p \ cA]lNlm oriiggChqtTsJ praeLsJeDrgvgemdk.w n WMAaHdeez dwFiQtuhM zI\nafTiqnKiQtpeY EA[lTgCeXbvrtaL n1]. Worksheet by Kuta Software LLC Name 12-2 Class Date Practice Form G Frequency and Histograms 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. 7. 6. 8. 8 Name 12-2 Class Date Practice (continued) Form G Frequency and Histograms 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 12. What is a histogram of the data that uses that uses intervals of 2? 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? 9 Kuta Software - Infinite Pre-Algebra Name___________________________________ Visualizing Data Date________________ Period____ Draw a dot plot for each data set. 1) Games per World Series 4 4 4 4 5 5 5 6 6 7 7 7 7 7 7 7 7 Age Assumed Office 2) Senator Age Mary Landrieu 41 Mike Crapo 47 John Cornyn 50 Senator Age Jon Tester 50 Tim Johnson 50 Jeff Sessions 50 Senator Age Mike Enzi 52 Dick Durbin 52 Bob Menendez 52 Senator Age Barbara Boxer 52 Sherrod Brown 54 John Barrasso 54 Senator Age Lamar Alexander 62 Richard Blumenthal 64 Angus King 68 Draw a stem-and-leaf plot for each data set. 3) Annual Precipitation (Inches) 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 10 -1©j U2n0[1d5w RKZu\tYaz vSLoVfEt[wia_rAeB yLzL_CY.N \ NAnlSlb ertisgThLtisG DrJePsterrjvieQdp.R U cMyavdAeq [wtiotthd ZIOnnfaiHnhiVtTer gPVrWex-[AplSgxeZbGrBaL. Worksheet by Kuta Software LLC 4) Per Capita Income Country US $ Central African Rep. 604 Country Uzbekistan Djibouti Yemen Laos Rep. of Congo 5,867 Mongolia 9,433 Grenada 11,498 2,998 3,958 4,812 US $ 5,167 Country Maldives US $ 11,654 South Africa 12,504 Botswana 15,675 Gabon 19,260 Country Chile US $ 21,911 Japan 36,315 Belgium 40,338 United Arab Emirates 58,042 Draw a box-and-whisker plot for each data set. 5) Test Scores 6) 37 38 39 44 44 45 46 47 47 47 47 48 51 52 52 53 54 Life Expectancy State Arkansas New Mexico Alabama Louisiana Wyoming Kansas Maine Hawaii Years 74.2 77.7 78.1 78.2 78.4 78.6 79.1 79.7 State Wisconsin Washington Colorado Indiana Nevada Pennsylvania Florida Massachusetts Years 79.8 80.3 80.9 81.3 81.3 81.6 81.7 83.8 11 -2©c q2]0d1M5Y YKFuut^ad QS`ovfftmwWaHrceB kLTLSCr.h P yAQl_lo srUi\gjhTtOsP NrZe_stesrLvleldx.` u JMnabdsef Hwii[tahs FIRncfgilnqiFtMey zPzrzem-yAfl^gFepbIrMaT. Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 1 Name___________________________________ Visualizing Data Date________________ Period____ Draw a dot plot for each data set. 1) Hits in a Round of Hacky Sack 2 3 4 5 5 5 5 6 7 7 7 7 8 13 2) 6 Hours Slept 7 4 6 7 9 7 6 7 6 8 7 7 6 7 6 5 Draw a stem-and-leaf plot for each data set. Nobel Laureates 3) Name Age Rudolf Ludwig Mössbauer 32 Wolfgang Ketterle 44 Joseph Leonard Goldstein 45 Aung San Suu Kyi 46 Kenneth Joseph Arrow 51 Barry James Marshall 54 Name Age Stanley Ben Prusiner 55 Torsten Nils Wiesel 57 Richard Axel 58 Robert Coleman Richards 59 James Alexander Mirrlees 60 Name Age Robert Merton Solow 63 Stanley Cohen 64 Peter Mansfield 70 Vernon Lomax Smith 75 Richard Fred Heck 79 Large US Cities 4) City Boston Population 617,594 Gilbert Stockton Austin 208,453 291,707 790,390 City Seattle Richmond Scottsdale Portland Population 608,660 204,214 217,385 583,776 City Irving Population 216,290 Santa Ana Fort Worth San Francisco 324,528 741,206 805,235 City Population Washington DC 601,723 Columbus Aurora 787,033 