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All Textbook Solutions for Mathematical Excursions (MindTap Course List)
30ESSolve the proportion. Round to the nearest hundredth. 120c=14425Solve the proportion. Round to the nearest hundredth. 6520=14aSolve the proportion. Round to the nearest hundredth. 4a=9534ES35ES36ESSolve the proportion. Round to the nearest hundredth. 2.50.6=165x38ESA management consulting firm recommends that the ratio of middle-management salaries to management trainee salaries be 5:4. Using this recommendation, what is the annual middle-management salary if the annual management trainee salary is 52,000?Medication The dosage of a cold medication is 2 mg for every 80 lb of body weight. How many milligrams of this medication are required for a person who weighs 220 lb?Fuel Consumption If your car can travel 70.5 mi on 3 gal of gasoline, how far can the car travel on 14 gal of gasoline under similar driving conditions?The scale on the architectural plans for a new house is 1 in. equals 3 ft. Find the length and width of a room that measures 5 in. by 8 in. on the drawing.43ESArt Leonardo da Vinci measured various distances on the human body in order to make accurate drawings. He determined that generally the ratio of the kneeling height of a person to the standing height of that person was 34. Using this ratio, determine the standing height of a person who has a kneeling height of 48 in.Art In one of Leonardo da Vincis notebooks, he wrote that... from the top to the bottom of the chin is the sixth part of a face, and it is the fifty fourth part of the man. Suppose the distance from the top to the bottom of the chin of a person is 1.25 in. Using da Vincis measurements, find the height of the person.A pre-election survey showed that two out of every three eligible voters would cast ballots in the county election. There are 240,000 eligible voters in the county. How many people are expected to vote in the election?One study estimated that in the U.S., the average family of four wastes 590 worth of food each year. Estimate the cost of food wasted by a. the average family of three and b, the average family of five.48ESNutrition A pancake 4 in. in diameter contains 5 g of fat. How many grams of fat are in apancake 6 in. in diameter? Explain how you arrived at your answer.50ES51ES52ESThe U.S. House of Representatives has a total of 435 members. These members represent the 50 states in proportion to each slates population. Asstated in Article XIV. Section 2, of the Constitution of the United States. Representatives shall be apportioned among the several states according to their respective numbers, counting the whole number of persons in each state. a. Find the population of each state according to the 2010 U.S. Census. Based on the state populations, determine how many representatives each state should elect to Congress. b. Compare your list against the actual number of representatives that each slate has. U.S. House of RepresentativesUse the 2015 Tax Rate Schedules to solve Exercises. Joseph Abruzzio is married and filing separately. He has an adjusted gross income of 63,850. Find Josephs tax liability.Use the 2015 Tax Rate Schedules to solve Exercises. Angela Lopez is single and has an adjusted gross income of 31,680. Find Angelas tax liability.Use the 2015 Tax Rate Schedules to solve Exercises. Dee Pinckney is married and filing jointly. She has an adjusted gross income of 58,120. The W2 form shows the amount withheld as 7124. Find Dees tax liability and determine her tax refund or balance due.Use the 2015 Tax Rate Schedules to solve Exercises. Jeremy Little field is single and has an adjusted gross income of 152,600. His W2 form lists the amount withheld as 36,500. Find Jeremys tax liability and determine his tax refund or balance due.Does a taxpayer in the 33 tax bracket pay 33 of his or her earnings in income tax? Explain your answer.6EEName three situations in which percent is used.Multiplying a number by 300 is the same as multiplying it by what whole number?Complete the table of equivalent fractions, decimals, and percents.Complete the table of equivalent fractions, decimals, and percents.Complete the table of equivalent fractions, decimals, and percents.Complete the table of equivalent fractions, decimals, and percents.Complete the table of equivalent fractions, decimals, and percents.Complete the table of equivalent fractions, decimals, and percents.Complete the table of equivalent fractions, decimals, and percents.Complete the table of equivalent fractions, decimals, and percents.Complete the table of equivalent fractions, decimals, and percents.Complete the table of equivalent fractions, decimals, and percents.e-Filed Tax Returns The IRS reported that as of April 17, 2015,it had received 132 million tax returns for 2014. Of these, 90 were filed electronically. How many of the returns were filed electronically? Round to the nearest million.A credit card company offers an annual 2 cash-back rebate on all gasoline purchases. If a family spent 6200 on gasoline purchases over the course of a year, what was the familys rebate at the end of the year?Charitable Contributions During a recent year, charitable contributions in the United States totaled 358 