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Financial Algebra advanced algebra with financial applications 1st edition Robert K. Gerver - Solutions
Courtney wants to sell her grandfather's antique 1932 Ford. She begins to set her price by looking at ads and finds these prices: $24,600, $19,000, $33,000, $15,000, and 20,000. What is the mean price?
Five Smithtown High School students are saving up to buy their first cars. They all have after-school jobs, and their weekly salaries are listed in the table.Emily ..........................$110Sam ............................$145Danielle .......................$130Katie
Rosanne is selling her Corvette. She wants to include a photo of her car in the ad. Three publications give her prices for her ad with the photograph: Lake Success Shopsaver ..................... $59.00 Glen Head Buyer .............................. $71.00 Floral Park Moneysaver
The Cold Spring High School student government polled randomly selected seniors and asked them how much money they spent on gas in the last week. The following stem-and-leaf plot shows the data they collected.a. How many students were polled? b. Find the mean to the nearest cent. c. Find the
A group of randomly-selected recent college graduates were asked how much the monthly payment is on their student loan. The responses are shown in the stem-and-leaf plot.a. What is the total frequency?b. How many people had monthly payments between $210 and $219?c. What is the mode monthly payment?
Express the mean of the data set shown in the frequency table algebraically. Price Frequency x ............................ y w ............................ 5 16 ........................... 4 18 ........................... v
Brian looked up prices of thirteen used Chevrolet HHR "retro" trucks in the classified ads and found these prices: $8,500, $8,500, $8,500, $9,900, $10,800, $10,800, $11,000, $12,500, $12,500, $13,000, $13,000, $14,500, and $23,000.a. Make a frequency table for this data set. b. Find the mean. Round
Enter the data from Example 1 in your calculator. a. Create a box-and-whisker plot using the data from Example 1. b. How would you determine if it would be appropriate to create a modified boxplot for this data? c. How many outliers are there in this distribution?
Megan has a friend at work who is selling a used Honda. The car has 60,000 miles on it. Megan comparison shops and finds these prices for the same car. a. Find the mean price of the 5 prices listed. b. How many of these cars are priced below the mean? c. Find the median price. d. How many of these
Megan, from Exercise 8, decides to get more information about the cars she researched. The table has prices and mileages for the same used car. In addition to the statistics she has learned in this chapter, Megan decides to use her linear regression skills from Chapter 2 to see if there is a
Jared's car slides into a stop sign during an ice storm. There is x dollars damage to his car, where x > 1,000, and the stop sign will cost y dollars to replace. Jared has $25,000 worth of PD insurance, a $1,000 deductible on his collision and comprehensive insurance, and $50,000 no-fault
Mollie has 100/300/50 liability insurance and $50,000 PIP insurance. She drives through a stop sign and hits a telephone pole and bounces into a minivan with 8 people inside. Some are seriously hurt and sue her. Others have minor injuries. Three passengers in Mollie's car are also hurt. a. The pole
The Schuster family just bought a third car. The annual premium would have been x dollars to insure the car, but they are entitled to a 10% discount since they have other cars with the company. a. Express their annual premium after the discount algebraically. b. If they pay their premium quarterly
Marc currently pays x dollars per year for auto insurance. Next year, his rates are going to increase 15%. If he completes a defensive driver course, the insurance company will lower his rate by d dollars. a. Express his annual premium for next year algebraically if he completes the course. b.
The stem-and-leaf plot gives the semiannual premiums for the girls and boys in Van Buren High School who currently drive. It is called a back-to-back stem-and-leaf plot, and combines two stem-and-leaf plots. The numbers between the two vertical lines represent the hundreds and tens digits. The
The following stem-and-leaf plot gives the number of juniors who took a driver education course at Guy Patterson High School over the last two decades. Construct a box-and-whisker plot based on the data.
Rachel has $25,000 worth of property damage insurance. She causes $32,000 worth of damage to a sports car in an accident. a. How much of the damages will the insurance company have to pay? b. How much will Rachel have to pay?
Ronald Kivetsky bought a new car and received these price quotes from his insurance company. a. What is the annual premium? b. What is the semiannual premium? c. How much less would Ronald's semiannual payments be if he dropped the optional collision insurance?