325,078 Draw a box-and-whisker plot for each data set. Minutes to Run 5km 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 12 -1©N [2t0j1t5a aKjuPtYa` \SxoZfctmwdaprJeZ jLTLeCm.i ] bAilclX PrPiEgJhsttsJ irBedsxearGvfe]d_.M W nMsa[duei dw\iztMhy wI[n[foimnBimtzew jAolUgWeRbFruaR Z1p. Worksheet by Kuta Software LLC 6) Age At Inauguration President Calvin Coolidge Age 51 Lyndon B Johnson Gerald Ford Theodore Roosevelt 55 61 42 Martin Van Buren 54 President Age James Madison 57 President Barack Obama Millard Fillmore Zachary Taylor James K Polk Chester A Arthur Grover Cleveland Harry S Truman 50 64 49 Age 47 51 55 60 President William McKinley James A Garfield William Howard Taft Abraham Lincoln Age 54 49 51 52 Draw a histogram for each data set. Average Time to Maturity 7) Plant Days Mesclun 40 Spinach 44 Endive 47 8) Plant Days Turnip 55 Swiss Chard 60 Kale 60 Plant Days Romano Pole Bean 60 Yukon Gold Potato 65 Cantaloupe 80 Plant Days Sweet Potato 90 Brussel Sprouts 90 Celery 95 Plant Tomatillo Gooseneck Gourd Pumpkin Days 100 120 120 Average Lifespan Animal Lion Cottontail Teal Years 35 10 20 Animal Chinchilla Bee (Queen) Congo Eel Years 20 5 27 Macaw Painted Turtle Asian elephant 50 11 40 Pheasant Prarie Dog Nutria 18 10 15 Grouse Rhinoceros 10 40 Flying Squirrel Pionus Parrot 14 15 13 -2©y G2X0z1^5A cKsuQtNaB lSBoTfftWwIaVrje` SLEL[CW.V ] YAxlxlt krdiSgvhitks` brWeIsqerrNvSeDdt.M r FMWa[dGeV wwYiQtphT MIMnwfSi[nSiQtiek qA`ljgBeVbxrYaf N1M. Worksheet by Kuta Software LLC Name Class Date Practice Form G 12-4 Box-and-Whisker Plots 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 14 Name Class Date Practice (continued) Form G 12-4 Box-and-Whisker Plots 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 Dipak’s: 93 79 78 82 91 87 80 99 Kiera’s: 17 50 26 39 6 49 62 40 8 Paul’s: 18 47 32 28 12 49 60 28 15 15 Name: ___________________________ Period:_____ Date: __________ Score:__________ ID: A 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. Use the box-and-whisker plot to answer the following question(s). 2. Find the median age of the clerks. 6. What is the median of the test scores of Class I? 3. Find the upper extreme of the data. 7. What is the median of the test scores of Class II? 4. Find the range of the data. 8. What is the difference of the median of the test scores of the two classes? 5. Find the lower quartile of the data. 1 16 ID: A 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% c. about 25% scored higher; about 75% scored lower scored lower b. about 75% scored higher; about 50% d. about 50% scored higher; about 50% scored lower scored lower Use the following data to answer the following questions. Evaluate the expression for the given values of the variables. 16, 22, 14, 12, 20, 19, 14, 11 13. 2v 3u, v 11, u 8 10. Find the range. Evaluate the expression. 11. Find the median. 14. 24 6 2 12. What is the median of the data shown in the stem-and-leaf plot? 2 17 15. 14 15 16. 6 ( 8) 17. 48 8 Name 5-7 Class Date Practice Form G Scatter Plots and Trend Lines 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? 20 Name 5-7 Class Date Practice (continued) Form G Scatter Plots and Trend Lines 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? 