MAT130 Coursepack.SPR2023 - Tagged

Table of Contents MAT130 Worksheets p. 5-58 Unit Reviews p. 59-112 MAT040 Worksheets p. 113-160 3

MAT130 Worksheet 1.1 Name: 3. The following sale was found in Harbor Freight's Thanksgiving sale flier. Is it correct? Show all your work and explain your reasoning. 6

MAT130 Worksheet 1.2 B Name: 1. The following data represents the success rate of Quantitative Reasoning students by semester. Make a bar graph of the data. 2. Explain why you cannot make a pie graph of the data. 9 MAT130/130A Semester % Successful 16/FL-17/SP 72.61% 17/FL-18/SP 69.50% 18/FL-19/SP 58.71% 19/FL-20/SP 71.97% 20/FL-21/WN 56.23%

MAT130 Worksheet 1.4 Name: Show all your work to receive full credit. 1. The one of the two most expensive Lego cost $799.99. The AT-AT (75313) is one of those sets and has 6785 pieces. (source: https://www.lego.com/en-us/product/at-at-75313) a. Write two conversation factors: dollars to pieces and pieces to dollars. b. Write a unit of dollars per piece and a unit rate of pieces per dollar. c. The World Map (31203) has 11695 pieces, calculate its price using your one of your unit rates from question b. d. The World Map costs $249.99. How many pieces would we expect it to have using one of the unit rates from question b. 12

MAT130 Worksheet 1.6 Name: Show all your work to receive full credit. 1. According to http://usdebtclock.org/2012.html the US national debt on 6/1/2016 was approximately $ 1.96279 x 10 13 . On 6/1/2021 the US national debt was $ 2.83545 x 10 13 . a. Find the actual change between the two years. Write the final number in decimal notation. b. Find the relative change between the two years. c. Explain the change in the context of the situation, using words to state the number. d. Explain the relative change in the context of the situation. 15

MAT130 Worksheet 2.2 Name: 3. The following table contains the wins for the Detroit Lions from 2007 to 2017. a. Let x=the number of years since 2007. Fill in the table b. Draw a scatterplot using desmos or excel. Paste the graph here or submit a link/file to jetnet. 18 Year x Wins 2007 7 2008 0 2009 2 2010 6 2011 10 2012 4 2013 7 2014 11 2015 7 2016 9 2017 9

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MAT130 Worksheet 2.5 Name: 1. The following data is from one of Erik Brown’s Fall 2018 MAT130 classes. a. Find the line of best fit. Round to 2 decimal places. b. State the correlation coefficient. Round to 2 decimal places. c. Identify the slope and interpret it in the context of the situation. d. Identify the y-intercept and interpret it in the context of the situation. e. Do the parameters provide useful information when predicting exam 1 grades from % attendance? Why? 22 % Attendance Exam 1 Grade % 100 76 100 91 100 89 100 84 100 85 100 33 100 83 100 87 100 42 95 94 95 67 95 94 95 85 95 71 90 90 90 82 86 26 86 62 86 91 76 45 76 60 67 78 67 25 62 36

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MAT130 Worksheet 2.6 Name: State whether the graph is exponential or linear. Identify the slope or the growth factor and the y-intercept from each. Write a sentence in context for each. 1. Using the graph at right fill in the table and answer the questions below. a. What type of growth is displayed by the graph at right? How do you know? b. Make a table of values using the graph. c. Find the slope if linear and the growth/decay factor if exponential. d. Write your answer to letter c in context. e. Find the y-intercept of the graph. f. Write your answer to letter e in context. 2. Using the graph at the right fill in the table and answer the questions below. 24 Time Height

a. What type of growth is displayed by the graph at right? How do you know? b. Make a table of values using the graph. c. Find the slope if linear and the growth/decay factor if exponential. d. Write your answer to letter c in context. e. Find the y-intercept of the graph. f. Write your answer to letter e in context. 25 x y

MAT130 Worksheet 2.6 Name: 3. You have $500 to invest for 10 years. You find an investment that pays 15% interest. a. Write an equation to model the situation. b. How much money is in your account after 10 years? c. Use your model and desmos/calculator to find when you will have $10,000 in the account. 4. The equation y = 10,000 ( .89 ) x models the value of your car after x years. a. Identify the growth/decay factor. b. Identify the growth/decay rate. c. Interpret the rate/factor in the context of the situation. d. Use a calculator/desmos to determine when your car is worth $1000. 5. The table represents the percent of the U.S. population that is foreign-born. Let t =then number of years since 1970. a. Find a regression equation the best models the data. Explain your choice. Round to 2 decimals places. 26 Year t % U.S. pop. foreign-born 1970 4.70% 1980 6.20% 1990 8.00% 2000 10.40% 2010 12.80%

b. Identify the y-intercept and interpret in the context of the situation. c. If it was exponential identify the growth factor, if it was linear identify the slope. Interpret your answer in the context of the situation. d. Predict the percent of the U.S. population that is foreign-born in 2016. e. According to www.pewresearch.org , the percent of the U.S. population that is foreign-born in 2017 was 13.6%. Calculate the relative error from your answer to d and the actual amount. 27

MAT130 Worksheet 2.8 Name: 1. According to www.treasurydirect.gov , the national U.S. historical debt outstanding is shown in the table. a. Let t = years since 1950. Complete the table for t . b. The debt is in really, large annoying numbers to type in your calculator. Rewrite the debt in terms of billions rounded to the nearest billion. c. Find a regression equation that best models the data. Round to 2 decimal places. d. Identify the parameters of your equation and explain both in the context of the situation. e. Predict the total U.S debt outstanding debt in 2025. 28 Year t Debt Debt (in billions) 1950 257,357,352,351.04 1951 255,221,976,814.93 1967 326,220,937,794.54 1984 1,572,266,000,000.00 1998 5,526,193,008,897.62 2012 16,066,241,407,385.80 2018 21,516,058,183,180.20

2. The number of architects employed in Indiana since 2007 is listed in the table below. Year x=years since 2007 Number of Architects 2007 1460 2009 1280 2011 1010 2013 950 a. Find a linear and exponential model for the data. b. Which model is best? Explain your choice. c. Use your model to predict the number of architects in 2012. d. Use desmos/calculator to predict when the number of Architects will be 500. Draw a rough sketch of the graph you used. 29

MAT130 Worksheet 3.1 Name: 1. Your relative was in desperate need of cash and asked you to loan them $2000. To avoid losing the case on Judge Judy (in the event they failed to repay you) you write a contract charging your relative 5.6% simple interest per year. a. Calculate the interest your relative would pay if they took 10 years to repay you. b. Complete the table. Years Future Value 0 5 10 15 20 25 c. Use desmos to find a linear regression model for your table. d. Interpret the parameters (slope and y intercept) in the context of the situation. e. Where does the slope show up in the future value formula (A=P+PRT)? Hint: Look at your interpretation from d . 30

2. After receiving the $2000 back, you decide to invest all $2000 for 10 years and received $600 in simple interest. What was the interest rate of your investment? 31

MAT130 Worksheet 3.2 Name: 1. You have $12,000 to invest for 5 years. Decide which investment is better. Show your formula and work and units for full points. a. A savings account offering 1.98% interest compounded continuously . b. A savings account offering 2.18% compounded monthly . c. A savings account offering 3.2% simple interest. d. Which investment is better? 2. Which of the three options is better if you have 50 years to invest? Show your work. a. A savings account offering 1.98% interest compounded continuously . b. A savings account offering 2.18% compounded monthly . c. A savings account offering 3.2% simple interest. d. Which investment is better? 32

3. Calculate the effective rate of a loan nominal rate of 7.35% compounded hourly . Explain what your answer means. 4. Compare and contrast simple and compound interest. Give at least 2 observations . 33

MAT130 Worksheet 3.3 Name: 1. You decide to purchase the 2018 Honda Pilot pictured below. Assume you had $2000 for a down payment and were able to secure a loan with an APR of 6.0%. a. What would your monthly payments be if your loan was for 60 months? b. You are lucky, won the lottery 29 months into your 60-month loan, and decide to pay off your loan early. Calculate the unearned interest using the rule of 78, if you pay the loan in full on the 30 th month. c. Calculate the payoff amount. 34