Ruth Fanelli has decided to drop her collision insurance because her car is getting old. Her total annual premium is $916, of which $170.60 covers collision insurance. a. What will her annual premium be after she drops the collision insurance? b. What will her quarterly payments be after she drops
Felix Madison has $10,000 worth of property damage insurance and a $1,000 deductible collision insurance policy. He had a tire blow- out while driving and crashed into a $1,400 fire hydrant. The crash caused $1,600 in damages to his car. a. Which insurance covers the damage to the fire hydrant? b.
How might those words apply to what you have learned?
A car is originally worth $34,450. It takes 13 years for this car to totally depreciate.a. Write the straight line depreciation equation for this situation. b. How long will it take for the car to be worth half its value? c. How long will it take for the car to be worth $10,000? Round your answer
The original price of a car is entered into spreadsheet cell A1 and the length of time it takes to totally depreciate is entered into cell B1. a. Write the spreadsheet formula that calculates the amount that the car depreciates each year. b. The spreadsheet user is instructed to enter a length of
The original price of a car is entered into spreadsheet cell A1 and the annual depreciation amount in cell B1. a. Write the spreadsheet formula to determine the number of years it will take for the car to totally depreciate. b. The spreadsheet user is instructed to enter a car value in cell
Winnie purchased a new car for $54,000. She has determined that it straight line depreciates to zero over 10 years. When she purchased the car, she made an $8,000 down payment and financed the rest with a 4-year loan at 4.875%. You can use the monthly payment formula from the last chapter to
Delia purchased a new car for $25,350. This make and model straight line depreciates to zero after 13 years. a. Identify the coordinates of the x- and y-intercepts for the depreciation equation. b. Determine the slope of the depreciation equation. c. Write the straight line depreciation equation
Vince purchased a used car for $11,200. This make and model used car straight line depreciates to zero after 7 years. a. Identify the coordinates of the x- and y-intercepts for the depreciation equation. b. Determine the slope of the depreciation equation. c. Write the straight line depreciation
Examine the straight line depreciation graph for a car.a. At what price was the car purchased? b. After how many years does the car totally depreciate? c. Write the equation of the straight line depreciation graph shown.
The straight line depreciation equation for a luxury car is y = −3,400x + 85,000. a. What is the original price of the car? b. How much value does the car lose per year? c. How many years will it take for the car to totally depreciate?
The straight line depreciation equation for a motorcycle is y = −2,150x + 17,200. a. What is the original price of the motorcycle? b. How much value does the motorcycle lose per year? c. How many years will it take for the motorcycle to totally depreciate?
The straight line depreciation equation for a car is y = −2,750x + 22,000. a. What is the car worth after 5 years? b. What is the car worth after 8 years?
The straight line depreciation equation for a car is y = −2,680x + 26,800. a. How much is the car worth after 48 months? b. How much is the car worth after 75 months?c. Suppose that M represents the length of time in months when the car still has value. Write an algebraic expression to represent
The graph of a straight line depreciation equation is shown.a. Use the graph to approximate the value of the car after 4 years.b. Use the graph to approximate the value of the car after 5 years.c. Use the graph to approximate when the car will be worth half its original value.
The historical prices of a car are recorded for 17 years as shown.a. Construct a scatterplot for the data.b. Determine the exponential depreciation formula that models this data. Round to the nearest hundredth.c. Determine the depreciation rate.d. Predict the value of this car after 140 months.
Raphael purchased a 3-year-old car for $16,000. He was told that this make and model depreciates exponentially at a rate of 5.45% per year. What was the original price of the car when it was new?
The car that Diana bought is 8 years old. She paid $6,700. This make and model depreciates exponentially at a rate of 14.15% per year. What was the original price of the car when it was new?
What is the exponential depreciation rate, expressed as a percent to the nearest tenth of a percent, for a car that originally sells for $30,000 when new but exponentially depreciates after 5 years to $18,700?
What is the exponential depreciation rate, expressed as a percent to the nearest tenth of a percent, for a car that originally sells for $52,000 when new but exponentially depreciates to $45,000 after 32 months?
A car originally sold for $25,900. It depreciates exponentially at a rate of 8.2% per year. Nina put $10,000 down and pays $550 per month to pay off the balance. After how many years will her car value equal the amount she paid for the car to that point? What will that value be?
Jazmine's car originally sold for $46,600. It depreciates exponentially at a rate of 10.3% per year. Jazmine put $12,000 down and pays $800 per month to pay off the balance. After how many years will her car value equal the amount she paid to date for the car? What will that value be?