billion. The graph at the right shows to whom this money was donated. Determine how much money was donated to educational organizations. (Source: Contributions in the Giving USA Foundation) Recipients of Charitable Contributions in the United StatesTelevision A survey by the Boston Globe questioned elementary and middle-school students about television. Sixty-eight students, or 42.5 of those surveyed, said that they had a television in their bed room at home. How many students were included in the survey?A survey of 1236 adults nation wide asked, What irks you most about the actions of other motorists The response tailgaters was given by 293 people. What percent of those surveyed were most irked by tailgaters? Round to the nearest tenth of a percent. (Source: Reuters/Zog by)Wind Energy In a recent year, wind machines in the United States generated 181.7 billion kWh of electricity, enough to serve over 16 million households. The nations total electricity production that year was 4094 billion kWh. (Source: Energy Information Administration) What percent of the total energy production was generated by wind machines? Round to the nearest tenth of a percent.During 1 year. Approximately 2,240,000 oz of gold went into the manufacturing of electronic equipment in the United States. This is 16 of all the gold mined in the United States that year. How many ounces of gold were mined in the United States that year?The two circle graphs how surveyed employees actually spend their time and how they would prefer to spend their time. Assume that employees have 112 hours a week that are not spent sleeping. Round answers to the nearest tenth of an hour. (Source: Wall Street Journal Supplement from Families and Work Institute) a. What is the actual number of hours per week that employees spend with family and friends? b. What is the number of hours that employees would prefer to spend on their jobs or careers? c. What is the difference between the number of hours an employee would prefer to spend on him- or herself and the actual amount of time the employee spends on him- or herself?A TurboTax online survey asked people how they planned to use their tax refunds. Seven hundred forty people, or 22 of the respondents, said they would save the money. How many people responded to the survey?Diabetes Approximately 9.3 of the American population has diabetes. Within this group. 21.0 million are diagnosed, while 8.1 million are undiagnosed. (Source: Centers for Disease Control and Prevention) What percent of Americans with diabetes have not been diagnosed with the disease? Round to the nearest tenth of a percent.Education Of the 78 million baby boomers living in the United States, 4.5 million have some college experience but no college degree. (Sources: The National Center for Education Statistics; U.S. Census Bureau; McCook Daily Gazette)What percent of the baby boomers living in the United States have some college experience but have not earned a college degree? Round to the nearest tenth of a percent.The number of Internet users worldwide went from 0.4 billion in 2000 to 3.2 billion in 2015. (Source: International Telecommunication Union) Find the percent increase in the number of Internet users from 2000 to 2015.The graph below shows the projected growth of the number of Americans aged 85 and older. a. What is the percent increase in the population of this age group from 1995 to 2030? b. What is the percent increase in the population of this age group from 2030 to 2050? c. What is the percent increase in the population of this age group from 1995 to 2050? d. How many times larger is the population in 2050 than in 1995? How could you determine this number from the answer to part c? Projected Growth (in millions) of the Population of Americans Aged 85 and Older SOURCE: U.S. Census BureauAuto Sales U.S. auto sales increased from 16.5 million in 2014 to 17.5 million in 2015. (Source: Los Angeles Times) Find the percent increase in auto sales from 2014 to 2015. Round to the nearest tenth of a percent.Cable TV In 2006. 65.4 million people subscribed to cable television. In 2013, that number had decreased to 54.4 million. (Source: Federal Communications Commission) Find the percent decrease in the number of cable TV subscribers from 2006 to 2013. Round to the nearest tenth of a percent.Consumption of Eggs During the last 50 years, the consumption of eggs in the United States has decreased by 17. Fifty years ago, the average consumption was 307 eggs per person per year. What is the average consumption of eggs today?Millionaire Households The following table shows the estimated number of millionaire house-holds (households with a net worth of at least 1 million, not including primary residence) in the United States for selected years. (Source: Spectrum Group) a. What is the percent increase in the estimated number of millionaire households from 2000 to 2007? Round to the nearest tenth of a percent. b. Find the percent decrease in the estimated number of millionaire households from 2007 to 2008. Round to the nearest tenth of a percent.The graph below shows the number of active-duty U.S. military personnel, in thousands, in 1990 and 2014. Which branch of the military had the greatest percent decrease in personnel