21 Kuta Software - Infinite Pre-Algebra Name___________________________________ Scatter Plots Date________________ Period____ State if there appears to be a positive correlation, negative correlation, or no correlation. When there is a correlation, identify the relationship as linear or nonlinear. 1) 2) 3) 4) 5) 6) 22 Worksheet by Kuta Software LLC -1- ©F C2T0h1K5W LKsuitOa] hSToafztTwJazrdeB VLpLRCJ.\ ] tAsl`lV lr_iJgZhGtLsL Ur]e[szeCrlv_ekdl.I ] pMCa_dEes cwKiDtjhF uIunDfWiEnKiwtAeo zPcrUeB-]AUlSgGesbgrGaO. Construct a scatter plot. 7) XY 300 1 XY 1,800 3 800 1 1,100 2 1,600 2 3,400 3 4,700 4 6,000 4 1,700 2 8,500 6 8) X Y 0.1 7.5 X Y 0.4 3.3 X Y 0.6 1.8 0.1 7.6 0.3 4.5 0.4 3.2 0.6 1.4 0.6 1.7 0.9 1.5 1 1.7 Construct a scatter plot. Find the slope-intercept form of the equation of the line that best fits the data. 9) X Y 10 10 30 30 X Y 40 300 60 200 70 100 700 800 400 500 10) X Y X Y 70 100 80 100 100 200 1 2 3 4 20 40 50 60 X 5 6 7 Y 70 80 80 X 7 9 10 Y 80 80 80 23 Worksheet by Kuta Software LLC -2- ©A f2q0H1E5` UKDuOtyaZ ASioof\tRwaa[rqeT PLCLnCm.S C jAJl^lB QrwiVgShmtisb lrAeUsmecrrvXezdF.P y SMua]dLeB mwGift`hX SInnBfUimnci[tcee mPBrfe`-XAtlBgNeibNrjaU. Kuta Software - Infinite Algebra 1 Name___________________________________ Scatter Plots Date________________ Period____ State if there appears to be a positive correlation, negative correlation, or no correlation. When there 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, or no correlation. When there is a correlation, identify the relationship as linear, quadratic, or exponential. 5) X Y 1,000 1,300 2,000 1,500 3,000 2,000 X Y 5,000 2,500 7,000 3,600 7,000 3,700 3,000 2,000 4,000 2,400 9,000 4,200 10,000 5,200 6) X Y 140 500 150 1,000 170 300 X Y 280 900 450 500 450 500 180 270 100 200 770 400 910 600 24 Worksheet by Kuta Software LLC ©c s2S0A1I5J BKbuztgaF kSmoAfitcwaabrvet XLELdCX.L V fAMlTlq IrIi]gEhGtYsL `r`egsweArwvOeXdY.I T [M^aPdoeg vwpiQtohM nIunZfHi^nciXtKei dAtlWgmeVbzrYaF j1d. Kuta Software - Infinite Pre-Algebra Name___________________________________ Using Statistical Models Date________________ Period____ 1) The height and weight of adults can be related by the equation yx where x is height in feet and y is weight in pounds. Weight (pounds) 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 the average daily temperature for that day. This relationship is given by yx where x is the temperature in °F and y is the amount of electricity consumed in kilowatt-hours (kWh). Electricity (kWh) Temperature (°F) a) What does the slope of the line represent? b) What does the y-intercept of this function represent? 26 Worksheet by Kuta Software LLC -1- ©f V2V0R1A5l CKNuRtZaF gSzoDf]txwraJrMeb OLGLECo.k O GAElolf _rwi_gWhAtGsj MrheJsHeErDv_edds.Z d ZMNazdEeL ew^iktrhW QIsntfUienHixtWeN PPkrZer-sAdlpgPekbIruad. 3) The number of marriage licenses issued by Clark County Nevada, the county where Las Vegas is located, has been decreasing since the year 2000: This can be modeled by the equation yx where x is the year and y is the number of marriage licenses issued. 