Seamus bought a car that originally sold for $40,000. It exponentially depreciates at a rate of 7.75% per year. Write the exponential depreciation equation for this car.
The July 2008 issue of Hemmings Motor News included a feature story on the 1957 Cadillac Eldorado Brougham. When sold as a new car in 1957, the price was $13,074. It depreciated in value over the next few years. Then, in 1967, something interesting began to happen as seen in this table of values.
Chris purchased a used car for $19,700. The car depreciates exponentially by 10% per year. How much will the car be worth after 6 years? Round your answer to the nearest penny.
Laura's new car cost her $21,000. She was told that this make and 5 model depreciates exponentially at a rate of 8 5/8% per year. How 8 much will her car be worth after 100 months?
Lisa purchased a used car for D dollars. The car depreciates exponentially at a rate of E% per year. Write an expression for the value of the car in 5 years, in A years, and in M months.
A graphing calculator has determined this exponential regression equation based upon car value data: y = a*bx, a = 20,952.11, and b = 0.785. What is the rate of depreciation for this car? How much is this car worth after 6 years; 78 months; w years?
A graphing calculator has determined this exponential regression equation based upon car value data: y = a*bx, a = 18,547.23 and b = 0.8625. What is the rate of depreciation 4 for this car? How much is this car worth after 6 years, 78 months, and w months?
The historical prices of a car are recorded for 11 years as shown.a. Construct a scatterplot for the data.b. Determine the exponential depreciation equation that models this data. Round to the nearest hundredth.c. Determine the depreciation rate. d. Predict the value of this car after 3 1/2 years.
How might the quote apply to what you have learned? Discuss in detail.
Complete the chart for entries a-l.
Alexandra uses her car for business. She knows that her tank was full when she started her business trip, but she forgot to write down the odometer reading at the beginning of the trip. When the trip was over, the odometer read 13,020.5. Alexandra's car gets 25 miles per gallon. When she filled up
A car averages 56 mi/h on a trip. a. Write an equation that shows the relationship between distance, rate, and time for this situation. b. Let time be the independent variable and distance be the dependent variable. Draw and label the graph of this equation. c. Use the graph to determine
A spreadsheet has been created so that the user enters information in the stated cells.a. Write a formula to calculate the speed of the car for the trip in cell C1. b. Write a formula to calculate the number of gallons of gas used in cell C2. c. Write a formula to calculate the total cost of gas
Complete the chart.1 USD ‰ˆ 1.07 Canadian dollars (CAD)1 USD ‰ˆ 0.69 Euros (EUR)1 USD ‰ˆ 1.16 Australian dollars (AUD) 1 USD ‰ˆ 89.85 Japanese yen (JPY)1 USD ‰ˆ 7.34 South African rand (ZAR)1 USD ‰ˆ 1.00 Swiss franc (CHF)
Complete the chart1 USD ‰ˆ 1.07 Canadian dollars (CAD)1 USD ‰ˆ 0.69 Euros (EUR)1 USD ‰ˆ 1.16 Australian dollars (AUD) 1 USD ‰ˆ 89.85 Japanese yen (JPY)1 USD ‰ˆ 7.34 South African rand (ZAR)1 USD ‰ˆ 1.00 Swiss franc (CHF)
While Willie traveled in India, he paid an average of 87.42 Indian rupees for a liter of gas.a. What expression represents the price of this gas in U.S. dollars if the exchange rate was x? b. What is this rate equivalent to in U.S. dollars per gallon? c. If Willie spent about $115, how many
Explain how the quote can be interpreted from what you have experienced.
Complete the chart for entries a-j.
David is driving on the highway at the legal speed limit of 70 mi/h. He notices that there is an accident up ahead approximately 200 feet away. His reaction time is approximately 3 / 4 of a second. Is he far enough away to bring the car safely to a complete stop? Explain your answer.