2. The following credit card had a previous months balance for $1302.63. Use the following statement to answer the questions. ( Note: 05/12/2012 means December 5, 2012 .) a. Find the average daily balance using the transaction date to calculate. (Note: December has 31 days) Average Daily Balance = ______________________ b. Find the finance charge if the monthly interest rate is 2.5%. c. Find the new balance on 1/1/2013. d. If the credit card company used the unpaid balance method to calculate interest how much would you owe on 1/1/2013? e. If you made no additional payments/purchases how much would you own after 4 months using the unpaid balance method? 35 Trans Date Balance # of days Balance x # of days Dec 1

MAT130 Worksheet 3.4 Name: 1. The following table represents the costs associated with attending Jackson College for the 2019-2020 school year. It assumes a student takes 16 credits. a. Calculate the total cost of a degree assuming the student completes it in two years and lives on campus. b. Calculate the total cost of a degree assuming a student lives in the community and completes it in two years. 2. Calculate the interest that would be charged ( for both students ) before the 1 st payment if the student took out an unsubsidized loan. Assume the first payment in 2.5 years after taking the loan. (Hint: Interest is charged until the first payment is made) 36

3. Calculate the monthly payment for a direct unsubsidized loan for both students. Assume it is a 10 year loan. (Note: P is the original amount of the loan plus the interest earned before the 1 st payment is made.) 4. What is the total cost of the degree for both students? 37

MAT130 Worksheet 3.5 Name: 1. Use the following stock table, accessed on 6/1/2021, to answer the following questions. a. What was the highest and lowest that the stock sold for during the last 52 weeks? b. Is the stock more or less volatile than the market as a whole? Explain how you know. c. How many shares are currently outstanding? d. On January 4, 2021 the price of GME $17.69 per share. If you had purchased 1234 shares of GME stock price on January 4 and paid a broker’s commission of 3.1%, what would have been the cost of the purchase. e. If you sold all your stock from d. for the current Bid price in the table above, what would be your profit? 38

MAT130 Worksheet 3.6 Name: 2. The table shows the tax brackets for 2018 and 2017. According to zippia.com the highest paid job in MI is a surgeon with an entry level salary of $195,670. a. Calculate the 2017 taxes (assuming the median salary is the taxable income) owed by a single surgeon in MI. b. Use the same assumptions from a to calculate the 2018 taxes owed. 39

c. What the difference in taxes owed from 2017 to 2018? d. What is the relative difference in taxes owed from 2017 to 2018? e. Interpret the relative difference in the context of the situation. 40

MAT130 Worksheet 4.1 Name: 1. Define probability. 2. What are the possible values for a probability? 3. If you roll a 20-sided die, what is the probability you will roll a seven? Provide your answer as a fraction, decimal, and percent. 4. The Michigan Power Ball 8 lottery requires you to do the following: “Select 5 white ball numbers from 1 to 69 and a single red Powerball number from 1 to 26 on your play slip.” ( https://www.michiganlottery.com/games/powerball ) To win the jackpot, you must correctly select the 5 white and one red numbers. There are 292,201,338 possible number combinations. a. Follow the directions and select a valid power ball play slip. b. What is the probability you selected the jackpot winning number? c. Go to https://www.powerball.com/games/powerball . Did you win the most recent drawing? Provide the date of the drawing used. 41

MAT130 Worksheet 4.4 Name: The following excerpt is from a poll conducted by Fox News asking respondents the following question: “Do you approve or disapprove of the job Joe Biden is doing as president?”. Respondents were given the following response options: Approve Strongly, Approve Somewhat, Disapprove somewhat, Disapprove Strongly, Don’t Know. The following is a screenshot of the report: Source: https://static.foxnews.com/foxnews.com/content/uploads/2021/05/Fox-News-Poll.pdf 1. Identify the sample. Be specific. 2. Identify the population. Be specific. According to the poll results, 54% selected approve (both strongly and somewhat) and 42% selected disapprove (both strongly and somewhat) and 4% selected Don’t Know. 3. Of the total people surveyed(see excerpt) how many said they approved of the job Joe Biden is doing as president? 4. The political ideology of the respondents was not identified in the study. Let’s assume more than 60% of the respondents identified as Democrats(we have no idea if this is true)? How might that assumption affect the survey results? 42

Source: https://www.eia.gov/dnav/pet/pet_pri_gnd_dcus_nus_m.htm The following table contains the total federal outlays (in millions) from 1993 to 2007 for the department of justice. 5. Construct a grouped frequency distribution of the data. 6. Construct a stem and leaf plot of the data. 43 9,369 9,485 10,149 11,049 13,076 14,045 16,181 16,846 18,443 20,790 21,178 22,361 23,324 23,349 29,601

MAT130 Worksheet 4.5 Name: _________________________________ The following table contains the total federal outlays (in millions) from 1993 to 2014 for the department of justice. 1. Create a stem and leaf plot of the data using 9 classes. 2. Create a grouped frequency distribution using your stems. Draw a histogram. 3. Find the median score. 4. Calculate the mean score. 5. Find the mode score. 6. Find the midrange. 7. What is the average score for this particular class? Explain your reasoning. 44 9,369 9,485 10,149 11,049 13,076 14,045 16,181 16,846 18,443 20,790 21,178 22,361 23,324 23,349 26,545 27,711 28,620 29,556 29,601 29,745 30,519 31,159

Grading Scale: Grading Policy: Your Grade 90 -100% 4.0 Class Participation: 6% 85 - 89% 3.5 Online ALEKS Homework: 12% 80 - 84% 3.0 Worksheets: 12% 75 - 79% 2.5 Project 1: 12.5% 70 - 74% 2.0 Project 2: 12.5% 65 - 69% 1.5 Project 3: 12.5% 60 - 64% 1.0 Project 4: 12.5% 50 - 59% 0.5 Midterm and Final: 20% 0-49% 0.0 The following grading criteria is copied directly from the MAT040.130 syllabus. Use it to answer the following questions 8. Write your current score for each category. (Class Participation, Online CM, etc.) 9. Calculate a weighted average of your category scores. 10. Predict your score for project 4. 11. Using your prediction from #10 and a 0% and 100% for the Final exam grade, determine the highest and lowest weighted averages you earn at the end of the semester. 12. Based on your answer to 11 what is the best and worst grade you could earn for the course? 45

MAT130 Worksheet 4.6 Name: The following table contains the total federal outlays (in millions) from 1993 to 2014 for the department of justice. 1. Calculate the mean. 2. Calculate the range. 3. Calculate the Standard deviation. 4. Calculate the coefficient of variation. Use the mean, range, standard deviation, and coefficient of variation to describe how the department of defense spent money from 1993 to 2014. Note: The spending is not listed in chronological order. 46 9,369 9,485 10,149 11,049 13,076 14,045 16,181 16,846 18,443 20,790 21,178 22,361 23,324 23,349 26,545 27,711 28,620 29,556 29,601 29,745 30,519 31,159

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MAT130 Worksheet 4.7 Name: The infamous MAT130 Exam 3 taken by 226 students at Jackson College during the Fall 2018 semester had a mean of approximately 61% and a standard deviation of about 22%. 1. Let us assume the data are approximately normal, fill in the normal curve above using the exam mean and standard deviation. 2. What percent of students scored below a 39%? 3. What percent of students scored above an 83% 4. How many students scored between a 39% and an 83%? 5. What evidence do we have that these scores are not normally distributed? 6. What was your exam 3 score? 7. Calculate the z-score of your exam 3 score. What does your z-score mean in relation to the average? 48

MAT130 Worksheet 4.9 1. Consider the following potential survey questions. Circle the words or phrase that contribute bias to the question. Explain how it introduces bias to the question. a. Athletes in the NFL have suffered from traumatic brain injury. Should the NFL be required to provide healthcare for all players? b. Is your professor an awesome instructor? 2. Rewrite question b so that the bias is eliminated. 3. Consider the following two graphs that contain the same information. a. Circle the graph that is misleading. Explain why it is misleading. b. Provide one reason why someone might use the misleading graph to talk about interest rates. 49

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Unit Reviews 51

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MAT130 Unit 1 Review A 1. a. Express 45% as a decimal. b. Express 37 4 as a percent 2. The cost per credit hour at Jackson college for the 2018-2019 school year was $152.80. The cost per credit hour at Jackson college for the 2021-2022 school year is $168.00. a. Calculate the percent increase. b. Interpret your answer from b in context. 2. Bestbuy.com has the following deal on Beats Studio by Dr. Dre. Calculate the percent discount. Show all your work. 53