from 1990 to 2014? What was the percent decrease for this branch of the service? Round to the nearest tenth of a percent. Number of Active-Duty U.S. Military Personnel SOURCE: Department of DefenseYour employer agrees to give you a 5 raise after 1 year on the job, a 6 raise the next year, and a 7 raise the following year. Is your salary after the third year greater than, less than, or the same as it would be if you had received a 6 raise each year?32ESNielsen Ratings Nielsen Media Research surveys television viewers to determine the numbers of people watching particular shows. They estimated that for the 2015- 2016 television season, there were an estimated 113.3 million U.S. households with televisions. Each rating point represents 1 of that number, or 1,133,000. Therefore, for instance, if 60 Minutes received a rating of 5.8, then 5.8 of all U.S. households with televisions, or (0.058)(113,300,000)=6,571,400 households, were tuned to that program. A rating point does not mean that 1,133,000 people are watching a program. A rating point refers to the number of households with television sets tuned to that program: there may be more than one person watching a television set in the household. Nielsen Media Research also describes a programs share of the market. Share is the percent of households with television sets in use that are tuned to a program. Suppose that the same week that 60 Minutes received 5.8 rating points, the show received a share of 11. This would mean that 11 of all households with a television turned on were tuned to 60 Minutes, whereas 5.8 of all households with a television were tuned to the program. a. If NCIS received a Nielsen rating of 10.1 and a share of 17. how many TV households watched the program that week? How many TV households were watching television during that hour? Round to the nearest hundred thousand. b. Suppose that The Big Bang Theory received a rating of 5.6 and a share of 11. How many TV house holds watched the program that week? How many TV households were watching television during that hour? Round lo the nearest hundred thousand. Suppose that Modern Family received a rating of 7.5 during a week in which 19,381,000 people were watching the show. Find the average number of people per TV household who watched the program. Round to the nearest tenth.Solve the equation and then check the solutions using the sum and product of the solutions. x210=3x2EE3EE4EE5EE6EE7EE8EE9EE10EE11EE12EE13EE14EE15EE16EEFirst try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. For equations with solutions that are irrational number, give exact solutions and approximate solutions to the nearest thousandth. r23r=102ESFirst try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. For equations with solutions that are irrational number, give exact solutions and approximate solutions to the nearest thousandth. t2=t+1First try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. For equations with solutions that are irrational number, give exact solutions and approximate solutions to the nearest thousandth. u2=u+35ES6ESFirst try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. For equations with solutions that are irrational number, give exact solutions and approximate solutions to the nearest thousandth. 9z218z=0First try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. For equations with solutions that are irrational number, give exact solutions and approximate solutions to the nearest thousandth. 4y2+20y=0First try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. For equations with solutions that are irrational number, give exact solutions and approximate solutions to the nearest thousandth. z2=z+4First try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. For equations with solutions that are irrational number, give exact solutions and approximate solutions to the nearest thousandth. r2=r1First try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. For equations with solutions that are irrational number, give exact solutions and approximate solutions to the nearest thousandth. 2s2=4s+512ES13ESFirst try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. For equations with solutions that are irrational number, give exact solutions and approximate solutions to the nearest thousandth. s2+6s=1First try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. For equations with solutions that are irrational number, give exact solutions and approximate solutions to the nearest thousandth. 2x2=9x+1816ESFirst try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. For equations with solutions that are irrational number, give exact solutions and approximate solutions to the nearest thousandth. 6x11=x218ESFirst try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. For equations with solutions that are irrational number, give exact solutions and approximate solutions to the nearest thousandth. 