Martine is driving on an interstate at 70 km/h. She sees a traffic jam about 50 meters ahead and needs to bring her car to a complete stop before she reaches that point. Her reaction time is approximately ¾ of a second. Is she far enough away from the traffic jam to safely bring the car to a
Model the total stopping distance by the equation y = x2 / 20 + x, where 20 x represents the speed in miles per hour and y represents the total stopping distance in feet. a. Graph this equation for the values of x, where x ≤ 70 mi/h. b. Use the graph to approximate the stopping distance for a car
Model the total stopping distance by the equation y = x2/170 + x/5, where x represents the speed in km/h and y represents the total stopping distance in meters. a. Graph this equation for the values of x, where x ≤ 100 km/h. b. Use the graph to approximate the stopping distance for a car
A spreadsheet user inputs a speed in miles per hour into cell A1. a. Write a formula that would enter the approximate equivalent of that speed in km/h in cell A2. b. Write a spreadsheet formula that would enter the approximate total stopping distance in feet in cell A3. c. Write a spreadsheet
There are 5,280 feet in a mile. Round answers to the nearest unit. a. How many miles does a car traveling at 65mi/h go in one hour? b. How many feet does a car traveling at 65 mi/h go in one hour? c. How many feet does a car traveling at 65mi/h go in one minute? d.
There are 5,280 feet in a mile. Round answers to the nearest unit. a. How many miles does a car traveling at 42mi/h go in one hour? b. How many feet does a car traveling at 42 mi/h go in one hour? c. How many feet does a car traveling at 42mi/h go in one minute? d.
Determine the distance covered by a car traveling 80 km/h for each unit and time given. Round answers to the nearest unit. a. Kilometers in one hourc. Meters in one minute b. Meters in one hourd. Meters in one second
Determine the distance covered by a car traveling 55 km/h for each unit and time given. Round answers to the nearest unit. a. Kilometers in one hour c. Meters in one minute b. Meters in one hour d. Meters in one second
Determine the distance covered by a car traveling x km/h for each unit and time given. a. Kilometers in one hour c. Meters in one minute b. Meters in one hour d. Meters in one second
Determine the distance covered by a car traveling 68 mi/h for each unit and time given. Round answers to the nearest unit. a. Miles in one hourc. Feet in one minute b. Feet in one hourd. Feet in one second
Edward is driving 52 mi/h on a one-lane road. He must make a quick stop because there is a stalled car ahead. a. What is his approximate reaction distance? b. What is his approximate braking distance?c. About how many feet does the car travel from the time he switches pedals until the car has
Explain how the quote can be interpreted from what you have learned.
Marielle was in an accident. She was traveling down a road at 36 mi/h when she slammed on her brakes. Her car left two skid marks that averaged 50 ft in length with a difference of 4 ft between them. Her brakes were operating at 80% efficiency at the time of the accident. a. What was the possible
The following measurements from yaw marks left at the scene of an accident were taken by the authorities. Using a 31-ft length chord, the middle ordinate measured approximately 3 ft. The drag factor for the road surface is 1.02. a. Determine the radius of the yaw mark to the nearest tenth of a
Juanita is an accident reconstruction expert. She measured a 70-ft chord from the outer rim of the yaw mark on the road surface. The middle ordinate measured 9 ft in length. The drag factor of the road surface was determined to be 1.13. a. Determine the radius of the yaw mark to the nearest tenth
The formula used to determine the radius of the yaw mark arc is derived from a geometric relationship about two intersecting chords in a circle. In the figure, chords AB and CD intersect at point E in the circle. The product of the two segment lengths making up chord AB, AE × EB, is
In the spreadsheet, the prompts for entering data are in column A. The user enters the data in column B.a. Write the spreadsheet formula that will calculate the radius in cell B4. b. Write the spreadsheet formula that will calculate the minimum skid speed in cell B5. The formula for finding that
Ghada works for an insurance company as an accident reconstruction expert. She measured a 52-ft chord from the outer rim of the yaw mark on the road surface. The middle ordinate measured x ft in length. The drag factor of the road surface was determined to be 1.05. a. What is the expression for
Rona was driving on an asphalt road that had a 35 mi/h speed limit posted. A deer jumped out from the side of the road causing Rona to slam on her brakes. Her tires left three skid marks of lengths 70 ft, 72 ft, and 71 ft. The road had a drag factor of 0.78. Her brakes were operating at 95%
In the spreadsheet, the prompts for entering data are in column A. The user enters the data in column B. a. Write the spreadsheet formula that will calculate the skid distance in cell B9. b. Write the spreadsheet formula that will calculate the minimum skid speed in cell B11. The format for
A car leaves four skid marks each 50 feet in length. The drag factor for the road is 0.9. Let x represent the braking efficiency. a. What is the range of values that can be substituted for x? b. Let the speed be represented by the variable y and x represent the braking efficiency. Write the skid
The college newspaper charges by the character for classified ads. Letters, numbers, spaces, and punctuation count as one character. They charge $34 for the first 100 characters, and $0.09 for each additional character. If x represents the number of characters, express the cost c(x) of an ad as a
The historical prices of a car with the same make, model, and features are recorded for a period of 10 years as shown in the table.a. Construct a scatterplot for the data. b. Determine the exponential depreciation formula that models this data. Round all numbers to the nearest hundredth. c.