3. The following table represents the 2018 primary results for governor of Michigan. Use the table to answer the following questions. Candidate Votes Percent Schuette, Bill 499,837 Calley, Brian 248,047 Colbeck, Patrick 129,102 Hines, Jim 108,263 Total d. Find the percent of the total that each candidate earned. Show your work in the “Percent” column. e. Create a pie graph using excel 4. The following pie graph represents the percent of the vote earned by each candidate in the 2020 democratic presidential primary. d. If the total amount of votes was 35,534,096 , how many people voted for Elizabeth Warren? e. How many people did NOT vote for Bernie Sanders? 54

5. If I buy 15 Ebay lots of Lego weighting a total of 342 lbs for a total of $3286 over a 1 year period, use dimensional analysis to find the following. (Note: 1 year = 365 days, 1 day = 24 hours, 1 hour = 60 minutes, 1 lb = 16 ounces) a. Cost per lot b. Cost per ounce c. Cost per day. d. Cost per minute. 55

6. According to the Insurance information Institute about 70% of U.S. households own a pet. That is a total of 90.5 million households with a least 1 pet. Pet Ownership Source a. Approximately how many households have a dog? b. If a total of 90.5 million households have a pet, approximately what percent of those households have a dog? c. Why would it not be appropriate to display this information in a pie chart? 56

MAT130 Unit 1 Review B Show all work to receive credit. Be sure to include units. 1. In 2007, the federal minimum wage was $6.55. Currently, the federal minimum is $7.25. a. Calculate the percent increase between the two years. (4 pts) b. Interpret the percent increase in the context of the situation. (4 pts) 2. Amazon had the deal pictured below. Calculate the original price. (5 pts) 57

3. The following pie graph represents the 176,771 federal inmates by gender (assuming gender is binary). Source: https://www.bop.gov/about/statistics/statistics_inmate_gender.jsp a. Calculate the number of males and females (the smaller slice) currently in federal prison (given)? (4 pts) b. How many degrees make up the sector “female”. Round to the nearest degree. (3 pts) c. The exact number of female inmates is 12,594. Explain why the number you calculated in a is different. ( 3pts) 58 93% 7% Inmate by Gender male female

4. The following bar graph represents the total federal outlays(spending) on National Defense from 2000- 2018. ( source: https://www.whitehouse.gov/omb/historical-tables/ ) a. What does each bar represent? What are the units for each bar? (3 pts) b. Which year was the spending the highest? Estimate the amount spent in that year. (3 pts) c. Describe the trend in federal spending displayed by the bar graph. (3 pts) 59 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 0 100000 200000 300000 400000 500000 600000 700000 800000 Federal Spending on National Defense by year (2000-2018) Year Dollars (in milions)

5. Bitcoin is a cryptocurrency that can be converted into US dollars (USD) or Euros(currency of the European Union. Currently 1 Bitcoin = 10,167.10 USD and 1 Euro = .00011 Bitcoins. a. Write a conversion factor relating Bitcoin to USD and Euro to Bitcoin. (2 pts) b. Convert 32,000 USDs into Bitcoins. Show work including units. (4 pts) c. Convert 1200 Euro into USDs. Show work including units. (6 pts) 6. How many inches is a 5-kilometer race? (Note: 2.54 cm =1 in, 1m=3.28 ft, 1.61 km = 1mi, 1 mi =5280 ft, 1km = 1000 m) (4 pts) 60

7. A model of the space shuttle Challenger has a scale of 1 in. : 64 ft. The actual shuttle was 122 feet in length. How long is the model? Provide your answer in inches. (4 pts) 8. In 1971 the cumulative US national debt was $ 3.9812974445554 x 10 11 . In 2014 the cumulative US national debt was $ 1.782407138073382 x 10 13 . a. Calculate the actual change. Write your answer in decimal form. (4 pts) b. Calculate the relative change. Round to the nearest hundredth. (4 pts) c. Interpret the relative difference in the context of the situation. (4 pts) 61

9. Michigan’s House of Representatives consists of 110 seats. In 2017, Michigan had a population of 9.962 x 10 6 people of voting age. Calculate the unit rate of people per district. (4 pts) 10. According http://house.michigan.gov the number of residents in a district can be between a minimum of 77,000 people and a maximum 91,000 people. a. Calculate the relative error between your answer from #9 and the estimated maximum from the website. Round to the nearest hundredth of a percent. (4 pts) b. Interpret the relative error in the context of the situation. (2 pts) 62

Math 130 Unit 2 Review A 1. The following table represents the average yearly income for a factory worker with 5 years of experience. a. Complete the table by letting x = the number of years since 1990. b. Draw a scatter plot of the data. Make sure to label the x and y axis. c. What does the scatter plot tell you about the average yearly income? 2. Lime Scooter rentals allow you to rent an electric scooter for an initial cost of $1 and $.10 per minute after that. a. Write a linear equation for the cost of renting a scooter. b. How much will it cost to rent the scooter for 35 minutes? c. How long can you rent the scooter if you only want to spend $15? 63

3. Comcast estimates the number of households in millions y with internet access can be modeled by y = 6.76x + 14.9 where x is the number of years since 1990. a. What is the slope? Interpret the slope in context of the situation. b. What is the y-intercept? Interpret the y-intercept in context of the situation. c. According to the model how many households had internet access in 2010? d. According to the model in what year would the number of households with internet reach 100 million? 4. Meijer is having a sale on two liters of Coke for $1.67. a. What is the unit price in dollars per liter? b. Explain what your answer to a means. c. You see 12 packs of 12 oz cans are on sale for $3.50. What is the unit rate in dollars per oz? d. If there are 33.8 oz in I liter what sale is the better deal? 64

5. The fastest marathon (26.2 miles) was ran in Berlin in 2014 by Dennis Kimmetto from Kenya his time was 123 minutes. Round all parts to 3 decimal places a. Calculate his unit rate in miles per minute. b. Calculate his unit rate in terms of minutes per mile c. What does your answer from part b mean? d. What is his speed in meters per hour? (note 1 mile = 1.61km, 1000m = 1 km, 1 m = 3.28 ft, 1 mile = 5280ft) 65

6. ‘ Below is the table for the pressure exerted the deeper you dive in water. Round to 2 decimal places. a. Find the model of best fit for the data b. What is your r value? What does this tell you about the data? c. Interpret the y-intercept in context d. If Linear – interpret the slope, if exponential – interpret the growth rate. e. Using your model what is the pressure when the depth is 100ft? f. What is the relative error between the value calculated in e. and the data value from the table? 66 Depth (feet) Pressure (pounds per square inch) 0 14.7 10 18.55 20 23.36 30 27.69 40 32.02 50 36.35 60 42.21 70 45.01 80 49.37 90 53.67 100 58

7. Below is a table representing the area of infestation of cane toads in Australia. Cane toads were first introduced in 1930. Round to 2 decimal places. a. Find the model of best fit for the data b. What is your r value? What does this tell you about the data? c. Interpret the y-intercept in context d. If Linear – interpret the slope, if exponential – interpret the growth rate. e. Using your model calculate the area of infestation in 1960? f. What is the relative error between the value calculated in part e. and the data value from the table? g. In what year will the area of infestation reach 1,000,000 square kilometers? Sketch the graph and give the max/min 67 Time (yr) Area (square kilometers) 0 36500 5 52000 10 78800 15 114200 20 170120 25 250000 30 352900 35 539700

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MAT130 Unit 2 Review B Show all your work to receive full credit. Be sure to include units where appropriate. 1. Walmart offers a 2 pack of 15 oz bags of Nacho Cheese Doritos for $7.65. Costco offers a 64 pack of 1.75 oz bags of Nacho Cheese Doritos for $32.99. a. Calculate a unit rate in terms of ounces per dollar for Walmart. Include all units. (4 pts) b. Calculate a unit rate in terms of ounces per dollar for Costco. Include all units. (4 pts) c. Which option is the better buy? Explain your answer. (4 pts) 69