415u=4u220ES21ES22ES23ES24ES25ES26ESRound answers to nearest hundredth where appropriate. Golf The height h, in feet, of a golf ball t seconds after it has been hit is given by the equation h=16t2+60t. How many seconds after the ball is hit will the height of the ball be 36 ft?28ESRound answers to nearest hundredth where appropriate. Mathematics In the diagram below, the total number of circles T when there are n rows is given by T=0.5n2+0.5n = O.5n2 + O.5n. Verify the formula for the four figures shown. Determine the number of rows when the total number of circles is 55.Round answers to nearest hundredth where appropriate. Astronautics If an astronaut on the moon throws a ball upward with an initial velocity of 6 m per second, its approximate height h, in meters, after r seconds is given by the equation h=0.8t2+6t. How long after it is released will the ball be 8 m above the surface of the moon?Round answers to nearest hundredth where appropriate. Demography The equation y=0.03x2+0.36x+34.6 describes the number of people y, in millions, aged 65 and older in the United States in year x, where x=0 corresponds to the year 2000. Approximate the year in which there will be 50 million people aged 65 and older in the United States.32ES33ES34ESRound answers to nearest hundredth where appropriate. Football The hang time of a football that is kicked on the opening kick off is given by s=16t2+88t+1, where s is the height in feet of the football t seconds after leaving the kickers foot. What is the hang time of a kickoff that hits the ground without being caught?36ES37ES38ESRound answers to nearest hundredth where appropriate. Soccer A penalty kick in soccer is made from a penalty mark that is 36 ft from a goal that is 8 ft high. A possible equation for the flight of a penalty kick is h=0.002x2+0.36x, where h is the height, in feet, of the ball x feet from the goal. Assuming that the flight of the kick is toward the goal and that it is not touched by the goalie, will the ball land in the net?Round answers to nearest hundredth where appropriate. Springboard Diving An event in the Summer Olympics is 10-meter springboard diving. In this event, the height h, in meters, of a diver above the water t seconds after jumping is given by the equation h=4.9t2+7.8t+10. What is the height above the water of a diver after 2s?41ES42ES43ES44ES45ES46ES47ES48ES49ES50ESSolve the equation. 5x+3=10x172RE3RE4RE5RE6RE7RE8RESolve the formula for the given variable. 4x+3y=12;y10RE11RE12REChemistry A chemist mixes 100g of water at 80C with 50g of water at 20C. Use the formula m1(T1T)=m2(TT2) to find the final temperature of the water after mixing In this equation. m1 is the quantity of water at the hotter temperature. T1 is the temperature of the hotter water, m2 is the quantity of water at the cooler temperature. T2 is the temperature of the cooler water, and T is the final temperature of water after mixing.Telemarketing At a telemarketing firm, an employee is paid 12 an hour plus 0.75 for each call completed. During an 8-hour day, the employees compensation was 159,75. How many calls did the employee complete?15RE16RESocial Media In July 2012, Instagram announced 80 million users of its photo sharing app. In September 2015, they announced that the number of users had reached 400 million. Find the percent increase in the number of Instagram users during that time period. Round to the nearest percent.City Populations The table below shows the population and area of the five most populous cities in the United States. a. The cities are listed in the table according to population, from largest to smallest. Rank the cities according to population density, from largest to smallest. b. How many more people per square mile are there in New York than in Houston? Round to the nearest whole number.19RE20REGardening Three tablespoons of a liquid plant fertilizer are to be added to every 4 gal of water. How many tablespoons of fertilizer are required for 10 gal of water?22RE23REDiet Americans consume 7 billion hot dogs from Memorial Day through Labor Day. This is 35 of the hot dogs consumed annually in the United States. (Source: National Hot Dog & Sausage Council: American Meat Institute) How many hot dogs do Americans consume annually?Boston Marathon In the 2015 Boston Marathon, 27,167 runners started the race and 26,598 finished. What percent of the runners who started the course finished the race? Round to the nearest tenth of a percent.26RE27RE28RE29REVacation Days In Italy, workers take an average of 42 vacation days per year. This number is 3 more than three times the average number of vacation days that workers take each year in the United States. (Source: World Tourism Organization) On average, how many vacation days do U.S. workers take per year?Model Rockets A small rocket is shot from the edge of a cliff. The height h, in meters, of the rocket above the cliff is given by h=30t5t2, where t is the time in seconds after the rocket is shot. Find the times at which the rocket is 25m above the cliff.32RE1T2T3T4T5T6T7T8TEnergy The cost of electricity in a certain city is 0.16 for each of the first 300 kWh and 0.20 for each kilowatt-hour over 300 kWh. Find the number of kilowatt-hours used by a family with a 74.25 electric bill.10T11T12TSocial Media In 2015, Twitter announced that they had 320 million monthly active users, and 80 of users were active on mobile devices. How many monthly active users were active on mobile devices in 2015?14TGardening The directions on a bag of plant food recommend 0.5 lb for every 50ft2 of lawn. How many pounds of plant food should be used on