5-1 Classified Ads - Home - Elgin Local Schools · 2018-01-16 · 22.50 + 5.75( x # 6) when x $ 6...

© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Key Math Concepts

64

Name ______________________________________________________ Date _______________________________

Guided Exercises

1. Enrique plans to sell his car and places a 6-line ad. His paper charges $42 for the !rst two lines and $6.75 per extra line to run the ad for one week. What will Enrique’s ad cost to run for three weeks?

Number of lines over 2: 6 – 2 = ______

Cost of extra lines = number of extra lines " cost of each extra line

Cost of extra lines = 4 " 6.75 = ______

Total cost of ad = number of weeks(cost of the !rst two lines + cost of extra lines)

Total cost of ad = ______(______ + ______) = ______

The total cost of Enrique’s car ad is ______.

2. The Fort Salonga News charges $29.50 for a classi!ed ad that is four or fewer lines long. Each line above four lines costs an additional $5.25. Express the cost of an ad algebraically as a piecewise function.

There are two rules: 1) the charges for ads ________________________ 2) the charges for ads above ________________________

For rule 1; c(x) = __________ when __________ For rule 2; c(x) = __________ + __________(x – 4) when __________

The piecewise function is:

c x( ) =______ when _________________ + _____(_______) when ____________

!"#

Sales tax = price of item " sales tax rate A piecewise function gives a set of rules for each set of the function. The domain is

de!ned by the inequalities that follow when.

Financial Algebra Guided Practice Workbook 5-1

Classified Ads5-1

© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 65

Name ______________________________________________________ Date _______________________________

Exercises

3. Ms. Boyrer is writing a program to compute ad costs. She needs to enter an algebraic representation of the costs of a local paper’s ad. The charge is $32.25 for up to three lines for a classi!ed ad. Each additional line costs $6. Express the cost of an ad f(x) with x lines as a function of x algebraically.

4. Roxanne set up the following split function which represents the cost of an auto classi!ed ad from her hometown newspaper.

f x

xx x

( ).. . ( )

=!

+ " >#$%

31 50 531 50 5 50 5 5

when when

If x is the number of lines in the ad, express the price c(x) of a classi!ed ad from this paper in words.

5. Dr. Mandel purchased a used car for $11,325. Her state charges 8% tax for the car, $53 for license plates, and $40 for a state safety and emissions inspection. How much does she need to pay for these extra charges, not including the price of the car?

6. Graph the piecewise function: c(x) = { 22.50 22.50 + 5.75(x # 6) when x $ 6 when x > 6

What are the coordinates of the cusp? What is the slope of the graph where x > 6? What is the slope of the graph where x < 6?

7. Express the classi!ed ad rate, $36 for the !rst four lines and $4.25 for each additional line, as a piecewise function. Use a “Let” statement to identify what x and c(x) represent.



Key Math Concepts

66

Name ______________________________________________________ Date _______________________________

Guided Exercises

1. Find the mean, median, mode, and range for the data set 34, 56, 44, 200.

Mean = sum of the data ÷ number of items

Mean = (34 + 56 + 44 + 200) ÷ 4 = 4

= _____

Median: write the numbers in ascending order: _____, _____, _____, _____

The number of items is even so frind the average of the middle two numbers. Median: (44 + 56) ÷ 2 = _____

Range = greatest number – least number = 200 – 34 = _____

The mean is _____, the median is _____, the range is _____, and there is no mode.

2. The data below gives the MPG ratings for cars owned by 15 Placid High School seniors. How many outliers are in this data set?

15.9, 17.8, 21.6, 25.2, 31.1, 29, 28.6, 32, 34, 14, 19.8, 19.5, 20.1, 27.7, 25.5

In ascending order: ____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____

Q% = the median = ______

Q& = the median of the lower half = ______ Q' = the median of the upper half = ______

IQR = Q' – Q& = ______ – ______ = ______

Upper boundary = Q& + 1.5(IQR) = ______ + ______(______) = ______

Lower boundary = Q' – 1.5(IQR) = ______ – ______(______) = ______

Any number above _____ or below _____ is an outlier. So, there are ___________.