2006 2007 2010 127,000 121,000 111,000 2011 2012 109,000 104,000 Marriage Licenses Year Marriage Licenses 2001 141,000 Year a) According to the model, how many marriage licenses were issued in 2004? Round your answer to the nearest hundred. b) Using this model, how many marriages licenses would you expect to be issued in 2023? Round your 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 in Cameroon have been able to produce more and more grain per hectare each year. Here are the crop yields for several years: The crop yield can be described by the equation yx where x is the year and y is the grain yield in kilograms per hectare (kg/ha). Year Yield (kg/hectare) 1962 656 1969 728 1974 846 Yield (kg/hectare) 1980 2000 2004 1,100 1,480 1,540 Year a) According to the model, what was the crop yield in 1988? Round your answer to the nearest whole 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? Round your answer to the nearest year. 27 Worksheet by Kuta Software LLC -2- ©d c2C0K1G5J QKZuytDav ES^o[fMtYwJabrCeX xLnLYCw.^ ` aAUl^lO ZrXiLgdhwtFsH zrAe\sPeZrvv_eFdj.z p XMXaSdkeB kwBi_tVhN bIonifeilnVivtSeh kPQrZed-SA]legqe]bLrqaT. Kuta Software - Infinite Algebra 1 Name___________________________________ Using Statistical Models Date________________ Period____ Oysters (metric tons) 1) The oyster population of the Chesapeake Bay has been in decline for over 100 years. This can be x expressed by the equation y where x is the number of years since 1900 and y is the amount of oysters harvested in metric tons. Years since 1900 What does the y-intercept of this function represent? 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 wind speed are related in the following way: yx where x is the air pressure in millibars (kPa) and y is the maximum sustained wind speed in knots (nautical miles per hour). Wind Speed (knots) 2) The Hurricane Hunters took the following measurements from a hurricane over several days as it developed: 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 wind speed? Round your answer to the nearest knot. c) The model indicates that a wind speed of 110 knots is associated with what air pressure? Round your answer to the nearest millibar. 28 Worksheet by Kuta Software LLC ©o x2w0I1`5w sKvuvtEaW rSRoZfrt[wAamrfex RLsLTCu.n s _AblBle JrpisgahLtVsG zrReXshelrcvZelde.x C \MraRdaeP vwtijt`hg yI^nsfpilntiWtHeq mAUlUgaeAbErbaE i1P. 3) The time for the fastest runner for their age in the Marine Corps Marathon is given for several ages: This can be modeled by the equation yx x where x is the age and y is the number of minutes taken. Age Time (minutes) 17 196 149 149 174 50 55 173 182 Time (minutes) 30 35 47 Age (years) a) Using this model, what would be the time for the fastest 41-year-old? Round your answer to the nearest hundredth. b) According to the model, what would be the time for the fastest 83-year-old? Round your answer to the nearest hundredth. c) What age(s) correspond to a time of 171 minutes? Round your answer(s) to the nearest tenth. This can be modeled by the equation yx where x is the corruption score and y is GDP per capita in dollars. GDP Per Capita ($) 4) Economists have found that the amount of corruption in a country is correlated to the productivity of that country. Productivity is measured by gross domestic product (GDP) per capita. Corruption is measured on a scale from 0 to 100 with 0 being highly corrupt and 100 being least corrupt: Corruption Score GDP Per Capita ($) 18 2,850 24 4,050 33 3,740 45 60 65 10,100 25,000 25,000 Corruption Score a) According to the model, what would be the GDP per capita of a country with a corruption score of 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 Worksheet by Kuta Software LLC ©q V2d0y1q5g kKouYtvaP LS`oDfotFwkaarqeW fLILgCa.e K cAllrlR grPiDgWhotws] frTeisEekrIvMeHdM.S O yMFa[dpel ZwRiItahD YIKn]fjiJn\iYtfeb gAPlDgAeIbhrDaS B1h. Name Class Date Practice Form G 12-7 Theoretical and Experimental Probability 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 . What is the 6 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? 