a lawn that measures 270ft2?16T17T18TCompact Disc Sales In 2005, the total number of music CDs sold was 598.9 million, while in 2015, it was 125.6 million. (Source: Soundscan) a. Find the percent decrease in the number of CDs sold from 2005 to 2015. Round to the nearest tenth of a percent. b. If the percent decrease in the number of CDs sold from 2015 to 2025 is the same as it was from 2005 to 2015, how many CDs will be sold in 2025?20T1EE2EE3EE4EE5EE1ES2ESDraw a line through all points with an x-coordinate of 2.Draw a line through all points with an x-coordinate of -3.Draw a line through all points with a y-coordinate of -3.6ESGraph the ordered-pair solutions of y=x2 when x=2,1,0,1 ,and2.8ES9ES10ESGraph the ordered-pair solutions of y=x32 when x=2,1,0,1, and 2.12ESIn Exercises 13 to 20, graph each equation. y=2x114ESIn Exercises 13 to 20, graph each equation. y=23x+116ES17ES18ES19ES20ES21ES22ESEvaluate the function for the given value. f(t)=t2t3;t=324ES25ES26ES27ES28ESSports The height h, in feet, of a ball that is released 4 ft above the ground with an initial upward velocity of 80 ft/s is a function of the time t, in seconds, the ball is in the air and is given by h(t)=16t2+80t+4,0t5.04 Find the height of the ball above the ground 2 s after it is released. Find the height of the ball above the ground 4 s after it is released.30ESSound The speed s, in feet per second, of sound in air depends on the temperature t of the air in degrees Celsius and is given by s(t)=1087t+27316.52. What is the speed of sound in air when the temperature is 0°C (the temperature at which water freezes)? Round to the nearest foot per second. What is the speed of sound in air when the temperature is 25°C? Round to the nearest foot per second.32ESPendulums The time T in seconds, it takes a pendulum to make one swing depends on the length of the pendulum and is given by T(L)=2L32, where L is the length of the pendulum in feet Find the time it takes the pendulum to make one swing if the length of the pendulum is 3 ft. Round to the nearest hundredth of a second. Find the time it takes the pendulum to make one swing if the length of the pendulum is 9 in. Round to the nearest tenth of a second.34ES35ES36ES37ES38ES39ES40ESGraph the function. F(x)=12x+342ESGraph the function. f(x)=x2144ESGraph the function. f(x)=x2+446ES47ES48ES49ES50ES51ES52ES53ES54ES55ES56ESThe graph at the left represents a car traveling on a straight road. Answer the following questions on the basis of this graph. Between what two times is the car moving to the right?2EE3EE4EE5EE6EE7EE8EE9EE10EE11EE1ES2ES3ES4ESFind the x- and y-intercepts of thegraph of the equation. y=x46ESFind the x- and y-intercepts of thegraph of the equation. 3x+4y=128ES9ES10ES11ES12ES13ES14ES15ESTravel An approximate linear model that gives the remaining distance, in miles, a plane must travel from Los Angeles to Paris is given by s(t)=6000500t where s(t) is the remaining distance t hours after the flight begins. Find and discuss the meaning, in the context of this application, of the intercepts on the vertical and horizontal axes.Refrigeration The temperature of an object taken from a freezer gradually rises and can be modeled by T(x)=3x15 where T(x) is the Fahrenheit temperature of the object x minutes after being removed from the freezer. Find and discuss the meaning, in the context of this application, of the intercepts on the vertical and horizontal axes.Retirement Account A retired biologist begins withdrawing money from a retirement account according to the linear model A(t)=100,0002500t where A(t) is the amount, in dollars, remaining in the account t months after withdrawals begin. Find and discuss the meaning, in the context of this application, of the intercepts on the vertical and horizontal axes.19ES20ESFind the slope of the line containing the two points. (1,4),(2,5)22ESFind the slope of the line containing the two points. (1,3),(4,5)24ES25ES26ESFind the slope of the line containing the two points. (2,4),(2,2)28ES29ES30ESFind the slope of the line containing the two points. (2,3),(1,3)32ES33ES34ESTravel The graph below shows the relationship between the distance traveled by a motorist and the time of travel. Find the slope of the line between the two points shown on the graph. Write a sentence that states the meaning of the slope in the context of this application.Depreciation The graph below shows the relationship between the value of a building and the depreciation allowed for income tax purposes. Find the slope of the line between the two points shown on the graph. Write a sentence that states the meaning of the slope in the context of this application.37ES38ESPanama Canal Ships in the Panama Canal are lowered through a series of locks. A ship is lowered as the water in a lock is discharged. The graph below shows the number of gallons of water N remaining in a lock t minutes after the valves are opened to discharge the water. Find the slope of the line. Write a sentence that explains the meaning of the slope.40ESGraph the line that passes through the point (2,3) and has slope 54.42ESGraph the line that passes through the point (2, 0) and has slope -1.44ESGraph using the slope and y-intercept. f(x)=23x346ESGraph using the slope and y-intercept. f(x)=34x