2. Usain Bolt holds the world record for the 100-meter run. He ran it in 9.58 seconds. a. Calculate a unit rate in terms of meters per second. (4 pts) b. Determine Usain’s speed in terms of miles per hour. (Note: 1 mi=1.61km, 1 m = 3.28 ft, 1 mi = 5280 ft) (4 pts) c. Calculate a unit rate in terms of minutes per mile. (Note: 1hr = 60 min.) (4 pts) d. What does your answer from c mean? (4 pts) 3. The following data is the number of wins and losses for the Detroit Pistons from 2008 to 2018. a. Complete the table by letting x=the number of years since the 2008-09 season. (2 pts) b. Draw a scatterplot using demos or excel of x and wins . Be sure to label the axes. Paste the graph below, or submit the link in jetnet. (5 pts) 70 Season x Wins Losses 2008–09 39 43 2009–10 27 55 2010–11 30 52 2011–12 25 41 2012–13 29 53 2013–14 29 53 2014–15 32 50 2015–16 44 38 2016–17 37 45 2017–18 39 43

c. What does the scatterplot tell you about the Detroit Pistons? (3 pts) 71

4. The US army is offering a one time bonus of $16,000 for shipping(ship to boot camp) in 30-days and a yearly wage of $25,558 for a specialist/Corporal (E4) with less than 2 years of experience. a. Write a linear equation modeling your total income assuming you will ship in 30-days. (4 pts) b. How long will it take to earn $345,000? (4 pts) 5. The population of Tasmanian Devils can be modeled by the equation y =− 12610 x + 256412 (with an R ≈ − 0.966 ) where x represents years after 1996 and y represents the number of Tasmanian Devils. a. Identify the slope and interpret it in the context of the situation. (4 pts) b. Identify the y-intercept and interpret it in the context of the situation. (4 pts) c. Is the equation a good model for the population of Tasmanian Devils? Explain.( 2pts) 72

6. Suppose you won Michigan’s Mega Millions lottery ticket (by matching 3 white balls + mega ball) and invested your $200 payout in a savings account chosen by me. Your account balance is provided in the table. a. Find the growth factor and growth rate. (4 pts) b. Interpret the growth rate/factor in the context of the situation. (4 pts) c. Write an equation to model the situation. (2 pts) d. What will your account be worth in 70 years? (4 pts) e. When will the account be worth $20,000? Sketch the graph. (4 pts) 73 Years Account Balance 0 200.00 1 210.00 2 220.50 3 231.53 4 243.10 5 255.26 6 268.02

7. The following equation models the amount of caffeine (in mg) in your blood system t hours after drinking coffee: y = 280 ( .89 ) t . a. What is the decay factor? Interpret it in the context of the situation. (4 pts) b. What is the y-intercept? Interpret it in the context of the situation. (4 pts) c. How much caffeine remains after 6 hours? (4 pts) d. When will 5 mg of caffeine remain in your system? Sketch a graph. (4 pts) 8. The following table shows the low end FICO score and the typical annual percentage rate(APR) received when purchasing a car with a 36-month loan for $15,000. a. Find an equation of best fit. Round parameters to 2 decimal places. (4 pts) 74 FICO Score APR (%) 720 3.7 690 5.13 660 7.3 620 11.01 590 16.04 500 17.19

b. State the correlation coefficient of the equation of best fit. What does it tell you about this equation? c. Use your equation to predict the APR of an individual with a 300 FICO credit score. d. The minimum possible FICO credit score is 300 and banks typically require at least a 500 FICO credit score to be approved for a loan. Why might your prediction from c not be accurate? 9. According to www.treasurydirect.gov , the national U.S. historical debt outstanding is shown in the table. a. Complete the table by letting t = years since 1954 . Use a scatterplot and R to determine the best model of the data. Write the model and round each parameter to 2 decimal places . (4 pts) b. Use the model to predict debt outstanding in 2018. (4 pts) 75 Years t Debt Outstanding (in billions) 1954 $271 1955 $274 1965 $317 1973 $458 1978 $772 1997 $5,413 2017 $20,245

c. What is R and what does it tell you about the model? (4 pts) d. The actual number debt outstanding in 2018 was $21,516 billion. Calculate the relative error between your answer from b and the $21,516 billion debt outstanding. (4 pts) 76

MAT130 Unit 3 Review A 1. Which savings account is better? a. A simple interest account earning 5.01% interest. b. An account earning 4.98% compounded monthly. c. An account earning 4.96% compounded daily. d. An account earning 4.90$ compounded secondly. 2. How much interest will you earn if you invest $6000 in an account for 20 years that earns 3.24% interest compounded continuously? 77

3. Should you make a down payment of $2000 when purchasing a $15,000 car with a 60 month loan at 7.35% interest? 4. You receive an unsubsidized loan for $23,000 at 4.35% interest to pay for your degree. If you are in school for 2 years and defer payments for 3 months after school, what is the total cost of your education? 78

5. Calculate the average daily balance for the following credit card if the ending balance in February was $211.14 . If the monthly interest charged is 2.5%, calculate the new balance in April. 79

6. What are the 2018 taxes owed of someone who had a taxable income of $32,456? 80

7. Which mortgage is better when purchasing a $225,000 home? a. A 15 year mortgage at 4.21% with 0% down payment b. A 30 year mortgage at 4% with 20% down payment 81

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MAT130 Unit Review 3 B For all problems, show work to receive full credit. Where appropriate provide two decimal places for the final answer. 1. Describe the three uses of the monthly payment formula from unit 3. How might you use them in your future? (5 pts) 2. What is the difference between compound and simple interest? (2pts) 3. How does the effective rate formula relate compound and simple interest? (2 pts) 83

Match the correct formula(s) ( by letter ) for each situation. Answers may be used more than once. (7pts) 4. Finding the interest on a loan charging 3.45% simple interest. _____________ 5. The monthly payments of a ten year subsidized student loan charging 5.05% interest. _____________ 6. The finance charge for a credit card charging 2.50% interest compounded monthly. _____________ 7. The future value of a savings account earning 1.95% interest compounded quarterly. _____________ 8. How much you save by paying off a 10 year car loan charging 4.85% APR in 5 years. _____________ 9. The future value of a savings account compounded continuously. _____________ 10. The equivalent simple annual interest rate of a 3.45% interest rate compounded daily. A. I = PRT B. A = P + PRT C. A = P ( 1 + r n ) nt D. M = P∙ r 12 1 − ( 1 + r 12 ) − 12 t E. E = ( 1 + r n ) n − 1 F. A = Pe rt G. u = fk ( k + 1 ) n ( n + 1 ) H. A = 12 M [ ( 1 + r 12 ) 12 i − 1 ] r _____________ 84

11. After receiving an inheritance, you decide to invest $14,250 for 15 years and received $9600 in simple interest. What was the interest rate of your investment? (4 pts) 12. Find the interest earned from a $21,172 investment with 18.25% interest compounded continuously for 30 years. (4 pts) 85

13. You have a large sum of money to invest for 1 year and want to pick the investment that will earn the most money. a. Which of the following investment is best? Explain your reasoning. (5 pts) Option 1: A simple interest rate of 5.63%. Option 2: An interest rate of 5.05% compounded monthly. b. If you had ten years to invest the money, which option is best? Explain your reasoning. (5 pts) 86

14. You need to purchase $500 worth of books to complete your masters in statistics from Eastern University. Unfortunately, you currently do not have enough cash. Pick two of the scenarios and calculate the total cost of the books for each of the following scenarios. (5 pts per scenario) Scenario 1 : Use amazon.com store card charging no interest if the balance is paid in full in 12 months. Otherwise you are charge 28.24% APR from the date of purchase. You pay the balance in full at the beginning of the 13 th month. Scenario 2: Use a credit card that charges a 1.1% monthly finance charge using the unpaid balance method. You pay the balance off in three months. Scenario 3: You use financial aid (6.6% interest rate) to pay for the books. The monthly payments for the $500 are $5.70 paid over 10 years. Of the two scenarios you chose, which is the best option. Explain your reasoning. (Note: It does not have to be the cheapest) (4 pts) 87

15. A $17,500 truck loan is to be purchased using a 48 month loan at 7.5% APR with a down payment of $3000. a. Calculate the monthly payment for the loan. (4 pts) b. How much would you save if you paid the loan in full on the 30 th month. (Note: The finance charge per $100 is $6.04 for this early payoff amount) (4 pts) c. What if we chose to not pay it off in the 30 th month and finished out the loan for 48 months. What is the cost of the truck ? (4 pts) d. Is it worth paying off the loan early? Explain your reasoning. (4 pts) 88