32 Name Class Date Practice (continued) 12-7 Theoretical and Experimental Probability 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? 33 Form G Name Class Date Practice 12-8 Probability of Compound Events 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) 34 Form G Name Class Date Practice (continued) Form G 12-8 Probability of Compound Events 19. The probability that Bob will make a free throw is 2 . What is the 5 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? 35 Kuta Software - Infinite Algebra 2 Name___________________________________ Probability with Combinatorics Date________________ Period____ 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? -1- Worksheet by Kuta Software LLC ©O h2p0D1u5K ]KduRtuaY vSloefetGw[a]rNeF NLMLWC^.d w _ATlZlc qrKiKgshttXsB BryeusUeHrqvaeldS.i q DMba[ddeV ]wDiptvhc CIgnefsicnXiwtyeF NALlGgkeXbrrbaW `2p. 36 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? -2- Worksheet by Kuta Software LLC ©\ ]2O0T1s5y eKluCtEar NS_odfwtIw[airBeN GLBLzC_.N f gATlMl[ lr]ijgShdtfsN Vrme_seeUrmvResdI.w C ZMDaWdQew EwfiMtGhr _IinRfPionSibtmeS BABlqg^eubsrPay R2H. 37 Name Class 3-1 Date Practice Form G Inequalities and Their Graphs 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 a. 3 b. 2 c. 10 3n 8. 2 4 Graph each inequality. 9. y < 2 10. t ≥ 4 11. z > 3 12. v ≤ 15 13. 3 ≥ f 5 14. c 3 38 Name 3-1 Class Date Practice (continued) Form G Inequalities and Their Graphs 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. 39 Kuta Software - Infinite Pre-Algebra Name___________________________________ Inequalities and Their Graphs Date________________ Period____ Draw a graph for each inequality. 1) x 2) m 3) x 5) a 6) x 7) b 8) x 9) r 10) n 11) n 12) x 4) m 13) n 14) k ©H G2c0C1a2r zKluUt8ac oSwoTfXtfwTa0rKec BLjL3Cl.y k xAWlBlf grDiWghhYthsv yrIeHsPezrPv5eddj.q R GMZaLdQeo Pw8ittDhW EIbnifRi5nFiWt3eK UP9r4eF-KAulmg9edbJrma4.0 40 -1- Worksheet by Kuta Software LLC 15) p 16) n 19) n 18) n 17) x 20) v Write an inequality for each graph. 21) 22) 23) 24) 25) 26) 27) 28) ©C 2200j1I2a EKmuxtgaa IStoafOtJwPa2r1ez 1LmLlCM.z 7 LA1lvlp wrYiTg1hPtDsF 9ryeosHezrOvveZdL.f X UM3a1dJen nw8iNtihP 1I5ngfiilnIiktEej IPDrKeF-7AElXgweRbvrfaa.5 41 -2- Worksheet by Kuta Software LLC Name Class 3-2 Date Practice Form G Solving Inequalities Using Addition or Subtraction State what number you would add to or subtract from each side of the inequality to solve the inequality. 1. x 4 < 0 3 2. 4. x + 3 ≥ 0 2 5. 5 4 7 5 3. 6.8 ≤ m 4.2 5 6. 3.8 > m + 4.2 S 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. C 4 7 6 7 1 1 2 2 14. p 1 1 42 Name Class 3-2 Date Practice (continued) Form G Solving Inequalities Using Addition or Subtraction Solve each inequality. Justify each step. 15. y 4 + 2y > 11 1 16. 7 2 17. 3 v 7 9 0 19. 4y + 2 3y ≤ 8 d 1 2 7 18. 2p 4 + 3p > 10 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? 43 Name Class 3-3 Date Practice Form G Solving Inequalities Using Multiplication or Division Solve each inequality. Graph and check your solution. x 1. 3 4 3. 