Q& is the median of the lower half of the data, Q% is the median( Q' is the median of the upper half of the data( and Q) is the maximum value of the data set*

IQR = Q' – Q& To determine outliers, use Upper boundary = Q& + 1.5(IQR) and

Lower boundary = Q' – 1.5(IQR)


Buy or Sell a Car5-2


Name ______________________________________________________ Date _______________________________

Exercises

3. A local charity wants to purchase a classic 1956 Thunderbird for use as a prize in a fundraiser. They !nd the following eight prices in the paper.

$48,000 $57,000 $31,000 $58,999 $61,200 $59,000 $97,500 $42,500

What is the best measure of central tendency to use to get a reasonable estimate for the cost of the car? Explain.

4. Find the value of x that will make the mean of the following data set equal to 80. 78, 90, 88, 70, x

Given is the list of prices for a set of used original hubcaps for a 1957 Chevrolet. They vary depending on the condition. Use the data for Exercises 5-12. $120 $50 $320 $220 $310 $100 $260 $300 $155 $125 $600 $250 $200 $200 $125

5. mean, to the nearest dollar

6. median

7. mode

8. four quartiles

9. range

10. interquartile range

11. boundary for the lower outliers; any lower outliers

12. boundary for the upper outliers; any upper outliers



Key Math Concepts

68

Name ______________________________________________________ Date _______________________________

Guided Exercises

1. The back-to-back stem-and-leaf plot gives data about the number of girls (on the left) and boys (on the right) at each high school in Greene County who purchased their own cars with money they earned working. How many high schools are in Greene County? What is the mean number of boys who bought their own cars? Find the median of the distribution of girls.

Count the pieces of data on one side. This is the number of schools.

Number of schools = ______

Mean = sum of the data ÷ number of items

Mean (boys) = (10 + 11 +12 + 23 + 24 + 31 + 37 + 39 + 42 + 51) ÷ 10 = ______

Median: The number of items is even. Find the average of the two middle numbers:

Median = 30 312+ = _____

There are ______ schools in Green County. A mean of ______ boys bought cars and a median of ______ girls bought cars.

2. The boxplot summarizes information about the numbers of hours worked in December for 220 seniors at Tomah High School. What is the interquartile range? What is the median? How many students worked 31 hours or less?

IQR = Q' – Q& = ______ – ______ = ______

Q% is the median, which is the ________ number.

The interquartile range is ______ and the median is ______.

______ of the data is before the median and ______ is after the median.

______ of the total number of students = ______ " ______ = ______

______ of the students work 31 hours or less.

Q& is the median of the lower half of the data, Q% is the median( Q' is the median of the upper half of the data( and Q) is the maximum value of the data set*

IQR = Q' – Q&


Graph Frequency Distributions5-3

345

121

7 9

3|1! 13 girls

2 11

7

1

0

1

1|2 !12 boys

1 0 1 24 32 3 41

010 31 68

80


Name ______________________________________________________ Date _______________________________

Exercises

3. Jerry is looking to purchase a set of used chrome wheels for his SUV. He found 23 ads for the wheels he wants online and in the classi!ed ads of his local newspaper and arranged the prices in ascending order, which is given below.

$350 $350 $350 $420 $450 $450 $500 $500 $500 $500 $600 $700 $725 $725 $725 $725 $725 $775 $775 $800 $825 $825 $850

Make a frequency table to display the data.

Draw a box-and-whisker plot for the data.

The side-by-side boxplots for distributions A and B were drawn on the same axes. Use the box plots to answer Exercises 4-8.

4. Which distribution has the greater range?

5. Which distribution has the smallest interquartile range?

6. What percent of the scores in distribution A is above distribution B’s maximum score?

7. Which distribution has scores that are the most varied?

8. What percent of scores in distribution A are less than distribution B’s !rst quartile?


A

B


Key Math Concepts

70

Name ______________________________________________________ Date _______________________________

Guided Exercises

1. Mr. Cousins has 100/300 bodily injury insurance. He was in an auto accident caused by his negligence. Five people were injured in the accident. They sued in court and were awarded money. One person was awarded $150,000, and each of the other two was awarded $95,000. How much will the insurance company pay for these lawsuits?

100/300 bodily insurance is $100,000 per person and $300,000 per accident.

Of the people with injuries: 1 had $150,000 in injuries.