16. According to www.jccmi.edu the cost of one semester including tuition ( 16 credit hours ), fees, and books/supplies is approximately $4345. a. How much does Jackson college charge for an associate’s degree if it takes you 4 semesters (2 years) to graduate? (4 pts) b. The current interest rates for a government loan is 4.529%. Find the amount of simple interest owed if a student borrowed the full cost to attend JC and interest accrued for 3 years. (4 pts) c. The monthly payments from b on a 10 year loan (unsubsidized) is $204.87. Calculate how much extra the student paid because they had to take out a loan. (4 pts) d. Explain why students use loans to pay for their education. Do you think it is worth doing? (4 pts) 89

17. The following stock table list the current stock information (4/3/2019) for Twitter, Inc. Use the table to answer the following questions. a. What was the value of the stock yesterday? (2 pts) b. Determine the number of shares issued using the Market Cap. (2 pts) c. You decide to purchase 500 shares at the current Bid price. If you use a broker that charges a 1.5% commission, how much does it cost to purchase the shares? (4 pts) d. Suppose you decide to sell your 500 shares (from question c ) two years after purchasing and the current value is $380.46. Calculate your annual return rate if you are charged a 1% commission for selling? (4 pts) 90

18. The table shows the tax brackets for single filers in 2017 and 2018. According to datausa.io the median salary in Jackson MI is $28,697. a. Calculate the 2018 taxes owed by a single Jackson, MI taxpayer earning the median income (assuming it is the taxable income.). (4 pts) b. The 2017 taxes for the same salary is $3,838.3. What is the relative difference between the 2017 and 2018 taxes owed? (4 pts) c. Interpret the relative difference in the context of this situation. (4 pts) 91

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MAT130 Unit 4 Review A SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1. In any experiment, the set of all possible outcomes is called the __________________. 2. When an event can’t possibly occur, its probability is ____________. When an event is certain to occur, its probability is _____________. 3. Which of the numbers that follow could represent a probability? 23 25 0.25 110% 6% -1/2 4. If a die is rolled one time, find the probability of getting a number greater than 2. 5. If a die is rolled one time, find the probability of getting a number less than 4 or an even number. 6. A box contains five blue, eight green, and three yellow marbles. If a marble is selected at random, what is the probability that it is green? 7. In a classroom, the students are 9 boys and 4 girls. If one student is selected at random, find the probability that the student is a girl. 93

You plan to sample members of exercise facilities in your city. Identify which of these types of sampling is used by indicating the correct number in the blank. (Each has only one correct answer.) 8. You obtain a list of all 15 facilities in your city, which you number from 01-15. Using random numbers, you choose 3 of the facilities and interview all the members in each facility. Random Systematic Cluster Stratified 9. You obtain a list of all the members of all 15 exercise facilities and randomly choose 400 members to interview. Random Systematic Cluster Stratified 10. You obtain a list of all the members of all 15 exercise facilities and put them in alphabetical order. You select every 50th member to interview. Random Systematic Cluster Stratified 11. You obtain a list of all the members of all 15 exercise facilities. You compile all the names into a master list and identify the age of each member as 18-25, 26-35, 36-45, 46-55, 55+. You randomly select 100 members from each of the age groups and interview them. Random Systematic Cluster Stratified 12. As an experiment in a botany class, plants are placed in a greenhouse, and their growth in centimeters after 25 days is recorded, with the results shown below in a stem and leaf plot. Stems Leaves 1 3 2 0 5 3 3 4 6 6 7 4 2 4 7 9 5 0 1 3 4 4 7 9 9 a. How many plants grew to 25 cm? b. How many plants grew to 36 cm? c. How many plants had their growth measured and recorded? d. What was the largest growth recorded for any plant? 94

13. A bookstore recorded the type of books 30 customers purchased during a weekend sale (R = romance novel, S = science fiction, N = nonfiction, C = children's fiction). Construct a frequency distribution for the data N R R C R S R C C S R R C N N R C S S S R R N C S R R C C N Genre Frequency 14. The grades on a college math exam are shown below. Construct a stem and leaf plot for the data. 79 77 50 83 71 65 50 70 71 84 79 99 87 89 92 73 95 76 90 80 76 95 88 83 15. The data shows hours spent at work for a group of men. Find the mean, median, mode, midrange and standard deviation for the data provided. Mean Median Mode Midrange Standard deviation Name Hours Alvin 64.3 Juan 58.3 Sean 56.9 Victor 45.7 Chan 43.3 Jack 40.7 Phillip 35.1 Robert 29.1 A. Which would be the best measure of Central Tendency? Why? 95

16. These data represent the grades on a college exam. Find the mean. Class Limits Frequency 50-59 1 60-69 3 70-79 14 80-89 18 90-99 7 17. Helga scored in the 70th percentile rank on an exam. If 300 students took the exam, how many students scored lower than Helga? 18. Which data set would be likely to have the larger standard deviation? EXPLAIN. Data set 1: Weights of all dogs at a golden retriever rescue shelter Data set 2: Weights of all dogs for sale in a pet store 19. A professor has two sections of Math 115 this semester. The 8:30 A.M. class has a mean score of 72% with a standard deviation of 3.2%. The 2 P.M. class also has a mean score of 72%, but a standard deviation of 18.2%. What can we conclude about the students’ averages in these two sections? 20. Assume a data set is normally distributed with mean 13 and standard deviation 3.5. Draw the normal distribution using the provided mean and standard deviation. Include the percentages under the curve. If the data set contains 50 data values, approximately how many of the data values will fall within the range 9.5 to 16.5? 96

21. Assume a data set is normally distributed with mean 126 and standard deviation 20. Draw the normal distribution using the provided mean and standard deviation. Include the percentages under the curve. If the data set contains 350 data values, approximately how many of the data values will fall within the range 86 to 166? 22. Assume that males have a mean height of 69.1 in. with a standard deviation of 2.9 in., and females have a mean height of 63.7 in. with a standard deviation of 2.7 in. Based on Z scores, would a 5'4" male or a 4'10" female be taller compared to the rest of their gender? Explain. 23. If a student scored 1,227 on the SAT test which has a mean of 1,026 and a standard deviation of 210 and then scored 110 on an IQ test with a mean of 100 and a standard deviation of 15, determine which test she did better on and explain your reasoning. 97

24. Suppose that the mean sale price for existing homes in the United States in is $213,000. Assume that sale prices are normally distributed with a standard deviation of $44,000. Draw the normal distribution using the provided mean and standard deviation. Include the percentages under the curve. Find the percentage of existing homes that: a. sold for between $125,000 and $301,000 b. sold for more than $257,000 98

MAT130 Unit 4 Review B 1. Select all the values that could represent a probability. ( 7 pts ) -1 53% 1.25 2 7 0 300% 5 2 2. The Michigan daily 3 lottery requires you to pick three numbers between 0 and 9 where the numbers can repeat. One bet type is called a box where the order of the numbers selected does not matter. a. You selected 5,7,8 as your three numbers. List all possible ways to arrange these numbers? ( 4 pts ) b. There are a 1000 possible pick 3 number combinations in the sample space. Calculate the probability your selection (5,7,8) in any order won . Write your answer as a fraction, decimal, and percent. ( 4 pts ) Circle the type of sampling used in the following situations. 3. A professor randomly selects 20 students from a list of all MAT130 students and calculates their average MAT130 grade. ( 1 pt ) Random Systematic Cluster Stratified 4. A company with full time and part time employees randomly selects 10 from each group and asks for their opinion about benefits. ( 1 pt ) Random Systematic Cluster Stratified 5. A county commissioner randomly selects 100 households in their county and surveys all adults in the household to determine the unemployment rate of the county. ( 1 pt ) Random Systematic Cluster Stratified 6. A quality control specialist selects every tenth car off an assembly line to inspect. ( 1 pt ) Random Systematic Cluster Stratified 99