6 5. w 1 2. 4 p 1 2 2 3 1 4. 1 x 6 2 3 y 2 k 3 . 8. 3t < 12 7. 3m > 6 9. 18 ≥ 6c 10. 3w < 21 11. 9z > 36 12. 108 ≥ 9d 44 Name 3-3 Class Date Practice (continued) Form G Solving Inequalities Using Multiplication or Division Solve each inequality. Graph and check your solution. 13. 2.5 > 5p 1 14. 2 15. 3 n4 t 6 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. 45 Kuta Software - Infinite Algebra 1 Name___________________________________ Two-Step Inequalities Date________________ Period____ Solve each inequality and graph its solution. 1) x m 2) 3) ( p) 8) (r) 10) ( p) 11) x 9) x 6) (n) n 7) 4) ( x) 5) b 12) ©2 C2V0g1M2y IKOu3t2aj PSsoHfStAweaKrGeh zLrL5C2.4 1 zAal1le zrfi0gCh3tusu frbeOsXexr8v3e9d8.i C lMhaIdYeB xwSi4tbhh IIAn3fCipn8i8tJew yApl5gieebVraai v1d.U a 46 -1- Worksheet by Kuta Software LLC 13) 15) x ©d Q2o0X1F2f GKuuItXau sSroqfRtSwLarr5e5 ALWLeCb.R y xAelxlf ArpiLgohwtRsL SrHeZsHeDrUvyeKdO.M c fMuaydhez HwUiitIh7 qIZnafpirnCi0ties 5AYlagaerbhrlah 61g.o m 24) r 22) x 23) 20) b 21) (v) 19) n 18) 16) (k) n n 17) 14) (n) v 47 -2- Worksheet by Kuta Software LLC Name 3-4 Class Date Practice Form G Solving Multi-Step Inequalities 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 48 Name Class 3-4 Date Practice (continued) Form G Solving Multi-Step Inequalities 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. 49 Kuta Software - Infinite Pre-Algebra Name___________________________________ Solving Multi-Step Inequalities Date________________ Period____ Solve each inequality and graph its solution. 1) n 2) x x 5) kk 6) p 7) a(a) 4) nn 3) x 8) x( x) ©C w240N172X YK7uBtSa4 xSootfstTwzasrjeQ 1L0LMCP.8 0 HAblplC mrLilglhttWsU yrUejspeCrivKe0dO.e J IMaa0dxex qwciJtKhp 6I0nSfKiIn2ihtleb QPRrlec-HANlUgaeFbHrmaN.n 50 -1- Worksheet by Kuta Software LLC 9) (n)n 10) (b)bb 11) n(n) 16) (k)(k)kk 17) ( x)( x) x x 14) n(n) 15) (b)(b) 12) ( p) p 13) x( x) 18) (r)rr(r) ©n h2L0W1k2y WKLuKtPaQ GS5oQfattwhaqrYej bLRLOCx.H d tAvlUld sr3iCgRh6tQsk GrMedsVe0rHvze1ds.C 2 yMMa0dZez Dwki9tghD pIkncfti9n0iIt9eQ fPZr3eF-pARlvgkeSbMraa4.O 51 -2- Worksheet by Kuta Software LLC Infinite Algebra 1 Name___________________________________ Multi-Step Inequalities Date________________ Period____ Solve each inequality and graph its solution. 1) nn 2) x x 3) p p 10) (r) 11) x x x x 8) (b) 9) (r) 7) (n) 6) ( x) 4) kk 5) m 12) x x ©f 12i0X1J2S zK9uOtiax rS7omfitewSavr8eW OLSLsCN.c 0 UAXljlz aroi1g6hjtEs3 Zrueas3eyr6voeDd7.l Z dMFavdEeh UwfiktThO uI8n1fViOnwiftbed qAZl9gaeJb5r1a9 D18.8 52 -1- Worksheet by Kuta Software LLC 13) aa 14) vv 17) n(n)n 20) x( x) 22) ( x)( x) 23) ( x) x 21) (k)(k) 18) ( p) p p 19) k(k) 16) x x( x) 15) nnnn 24) (n)(n) ©8 s2k0q1R2G xKYu8twar eSLo9fVtww7abrBeS nLbL1CA.w P eA1llli creiQgGhdtYsd 4rYe3sfeBrcvqecdB.K b eMXaRdueX bwUi3tnhu MI7n1fZiLnKi7tjeo MANlkgMeIb8r1a0 m1Z.Y 53 -2- Worksheet by Kuta Software LLC Name Class 3-6 Date Practice Form G Compound Inequalities 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. 3 9. 3d + 3 1 or 5d + 2 12 10. 9 c < 2 or 3c 15 4 y + 2 3(y 2) + 24 12. 5z + 3 < 7 or 2z 6 8 11. 11 k 3 4 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. 56 [25, 50) Name Class 3-6 Date Practice (continued) Form G Compound Inequalities 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 29. y2 2 5 3or 1 2y 3 41 28. 3 0.25v 2.5 30. 3 2 5 6 w 3 2 4 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? 