$150,000 > $100,000, so insurance will pay $100,000.

2 people had < $100,000, so insurance will pay $95,000 each.

Add: ____________ + ____________ + ____________ = ____________

$290,000 < $300,000, so the insurance company will pay ____________ of these lawsuits.

2. The Chow family just bought a second car. The annual premium would have been a dollars to insure the car, but they are entitled to a 12% discount since another car is insured by the company. If they pay their premium semiannually, and have to pay a b dollars surcharge for this arrangement, express their semiannually payment algebraically.

Discount = decimal " annual premium = 0.12a

Discounted premium = annual premium – discount

Discounted premium = ______ – ______ = ______

insurance payment annual premiumnumber of payments per yea

=rr

surcharge+

Insurance payment = � b

The Chow’s discounted annual premium is ________ and their payment is � b .

Substitute the discounted premium.

a is the same as 1(a).

100/200/50 represents 100/200 BI insurance and 50,000 PD insurance.

insurance payment annual premiumnumber of payments per yea

=rr

surcharge+


Automobile Insurance5-4


Name ______________________________________________________ Date _______________________________

Exercises

3. Cai’s annual premium is p dollars. If she pays her premium semiannually, there is a 1% surcharge on each payment. Write an expression for the amount of her semiannual payment.

Jake has $25,000 worth of property damage insurance and $1,000-deductible collision insurance. He caused an accident that damaged a $2,000 sign, and he also did $2,400 worth of damage to another car. His car had $2,980 worth of damage done. Answer Exercises 4-6.

4. How much will the insurance company pay under Jake’s property damage insurance?

5. How much will the insurance company pay under Jake’s collision insurance?

6. How much of the damage must Jake pay for?

7. Allen Siegell has a personal injury protection policy that covers each person in, on, around, or under his car for medical expenses up to $50,000. He is involved in an accident and !ve people in his car are hurt. One person has $3,000 of medical expenses, three people each have $500 worth of medical expenses, and Allen himself has medical expenses totaling $62,000. How much money must the insurance company pay out for these !ve people?

Mrs. Lennon has 100/275/50 liability insurance and $50,000 PIP insurance. During an ice storm, she hits a fence and bounces into a store front with 11 people inside. Some are hurt and sue her. A passenger in Mrs. Lennon’s car is also hurt.

8. The store front will cost $24,000 to replace. There was $1,450 worth of damage to the fence. What insurance will cover this, and how much will the company pay?

9. The passenger in the car had medical bills totaling $20,000. What type of insurance covers this, and how much will the insurance company pay?



Key Math Concepts

72

Name ______________________________________________________ Date _______________________________

Guided Exercises

Katie purchased a new car for $27,599. This make and model straight line depreciates for 13 years.

1. Identify the coordinates of the x- and y-intercepts for the depreciation equation. Determine the slope of the depreciation equation.

y-intercept: (0, maximum car value) x-intercept: (maximum lifespan, 0)

y-intercept: (________, ________) x-intercept: (________, ________)

Slope ratio = xy

Slope ratio =27 599 0

0 13. !!

= = ________

Katie’s new car depreciates at a rate of ________ a year.

2. Write the straight line depreciation equation that models this situation. Draw the graph of the straight line depreciation equation.

m = slope = ________

b = y-intercept (original price of car) = ________

y = mx + b

y = ________x + ________

Use the Y= function of the graphing calculator to create the graph.

Straight line depreciation equation: y = mx + b, where y is the value of the car, x is the number of years, m is the slope of depreciation, and b is the original price of the car.

Slope ratio = xy

y-intercept: (0, maximum car value); x-intercept: (maximum lifespan, 0)


Linear Automobile Depreciaton5-5

ΔΔ

ΔΔ


Name ______________________________________________________ Date _______________________________

Exercises

3. The graph of a straight line depreciation equation is shown. Write the straight line appreciation equation. Use the graph to approximate when the car will be worth half its original value.

4. Caroline purchased a car four years ago at a price of $28,400. According to research on this make and model, similar cars have straight line depreciated to zero value after 8 years. How much will this car be worth after 51 months?

5. The straight line depreciation equation for a luxury car is y = #4,150x + 49,800. In approximately how many years will the car’s value drop by 30%?