7. From November 21 - 25, Quinnipiac University surveyed 1,355 self-identified registered voters nationwide to determine the 2020 Democratic Presidential nomination. The survey found that 24% supported Joe Bide, 13% supported Bernie Sanders and 15% supported Elizabeth Warren. All other candidates had support under 10 % a. Identify the sample of the study. Be specific. ( 2 pts ) b. Identify the population of the study. ( 2 pts ) c. How many people in the sample claim they will vote for Joe Bide? ( 2 pts) 8. Circle the variables that are categorical? ( 5 pts ) weight height eye color age hair color 9. The infamous MAT130 Exam 3 taken by 226 students at Jackson College during the Fall 2019 semester had a mean of approximately 61% and a standard deviation of about 22%. Two students both scored a 68%. Student A calculated their z-score as .318 and Student B calculated their z-score as 65.23. a. Student _____________ was correct. Explain how you know. ( 2 pts ) b. Student _____________ was incorrect. Explain how you know. ( 2 pts ) 100

10. The following data is the number of hours (rounded to the nearest hour) students in Erik’s MAT130 class spent logged into ALEKS. 1, 1, 1, 1, 2, 2, 3, 5, 6, 7, 9, 9, 11, 11, 12, 13, 16, 16, 17, 21, 22, 24, 28, 28, 31, 33, 66 a. Using 6 classes, calculate the class width. ( 2 pts ) b. Create a group frequency distribution. ( 6 pts ) Class Tally (not required) Frequency c. There are 30 ALEKS assignments. If it takes on average 30 minutes to complete 1 assignment, how many of Erik’s students are spending a reasonable amount of time completing homework? Explain ( 4 pts ) d. What does the grouped frequency distribution suggest about the study habits of the students in this class? ( 2 pts ) 101

11. The following grouped frequency distribution contains the exam 3 scores of all MAT130 students. a. Complete the table and use it to calculate the mean of the exam 3 scores. ( 4 pts ) b. Why is the mean you calculated an approximation? ( 2 pts ) c. Draw a histogram of the data set. Be sure to include labels. ( 4 pts ) d. What do the weighted mean and the histogram tell you about the scores on exam 3? ( 4 pts ) 102 Class Midpoint Frequency 0%-9% 1 10%-19% 10 20%-29% 16 30%-39% 18 40%-49% 29 50%-59% 35 60%-69% 34 70%-79% 36 80%-89% 28 90%-100% 19

12. Observe the hours spent logged on to ALEKS again. 1, 1, 1, 1, 2, 2, 3, 5, 6, 7, 9, 9, 11, 11, 12, 13, 16, 16, 17, 21, 22, 24, 28, 28, 31, 33, 66 a. Construct a stem and leaf plot. Include a key. ( 4 pts ) b. Find all of the following show work where necessary: Mean ( 1 pt ) Median ( 1 pt ) Mode ( 2 pts ) Midrange ( 2 pts ) Range (2 pts ) Standard Deviation ( 1 pt ) Coefficient of Variation ( 2 pts ) c. What is the best measure of central average? Explain your reasoning. ( 3 pts ) d. Describe the variation of the data using the standard deviation and coefficient of variation. ( 3 pts ) 13. Which data set is likely to have a larger standard deviation? Explain your reasoning. ( 4 pts ) Data set 1: The height of NBA basketball players. Data set 2: The height of high school boys. 103

14. Monthly charges for cell phone plans in the United States are normally distributed with a mean of $62 and a standard deviation of $18. a. Draw the normal distribution using the provided mean and standard deviation. Include the percentages under the curve. ( 7 pts ) b. What percent of cell phone plans cost more than $80? ( 2 pts ) c. If we randomly selected 300 people with cell phone plans, how many would we expect to pay between $26 and $62? ( 4 pts ) d. My cellphone plan costs $83. Calculate the z-score for my plan. Is my plan above or below the mean. Explain. ( 4 pts ) 104

MAT040 Worksheets 105

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MAT 040: 1.1 Worksheet Name:________________________ 1. What are the rules for rounding? 2. Round 654.8235983 to the following number of decimal places. a. 1 decimal place b. 2 decimal places c. 3 decimal places d. 4 decimal places e. To the nearest whole number 3. How do we convert decimal to percent and percent to decimal? 4. Convert the following percent to decimal. a. 36% b. 7% c. 25.3% d. 0.6% e. 300% 5. Convert the following decimals to percent a. 0.45 b. 0.06 c. 0.99 d. 1.36 e. 0.0035 6. What are some of the English to math translations we learned this section for solving percent word problems? 107

MAT 040: 1.1 Worksheet Name:________________________ 7. Solve the following: a. 28% of 300 is what number? b. 15% of what number is 12.99? c. What percent of 60 is 45? 8. If you got Kohl’s and you see a sign that reads “30% off all regular-priced items”, you can think about this in a few different ways…. Either a. What % am I getting rid of otherwise known as the discount percent? b. What % am I keeping, the % I am paying of the original price is? c. How are the two % related? d. What is the sale price of a shark vacuum originally priced $249.99? 108

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MAT 040: 1.2 Worksheet Name:________________________ 1. A group of students were asked about the kind of pets they had in their household. The table below is their answers. Make a bar chart of the data labeling the axes and scale. Animal # of students Cat 25 Dog 15 Fish 4 Reptile 2 Rodent 3 None 5 2. The same group of 40 students were asked about the number of pets they had in their household. The table below is their answers. Make a pie chart of the data labeling the axes and scale. a. Fill out the table for the percent of students(round to the nearest percent. that have each specific number of pets. b. Make a pie chart of the data. Don’t forget to label appropriately. # of pets # of students % of students 0 5 1 10 2 15 3 6 4 3 5 1 110

MAT 040: 1.2 Worksheet Name:________________________ 3. According to AVMA.org the average yearly cost of veterinary care for a dog was $378 in 2012 and went up to $410 in 2017. What is the percent increase in the cost of veterinary care? 111

MAT 040: 1.3 Worksheet Name:________________________ 1. Round 123.424673 to the indicated place value. a. To nearest tenth b. To the nearest hundredth c. To the nearest thousandth d. To the nearest whole number 2. Use the correct inequality sign to make a true statement a. 250 _____ 350 b. 125 ______ 100 c. 45 ________ 44 d. 67000 ______670000 3. Plot the following values on the number line. a. -1. 4 b. -1. 8 c. 0.4 d. 0.7 e. 1.3 f. -0.5 4. Use the correct inequality sign to make the statement true. a. -1.8 ______ -1.4 b. 0.4 ______ 0.7 c. -0.5 ____ -1.4 d. 1.3 ______ -0.5 5. Translate the English into an inequality. a. The value in my bank account B is more than $100 b. I owe less than $5500 on my car C. c. I think I got at least 75% on my last test T. d. The calories in my meal M were no more than 1500. 112

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MAT 040: 1.4 Worksheet Name:________________________ 1. Convert 4,910 yards to miles. 2. Convert 30 days to seconds. 3. Convert 2 L to gallons. 4. Convert 0.95 meters to inches. 5. Convert 25.06 years to minutes. 6. Convert 29.8 feet to cm. 7. Convert 10,000 inches to miles. 114

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MAT040 1.5 Worksheet Name: _________________________________ 1. Round 415.1647 to the indicated place value. a. To nearest tenth b. To the nearest hundredth c. To the nearest thousandth d. To the nearest whole number 2. Convert the following percent to decimal. a. 6% b. 4.5% c. 62% d. 0.9% e. 450% 3. Convert the following decimals to percent a. 0.35 b. 0.015 c. .089 d. 1.50 e. 0.0099 4. According to AVMA.org the average yearly cost of veterinary care for a dog was $410 in 2017 in 2020 the cost was $527. a. What is the actual change in cost? b. What is the relative change? c. Interpret the relative change in context. 5. You are in the grocery store and are estimated your total cost as you shop. You estimate your cost to be $75, the actual cost is $67.85. a. What is the error in your estimate? b. What is the percent error in your estimate? 116

c. Interpret the percent error in context. 117

MAT 040: 1.6 Worksheet Name:________________________ 1. Convert each number to scientific notation. a. 0.067 b. 1234 c. 8,002,000,000 d. 0.00000079 2. Convert each number to decimal notation. e. 1.234 E-4 f. 5.537 E6 g. 9.103 x 10 -5 h. 3.5888 x 10 7 3. What do we know about the number based on if the power of ten is negative or positive? 4. Use the correct inequality to make the statement true: a. 1.03 x 10 -6 ______ 9.103 x 10 -5 b. 1.45 x 10 3 _____ 3.45 x 10 4 c. 1.34 x 10 -8 ______ 1.56 x 10 -9 d. 9458 ____ 9.458 x 10 4 5. Use Desmos to find the answer – Write your answer in Scientific and Standard Notation. a. 4.925 x 10 12 2.654 x 10 7 b. 1.463 x 10 − 5 9.526 x 10 − 3 118