57 Name Class Date Practice 3-7 Form G Absolute Value Equations and Inequalities Solve each equation. Graph and check your solutions. 1. b 2 2. 10 = |y| 3 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 10. 2 m 2 8. |c + 3| = 15 9. 1 = |g + 3| 11. 2|3d| = 4 12. 3|2w| = 6 14. 3|d 4| = 12 15. |3f + 0.5| 1 = 7 3 13. 4|v 5| = 16 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. 2t 2 3 58 4 Name Class Date Practice (continued) 3-7 Form G Absolute Value Equations and Inequalities Solve each equation or inequality. If there is no solution, write no solution. 24. |d| + 3 = 33 25. 1.5|3p| = 4.5 26. d 2 3 27. f 1 5 3 15 30. 1 |c + 4| = 3.6 28. 7|3y 4| 8 48 31. y 3 0 4 29. |t| 1.2 = 3.8 32. |9d| 6.3 3 4 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. 59 Kuta Software - Infinite Algebra 2 Name___________________________________ Absolute Value Inequalities Date________________ Period____ Solve each inequality and graph its solution. 1) n 3) m 5) 9) 6) m 8) n x 7) r 4) x x p 2) 10) 12) v 13) p x 11) b 14) x ©G E290m1m2q FKDu5tCau 9SVoEfCt3wVakrCe9 ILVLyC9.4 7 vANlkla sr7iFgxhbtPsP Kr9ensZekrnvcexdA.P G bMPapdhe8 lwViOt5hw zIznvfLidnbimtre3 mAzlYgreRbdrwaY c2H.p 60 -1- Worksheet by Kuta Software LLC 15) a 16) k 17) m 20) 21) b 24) n 25) x 22) v 23) a n 18) x 19) r 26) n ©0 b2g001w2F DKeuztiar YSZonfbtVw7a5rieR zLZL1Ch.u k FA7lBlH IraiBgChAtosQ 0r7eBsIearzvKerdi.l J EMXaadVem FwwiWtehE OIknkfJiPnSi8tdex lABlsggeWbZr9aY W2m.J 61 -2- Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 1 Name___________________________________ Absolute Value Equations Date________________ Period____ Solve each equation. 1) 6m = 42 2) −6 x = 30 3) k − 10 = 3 4) 5) 7 + p = 7 6) −3 p = 15 7) 7 n = 56 8) 9) −3 p = −12 a−5 8 12) −9 + v 8 16) =3 x 7 =5 x − 8 = −7 7 18) −10 v + 2 = −70 =3 ©L m2L0a1s24 lKsuAtsaB JSqoffYtnwMarrvef wLFLHC2.U w PAclFlr or1iigRhntpsS 0rMeashe5revQeIdg.X s 5MLaEdceN swqiztdh1 uIfnpfniIngiDtZef vAblqg3edb3rKa8 Q1L.Q 5 14) 4 n + 8 = 56 =5 15) 7m + 3 = 73 17) m 10) m + 2 = 11 11) n + 1 = 2 13) x =3 7 62 Worksheet by Kuta Software LLC Name 6-5 Class Date Form G Practice Linear Inequalities Graph each linear inequality. 1. x ≥ 4 4. 4x + 5y < 3 7. 3x 5y > 6 2. y < 2 3. 3x y 6 5. 3x + 2y > 6 6. y < x 8. x y 9 9. 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. 65 x 4y 3 4 Name Class 6-5 Date Form G Practice (continued) Linear Inequalities 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. x 1 y 3,(9,12) 2 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? 66 Kuta Software - Infinite Pre-Algebra Name___________________________________ Graphing Linear Inequalities Date________________ Period____ Sketch the graph of each linear inequality. 1) y x 2) y x y x x x 4) x y y 3) y x y x ©6 F2D0s1N2z eKtubtCaT wSLoQfktdwZa9rgeQ uLyLRCN.B F 7ANlQl5 zrsilgShctvsI BrneNsWeRrUvIeQdb.u T dM0a4d5ei ywfi5tQhg eIYnufMiunbi7tyeB rPSrEeZ-hAYlLgveKbtrwaZ.f 67 -1- Worksheet by Kuta Software LLC 5) y x 6) y x y x 7) x y x x 8) x y y y x ©L N2V0h1J2H cKxuptDa2 NSLozfptSwSa1rVex FLwLdCD.o E JAZlvlI frHixgYhut8sL CrZeusCe3rrvTeQdT.C j XMXaRdWeH 8wrietahH HIOnyfMiVnmiMtSeV lP4rveb-RAEl6gcembArNaH.Z y 68 -2- Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name___________________________________ Graphing Linear Inequalities Date________________ Period____ Sketch the graph of each linear inequality. 