Gina has 250/500/50 liability insurance and $50,000 PIP insurance. She changes lanes too quickly, hits the metal guard rail, and then hits a tour bus. Four people are seriously hurt and sue her. Twenty others have minor injuries. Gina's boyfriend, who was in her car, was also hurt. Historical
Joshua just purchased a 4-year-old car for $12,000. He was told that this make and model depreciates exponentially at a rate of 5.8% per year. What was the original price to the nearest hundred dollars?
A graphing calculator has determined the following exponential regression equation: y = a*bx, a = 28,158.50, b = 0.815. a. What is the rate of depreciation for this car? b. How much is this car worth to the nearest dollar after 6 years? c. How much is this car worth to the nearest hundred dollars
Tricia is driving 64 miles per hour on an interstate highway. She must make a quick stop because there is an emergency vehicle ahead. a. What is her approximate reaction distance? b. What is her approximate braking distance? c. About how many feet does the car travel from the time she starts to
Marlena is driving on an interstate at 65 km/h. She sees a traffic jam about 30 meters ahead and needs to bring her car to a complete stop before she reaches that point. Her reaction time is approximately ¾ of a second. Is she far enough away from the traffic jam to safely 4 bring the car to a
The Classic Car Monthly charges $49 for a three-line classified ad. Each additional line costs $9.50. For an extra $30, a seller can include a photo. How much would a five-line ad with a photo cost?
The straight line depreciation equation for a car is y = −2,400x + 36,000. a. What is the original price of the car? b. How much value does the car lose per year? c. How many years will it take for the car to totally depreciate?
A car is originally worth $43,500. It takes 12 years for this car to totally depreciate. a. Write the straight-line depreciation equation for this situation. b. How long will it take for the car to be worth one quarter of its original price? c. How long will it take for the car to be worth
Prices for used stainless steel side trim for a 1957 Chevrolet convertible are $350, $350, $390, $400, $500, $500, $500, $600, $650, $725, $800, $850, $900, and $1,700. The prices vary depending on the condition. a. Find the mean of the trim prices to the nearest dollar. b. Find the median of the
Kathy purchased a new car for $37,800. From her research she has determined that it straight-line depreciates over 14 years. She made a $7,000 down payment and pays $710 per month for her car loan.a. Create an expense and depreciation function where x represents the number of months. b. Graph these
Grahamsville High School recently polled its teachers to see how many miles they drive to work each day. At the left is a stem-and- leaf plot of the results. a. How many teachers were polled?b. Find the mean to the nearest mile. c. Find the median. d. Find the mode(s). e. Find the range.f. Find the
Stewart has $25,000 worth of property damage insurance and a $1,000 deductible collision insurance policy. He crashed into a fence when his brakes failed and did $7,000 worth of damage to the fence. The crash caused $3,600 in damages to his car. a. Which insurance covers the damage to the fence?
Interpret the quote in the context of what you learned about job seeking?
Kareem earns y dollars per month at his accounting job. Express his annual salary using the K abbreviation found in classified ads?
Mike is a veterinarian. He is placing a 9-line classified ad for an assistant. The following piecewise function gives the price of an x-line ad.a. Find the difference between the cost of a 2-line ad and the cost of a 3-line ad.b. Find the cost of a 10-line ad.c. Find the cost of an 11-line ad.d.
Joanne is looking for a job as a teacher. She plans to send resumes to 123 schools in her county. Her local printer charges $23 per 100 copies, and sells them only in sets of 100. a. How many copies must Joanne purchase if she is to have enough resumes? b. How much will the copies cost her,
Cathy is looking for a job as a bookkeeper. One classified ad lists a job in a stereo store that pays 34.6K. Another job, in a clothing store, has a weekly salary of $620. a. Which job is the higher-paying job? b. What is the difference in the weekly salaries of these two jobs? Round to the
An online job seeking service allows job seekers to post their resumes for free. The service charges employers looking for applicants a fee to look through the resumes. The fee is based on how long the employer wants access to the resumes, and how many miles from the workplace address the employer
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