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MAT 040: 2.1 Worksheet Name:________________________ 1. Convert the following percents to decimals. a. 8.25% b. 0.67% c. 130% d. 36% 2. Convert the following decimals to percents. a. 2.0 b. 0.21 c. 0.0345 d. 0.0025 3. Put the following in Desmos and write down the answer. This is to check that you can plug complicated equations into Desmos. a. 450(1 + 0.25) 15 b. 7500(1 + 14 ∙ 0.05) 4. What is the difference between exponential and linear growth. Be specific. For 5-8 identify if the pattern is linear or exponential, identify the constant, and write the next 3 values in the pattern . 5. Pattern: 5, 10, 15, 20, 25, 30, … a. Linear or exponential? b. Constant? c. Next 3 values? 6. Pattern: -4, -8, -16, -32, -64, -128, … a. Linear or exponential? b. Constant? c. Next 3 values? 7. Pattern: 2, 5, 12.5, 31.25, 78.125, … 120

a. Linear or exponential? b. Constant? c. Next 3 values? 8. Pattern: -20, -14, -8, -2, 4, 10, … a. Linear or exponential? b. Constant? c. Next 3 values? 121

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MAT 040: 2.2 Worksheet Name:________________________ Use the graph below to answer #1-3 below. 1. Estimate the highest percent unemployment for Black and White Americans. 2. When is the unemployment rate increasing? Decreasing? 3. Using the graph to describe the trends in unemployment for Black and White Americans. 123

MAT 040: 2.2 Worksheet Name:________________________ 4. Graph the following points on the given coordinate plane. Label the points on the coordinate plane. a. Point A: (0, 4) b. Point B: (5,-2) c. Point C: (-1, -4) d. Point D: (3, 0) e. Point E: (5, 3) 124

MAT 040: 2.3 Worksheet Name:________________________ 1. What is a unit rate? Give an example of one that we use every day. 2. If you make $1000 gross a week after working 40 hours. What is your hourly rate? How does this relate to question 1? 3. Gemma is a really slow runner, and she can run a 5Km in 47.5 minutes. What is the unit rate in Km/min round to 2 decimal places. 4. Using the rate from #3, find Gemma’s rate in miles per hour. *Remember 1.6km = 1 mile and 60min = 1hr round to 2 decimal places. 5. Jamie went shopping at the official Real Madrid store, he managed to spend $700 Euros in 45 minutes. How many dollars (USD) did he spend per hour? In June when he was there 1 Euro = $1.06 USD. 6. Use the formula for slope to find the slope of the following points. a. (2, 5) and (7, 25) b. (-1, 28) and (14,-2) 125

MAT 040: 2.3 Worksheet Name:________________________ 7. Allison is filling her swimming pool for the summer. She already has 20 gallons of water in the pool and it is filling at a constant rate of 4 gallons per minute. Use the table and the graph below to answer the following questions. a. Find the y-intercept of the graph and explain what it means. b. Find the slope of the line and explain what it means. c. Estimate the number of gallons after 4.5 minutes. d. Estimate the number of minutes it took to get to 30 gallons. MAT 040: 2.4 Worksheet Name:________________________ 1. 126 0 1 2 3 4 5 6 0 5 10 15 20 25 30 35 40 45 Time in minutes Water in pool in gallons Time (mins) Water in pool (gal) 0 20 1 24 2 28 3 32 4 36 5 40

a. Find the y-intercept of the graph and explain what it means. b. Find the slope of the line and explain what it means. In particular, what’s the significance of the sign? c. Estimate the value of the car after 42 months. d. Estimate the number of years it took for the car to reach a value of $6,000. e. Write an equation that represents the value of the car in terms of the number of years since it was bought. f. Make sure you clearly identify what each variable in your equation represents. (use the table or the graph to help) 127

MAT 040: 2.4 Worksheet Name:________________________ Write the linear equation that represents the situation. Identify what the variables x and y represent in the equation. 2. You want to get somewhere fast and decide to use a Lime electric scooter rental. You swipe your card and are changed automatically $2.00. It then cost $0.15 per minute that you have the scooter. 3. You have $100 dollars in your savings account. You are trying to make an emergency fund, so you contribute $25 per week. 4. You choose unwisely and buy a share of Netflix Stock for $298, and it has been losing value at an average rate of $1.17 per day. 128

School Year x Cost 2000-2001 0 10820 2001-2002 1 11380 2002-2003 2 12014 2003-2004 3 12953 2004-2005 4 13793 2005-2006 5 14634 2006-2007 6 15483 2007-2008 7 16231 2008-2009 8 17092 2009-2010 9 17649 2010-2011 10 18497 MAT 040: 2.5 Worksheet Name:________________________ 1. The table below shows the average annual cost for tuition, room and board at all colleges in the U.S. between the 2000 and 2010 school years. Where x is the number of years since 2000 and y is the total cost in dollars. a. Use a technology to find the line of best fit (regression line) for the data. What is the equation? b. What is the correlation coefficient for the data? What does this tell us about the line of best fit? c. What is the slope of model of best fit? What does it mean? d. What is the y-intercept of the model of best fit? What does it mean? e. How many years since 2000 is 2019? X = _____ f. Use your equation to predict total tuition, room and board costs for the 2019-2020 school year. g. The average room and board cost in 2019 was actually $34,345, What is the residual or error with what you calculated in f? 129

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MAT 040: 2.6 Worksheet Name:________________________ 1. Convert to a percent or decimal as requested. a. 101% to a decimal b. 0.025 to a percent c. 2 to a percent d. 14% to a decimal 2. How is exponential growth and linear growth related to the “change” and the “relative change” in the y-values? 3. How do we know if an exponential equation represents growth or decay? 4. Given the following values for b – state if growth or decay and the give the rate as a percent. a. b = 1.05 b. b = 0.85 c. b = 1.015 d. b = 0.73 5. After looking at your answers to #2. Explain how b is related to the growth or decay rate – be specific. 6. The number of bacteria on a table grows by 30% every minute. If the table starts with 25 bacteria write the equation that represents the exponential equation. a. Does this situation represent exponential growth or decay? b. What is the starting amount of bacteria? What variable is this? c. What are we multiplying by every minute? What variable is this? What is it called? d. Write the exponential equation. e. How many bacteria will be on the table after 30 minutes? 131

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MAT 040: 2.6 Worksheet Name:________________________ 7. Iodine-123 is a radioactive substance used in diagnosing thyroid conditions. An initial sample of 200mg is given, this isotope loses 5% of the initial sample each one-hour period. a. Does this situation represent exponential growth or decay? b. What is the starting amount of the Iodine-123 sample? What variable is this? c. What are we multiplying by every hour? What variable is this? What is it called? d. Write an equation that describes the amount remaining after x hours. e. How much of the initial 200 mg sample remains after 8 hours? 133

MAT 040: 2.8 Worksheet Name:________________________ 1. The table below shows the number of women serving in the U.S. House of Representatives for selected years from 1980 to 2020. Source a. Fill in the x column where x is the number of years since 1980. b. Find a linear model for the data. c. What is the correlation coefficient for the linear model? d. Find an exponential model for the data. e. What is the correlation coefficient for the exponential model? f. Which model do you believe is a better fit for the data? Explain using the scatter plot and correlation coefficient. g. Use the model you chose in f to predict the number of women in the House of Representatives in 2022. h. In 2022, there were 123 women is the US House of Representatives. What is the error? Interpret the error. 134 Year X Women in House 1980 16 1982 21 1986 23 1990 29 1994 47 1998 54 2002 59 2006 68 2010 73 2014 80 2018 87 2020 101

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MAT 040: 3.1 Worksheet Name:________________________ 1. Phillips Health and Beauty Spa is replacing one of its workstations. The interest on the loan secured by the spa was $93.50. The money was borrowed at 5.5% simple interest for two years. What was the amount borrowed? i. What information is being given in the problem? j. What is it you’re being asked to find? k. Use the simple interest formula to set up and solve an equation to solve the problem. What was the amount borrowed? Show all of your work. 2. After receiving an inheritance, a newly married couple invested $15,250 for 10 years and received $9,150 in interest. a. What was the rate that the investment paid? b. If that couple had been paid 9%, how much more quickly would they have made their $9,150 in simple interest? 3. You put $5000 into a Roth IRA at the age of 20. You expect the IRA to earn you an average of 5% simple interest. How much interest will you earn if you cash it out at the age of 55? What is the total value of the investment at that time? 136