1) y x 2) y x 3) x 4) y x 6) y x 5) y x ©D 62e0m1335 IK2ugtFaU QS1oefwttw8aXr8ek jLwLLCT.u c SAVl7lE frAiygLh0tLse JrseYsKenrvvweodX.9 r AMgaod2ek RwMiRtUhp 0Ixn7f4iynRiytQew qA4l4g0eBb4rwa0 x2z.J 69 -1- Worksheet by Kuta Software LLC 7) x y 8) x y 10) x y 9) y 11) x y 12) x y Critical thinking questions: 13) Name one particular solution to # ©K e210f1o35 zKcu7t2aY fScoxfFtTwyaPrhey JLdL5Ca.T x IAjljlj ZrUiSgchptNsF 1rxeMsweQravPefdJ.m Y iMqapdpeK TwEi2tBhq bIKn3f6iSnliztqee 2AWligYesbdrMa3 226.p 14) Can you write a linear inequality whose solution contains only points with positive x-values and positive y-values? Why or why not? 70 -2- Worksheet by Kuta Software LLC Name 6-6 Class Date Practice Form G Systems of Linear Inequalities Solve each system of inequalities by graphing. 1. 3x + y ≤ 1 xy≤3 2. 5x y ≤ 1 x + 3y ≤ 2 3. 4x + 3y ≤ 1 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. xy≥3 y < 2 x≥1 Determine whether the ordered pair is a solution of the given system. 7. (0, 1); 1 x ≥ 3y 3y 1 > 2x 9. (1, 4); 8. (–2, 3); 2x + 3y > 2 2x + y > 3 –3x y ≤ 5 3x + 5y > 1 71 Name 6-6 Class Practice (continued) Form G Systems of Linear Inequalities 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 x + 3y < 1 15. Date 14. x + 4y 2 ≥ 0 2x y + 1 > 2 x 5 6 y 2 3x + y > 2 72 Kuta Software - Infinite Algebra 2 Name___________________________________ Systems of Inequalities Date________________ Period____ Sketch the solution to each system of inequalities. 1) y > 4 x − 3 y ≥ −2 x + 3 −5 −4 −3 −2 2) y ≥ −5 x + 3 y > −2 5 5 4 4 3 3 2 2 1 1 −1 0 −1 1 2 3 4 5 −4 −3 −2 −4 −3 −2 −1 0 −1 −2 −2 −3 −3 −4 −4 −5 −5 3) y < 3 y ≤ −x + 1 −5 −5 1 2 3 4 5 1 2 3 4 5 4) y ≥ x − 3 y ≥ −x − 1 5 5 4 4 3 3 2 2 1 1 −1 0 −1 1 2 3 4 5 −5 −4 −3 −2 −1 0 −1 −2 −2 −3 −3 −4 −4 −5 −5 ©j M230g1q1C QK8uWtKaB CSQovfWt0wka9rTeY 0LlLFCg.1 m WAIlFlT hrhisgRhTtRsz Yr2eLsAemrnvPeSdg.6 0 nMnaad5eC LwjiXtyhr rIZnQfJiOnKiHtRe9 4A4lcgiepbCrAaX p2a.H 73 -1- Worksheet by Kuta Software LLC 5) x ≤ −3 5 x + 3 y ≥ −9 −5 −4 −3 −2 6) 4 x − 3 y < 9 x + 3y > 6 5 5 4 4 3 3 2 2 1 1 −1 0 −1 1 2 3 4 5 −4 −3 −2 −4 −3 −2 −1 0 −1 −2 −2 −3 −3 −4 −4 −5 −5 7) x + y > 2 2x − y > 1 −5 −5 1 2 3 4 5 1 2 3 4 5 8) x + y ≥ 2 4 x + y ≥ −1 5 5 4 4 3 3 2 2 1 1 −1 0 −1 1 2 3 4 5 −5 −4 −3 −2 −1 0 −1 −2 −2 −3 −3 −4 −4 −5 −5 ©k j23031B1a mKhudteac BSBoAfJtlwvaRrxe3 FLALsCO.S W vAJlvlR NraiNgWhpt8ss ErveIsDeNrHvAeidv.Y B jMHa5d5ez CwgintAh1 RItnAfIiQn5ijtdeH tAflvghesbXrIa5 52H.h 74 -2- Worksheet by Kuta Software LLC 9) 4 x + 3 y > −6 x − 3 y ≤ −9 −5 −4 −3 −2 10) y < −2 x+ y≥1 5 5 4 4 3 3 2 2 1 1 −1 0 −1 1 2 3 4 5 −4 −3 −2 −4 −3 −2 −1 0 −1 −2 −2 −3 −3 −4 −4 −5 −5 11) 3 x + y ≥ −3 x + 2y ≤ 4 −5 −5 1 2 3 4 5 1 2 3 4 5 12) x + y ≥ −3 x+ y≤3 5 5 4 4 3 3 2 2 1 1 −1 0 −1 1 2 3 4 5 −5 −4 −3 −2 −1 0 −1 −2 −2 −3 −3 −4 −4 −5 −5 Critical thinking questions: 13) State one solution to the system y < 2x − 1 y ≥ 10 − x ©y 32P0J1d1w PKTupt9aj BSzoqfytZwOa4reeD TLkLSCI.m y AAkl4l4 RrriugPhItDsu jrfe8sPeZrzvleCd2.B L FMjaXd4eE Qw5ihtrhL yIbn1fZiDn4ictfea lAFlggre6borYaS I2k.b 14) Write a system of inequalities whose solution is the set of all points in quadrant I not including the axes. 75 -3- Worksheet by Kuta Software LLC 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 customblended, 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
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