6. A new car sells for $29,250. It straight line depreciates in 13 years. What is the slope of the straight line depreciation equation?

7. A new car straight line depreciates according to the equation y = #1,875x + 20,625. What is the original price of the car? How many years will it take for this car to fully straight line depreciate?


$19,200

14

years

value

0

$12,800

$3,200

2 4 6

$6,400

$9,600

$16,000

8 10 12

© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.74

Name ______________________________________________________ Date _______________________________

Guided Exercises

1. Tanya’s new car sold for $23,856. Her online research indicates that the car will depreciate exponentially at a rate of 6 3 __ 8 % per year. Write the exponential depreciation formula for Tanya’s car.

A is the starting value, or 23,856

r is the percent depreciation or, 6 3 __ 8 %, or __________.

y = A(1 – r)x

y = ________(1 – ________)x

The exponential depreciation formula is y = ________(1 – ________)x .

2. Sharon purchased a used car for $24,600. The car depreciates exponentially by 8% per year. How much will the car be worth after 5 years? Round your answer to the nearest penny.

A = ________

r = ______ or ______

x = ________

Write a depreciation equation.

y = A(1 – r)x

y = ________(1 – ________) ___

y = ____________

Sharon’s car will be worth ____________ after 5 years.

Substitute.

Write 638% as a decimal.

The exponential depreciation formula is y = A(1 – r)x, where A is the car’s standing value, x is the elapsed time in years, r is the percent of depreciation, and y is the value of the car after x years.

Key Math Concepts


Historical and ExponentialDepreciation

5-6


Name ______________________________________________________ Date _______________________________

Exercises

3. Brad purchased a !ve-year old car for $14,200. When the car was new, it sold for $24,000. Find the depreciation rate to the nearest hundredth of a percent.

4. A car exponentially depreciates at a rate of 8.5% per year. Mia purchased a 4-year-old car for $17,500. What was the original price of the car when it was new? Round your answer to the nearest thousand dollars.

5. The screen to the right is from a graphing calculator after running an exponential regression analysis of a set of automobile data. X represents years and y represents car value. Using the numbers on the screen, write the exponential regression equation.

6. Nancy and Bob bought a used car for $22,800. When this car was new, it sold for $30,000. If the car depreciates exponentially at a rate of 9.2% per year, approximately how old is the car? Round your answer to the nearest hundredth of a year.

7. A new car sells for $31,400. It exponentially depreciates at a rate of 4.95% to $26,500. How long did it take for the car to depreciate to this amount? Round your answer to the nearest tenth of a year.


y=a*b^xa=43754.00259

ExpReg

b=.8223288103r =.8405850061r=-.91683423042

Bill Clem


Key Math Concepts

76

Name ______________________________________________________ Date _______________________________

Guided Exercises

1. Ruth is planning a 1,543-mile trip to a math teachers’ conference in San Diego. She plans to average 50 miles per hour on the trip. At that speed, for how many hours will she be driving? Express your answer to the nearest hour.

D is the distance, or ____________

R is the miles per hour, or ____________

D = R " T

T = D ÷ R

T = ____________ ÷ ____________ + ____________

Ruth will travel about ______ hours.

2. Francois’ car gets about 12.5 kilometers per liter. He is planning a 1,600-kilometer trip. About how many liters of gas should Francois plan to buy? Round your answer to the nearest liter At an average price of $1.18 per liter, how much should Francois expect to spend for gas?

D is the distance, or __________

M is the miles per gallon, or __________

D = M " G

G = D ÷ M

G = __________ ÷ __________ + __________

The total cost will be __________ " __________ = __________

Francois will buy about __________ and spend about __________.

Rewrite to solve for G.

Rewrite to solve for T.

D = R " T, where D is distance, R is the rate, and T is time in hours. D = M " G, M is miles per gallon, and G is the number of gallons used.


Driving Data5-7


Name ______________________________________________________ Date _______________________________

Exercises

3. A car travels at an average rate of speed of 60 miles per hour for 7 1 __ 2 hours. How many miles does this car travel?

4. A car travels m miles in t hours. Express its average speed algebraically.

5. Abby’s car gets approximately 24 miles per gallon. She is planning a 1,200-mile trip. About how many gallons of gas should she plan to buy? At an average price of $4.20 per gallon, how much should she expect to spend for gas?