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MAT 040: 3.2 Worksheet Name:________________________ 1. Fill in the blanks below: a. Compounding daily n = ___________ b. Compounding monthly n = ___________ c. Compounding semi-annually n = ___________ d. Compounding quarterly n = ___________ e. Compounding Weekly n = ___________ f. Compounding Hourly n = ___________ 2. Do not solve the following just identify the formula you would use to get the answer. a. The future value on a loan that is compounded monthly b. The interest on a loan that is borrowed at 4% simple interest c. The future value of a bank account where the bank compounds your interest continuously. d. The interest on a loan that has interest compounded daily e. The future value of a loan that the interest compounds annually. 3. Determine which is the better investment: 3.85% compounded daily or 4.01% compounded weekly? Round your answers to 2 decimal places. 138

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MAT 040: 3.3 Worksheet Name:________________________ 1. Laney bought a refrigerator for $1750. She made a down payment of 13% and financed the rest for 6 months with payments of $261.95. a. What is the amount of her down payment on the refrigerator? b. What is the total installment price? c. What is the finance charge? 2. Nolan bought a used pontoon for $8300. His down payment was $1700. The balance was to be paid off in 36 monthly payments of $206.82. Nolan was able to pay off his loan at the end of 24 months. a. What is the total installment price? b. What is the finance change? What variable is this in our unearned interest formula? c. How many months early is he paying off his loan? What variable is this? d. What is the original number of payments? What variable is this? e. What is the unearned interest? f. What is the payoff amount? 140

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MAT 040: 3.4 Worksheet Name:________________________ 1. David and Jillian bought a home with these terms: Purchase price $415,000, 20% down payment, 30-year mortgage with a rate of 3.4%. a. How much will the down payment be? b. What is the amount financed or the principal amount of the loan? c. What will the monthly payment be? d. What is the total that they will actually pay for the home? e. How much interest will they end up paying over the 30yrs? 2. Emma is attending college and she takes out an unsubsidized loan to cover her expenses for nursing school of $9750 until she graduates in 2 years at the rate of 7.5%. Payments do not begin until 6 months after graduation. a. What is the total amount of interest that accrues before her first payment? b. What is the principal amount of the loan when payments begin? c. Student loans are calculated for a payoff period of 10 years (120 payments) what would be the monthly payment? d. How much did her degree actually end up costing? 142

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MAT 040: 3.5 Worksheet Name:________________________ 1. Below is a snapshot of the value of The Walt Disney Company on Friday, April 17, 2020 amid the Coronavirus Pandemic that has caused a downturn in the U.S economy. Answer the following questions. a. What is the current price of the stock? b. Is this stock more or less volatile than the market as a whole? How do you know? c. What’s the highest stock price in the last 52 weeks? d. What’s the lowest stock price in the last 52 weeks? e. Does Disney pay a dividend to shareholders? If so, how much? 144

MAT 040: 3.5 Worksheet Name:________________________ 2. In early 2020 the market was doing so well Jenna decided to buy 10 shares of Disney stock on February 20, 2020 for $140.37 a share. As the Coronavirus spread throughout the world, the U.S stock market plunged and Jenna decided to sell her 10 shares. Just a month later on March 20, 2020 she sold those 10 shares for $85.98 a share. If she paid a 2% commission on both the purchase and sale of the stock, how much money did she lose in just one month? Let’s break it down. a. How much money did she pay in commission to buy the stock? b. What was the total cost of buying the 10 shares of stock? c. How much money in commission did she pay when she sold her stock shares? d. How much money did she get when she sold her shares of stock? e. What is her profit? 145

MAT 040: 4.1 Worksheet Name:________________________ 1. We have a 6-sided die and we roll it once. a. What is our sample space (list all outcomes) b. What is the probability that we roll a 5? c. What is the probability that we roll a value less than 5? 2. Decide if the stated situation is theoretical or empirical probability a. You flick a spinner 100 times and record the number of times it lands on green. b. A spinner is broken up into 8 equal sections. Three sections are red, two are green, and three are yellow. You calculate that the probability of you landing on green if you flick the spinner is two out of eight. c. Based on previous classes you estimate that 40% of your class will be female. d. You buy a Powerball ticket where the odds of winning the jackpot are 1 in 292 million. 3. Write the complement to each situation in words and then use the complement formula to find the probability. a. The probability of getting an even number on a 6-sided die b. The probability of drawing a heart from a deck of 52 cards. (there are 13 cards in each suit) c. The probability of getting two heads in a row when tossing a coin two times. 146

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MAT 040: 4.4 Worksheet Name:________________________ 1. For each of the following situations, circle the sampling technique described. a. The students in a university statistics course are divided into freshman, sophomores, juniors, and seniors. One of the groups is randomly selected and all the students in that group are asked to fill out a survey. Cluster Stratified Systematic Random b. An instructor in a large lecture course of 180 students would like to get a student sample, so she selects every 10 th student name from the class roster. Cluster Stratified Systematic Random c. You are researching what writing courses students at Jackson College take. We have a list of all JC students sorted by Pathway. We take a random sample from each list by Pathway Cluster Stratified Systematic Random d. In order to select a winner for the grand prize at a fundraiser, the organizer collects all ticket stubs and uses her TI-84 calculator to select a “randint” out of all the ticket numbers sold. Cluster Stratified Systematic Random 2. We have a dataset that has data ranging from 30 – 95 and you want to create a frequency distribution with 5 classes. a. What would your width of each class be? b. Use your width to create a frequency distribution and a histogram for the data set of scores on the midterm from a MAT 130 class. 30 43 52 55 56 60 63 64 67 69 70 74 76 76 78 79 82 83 85 85 86 87 90 91 93 95 148 Class Frequency

MAT 040: 4.4 Worksheet Name:________________________ 3. Below are the scores on Exam 1 from a MAT 130 class. 30 43 52 55 56 60 63 64 67 69 70 74 76 76 78 79 82 83 85 85 86 87 90 91 93 95 a. Create a stem and leaf plot of the data. Stem Leaf 3 4 5 6 7 8 9 b. How many students scored at least a 70% on the exam? 4. How are stem and leaf plots similar and different from histograms? 149

MAT 040: 4.5 Worksheet Name:________________________ 1. The height in inches of nine army recruits are below. 78 72 68 73 75 69 74 73 72 a. Compute the mean. b. Compute the median. c. Compute the midrange. d. What is the mode? 2. Thirty-five new automobiles were tested for fuel efficiency by the Environmental Protection Agency (in miles per gallon). The individual MPG value are displayed below. 11 13 17 17 18 20 20 20 20 20 22 24 25 25 25 25 25 26 26 27 27 27 28 30 30 30 31 32 32 32 36 36 37 37 37 a. What is the class width if the data is split into 6 classes? b. Fill out the table below. Lower Class Bound Upper Class Bound Midpoint Frequency c. What is the mean? What does it mean in context? d. Why is the mean just an estimate? 150

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MAT 040: 4.6 Worksheet Name:________________________ 1. The 12 states with the highest unemployment rates in December 2015 and their rates of unemployment are given below: State Rate New Mexico 6.8 West Virginia 6.6 Nevada 6.5 Alaska 6.4 Louisiana 6.3 Mississippi 6.0 Arizona 6.0 Alabama 6.0 Oregon 5.7 North Carolina 5.7 Illinois 5.7 California 5.7 a. What is the mean? b. What is the median? c. Which measure, the mean or the median best describes the center of the data? Why? d. What is the range of the data? e. What is the standard deviation of the data? What does it mean in context of the situation? f. What is the coefficient of variation? 152

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MAT 040: 4.7 Worksheet Name:________________________ 1. The mean time for female marathon runners to finish the race is 294.45 minutes with a standard deviation of 39.9 minutes. a. Fill in the normal curve diagram below using the mean time to finish the marathon and the standard deviation given above. b. If there were 400 runners how many of them would finish between 254.55 and 334.35 minutes? c. What percent of runners would finish in less than 254.55 minutes? d. Mrs. Main finished her marathon in 553 minutes. What was her z-score? Was her time considered unusual? 154

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