6. Raquel is driving from New York City to Daytona, Florida, a distance of 1,034 miles. How much time is saved by doing the trip at an average speed of 60 mph as compared with 55 mph? Round to the nearest half-hour.

7. Ace Car Rental charges customers $0.18 per mile driven. You picked up a car and the odometer read x miles and brought it back with the odometer reading y miles. Write an algebraic expression for the total cost Ace would charge you for mileage use on a rented car.

8. Juanita has a hybrid car that averages 44 miles per gallon. Her car has a 12-gallon tank. How far can she travel on one full tank of gas?



Key Math Concepts

78

Name ______________________________________________________ Date _______________________________

Guided Exercises

1. How many feet does a car traveling at 57 mph cover in one hour? in one minute? in one second?

57 " 5,280 = 300,960 feet

300 960, fthr

1 hr60 min

5,016 feet! =

5,016 ftmin

1 min60 s

feet! = 83 6.

A car traveling 57 mph covers ____________ in one hour, ____________ in one minute, and ____________ in one second.

2. Jerry is driving 35 miles per hour as he approaches a park. A dog darts out into the street between two parked cars, and Jerry reacts in about three-quarters of a second. What is his approximate reaction distance?

35 mph " 5,280 ft = ____________ ft per hour

________________ ÷ 60 min = ________ ft per min

________________ ÷ 60s sec + ________ ft per second

Jerry’s car is traveling about __________ per second.

Write a proportion where x is the distance traveled where the reaction time is 0.75 s.

510.751

" x

51(0.75) = x

__________ = x

Jerry’s reaction distance is about ________.

Braking distance = s2

20, where s is the speed of the car in miles per hour.

Total stopping distance = reaction distance + braking distance


Driving Safety Data5-8

One mile = 5,280 feet

One hour = 60 minutes

One minute = 60 seconds


Name ______________________________________________________ Date _______________________________

Exercises

3. How many feet does a car traveling at a mph cover in one hour? in one minute? in one second?

4. How many kilometers does a car traveling at 50 kph cover in one hour? How many meters does a car traveling at 50 kph cover in one hour? in one minute? in one second?

5. Manuel is driving 60 miles per hour on a state road with a 65 mph speed limit. He sees a fallen tree up ahead and must come to a quick, complete stop. What is his approximate reaction distance? What is his approximate braking distance? About how many feet does the car travel from the time he switches pedals until the car has completely stopped?

6. Anita is driving on the highway at the legal speed limit of 63 mph. She sees a police road block about 300 feet ahead and must come to a complete stop. Her reaction time is approximately 3 __ 4 of a second. Is she far enough away to safely bring the car to a complete stop? Explain your answer.



Key Math Concepts

80

Name ______________________________________________________ Date _______________________________

Guided Exercises

1. Mark was traveling at 40 mph on a road with a drag factor of 0.85. His brakes were working at 80% e,ciency. To the nearest tenth of a foot, what would you expect the average length of the skid marks to be if he applied his brakes in order to come to an immediate stop?

S = 30Dfn

D = 50 feet; f = 1.1; n = 0.85

S " 30( ( ( ) ) )

S " + ______ mph

The minimum speed of the car is ______ mph.

2. Determine the radius of the yaw mark made when brakes are immediately applied to avoid a collision based upon a yaw mark chord measuring 59.5 feet and a middle ordinate measuring 6 feet. Round your answer to the nearest tenth.

r CM

M= +2

8 2

r = +((

( ) )

)2

8 2 r + ________

The radius of the yaw mark is about ________.

Substitute.

Substitute.

S D f n= ! ! !30 or 30Dfn , where S is the speed of the car, D is the skid distance, f is the drag factor, and n is the braking e,ciency written as a decimal

S fr" 15 , where r is the radius of the yaw mark.

r CM

M= +2

8 2, where r is the radius of the yaw mark, C is the length of the chord, and

M is the length of the middle ordinate.


Accident Investigation Data5-9


Name ______________________________________________________ Date _______________________________

Exercises

3. A car is traveling at 52 mph before it enters into a skid. The drag factor of the road surface is 0.86, and the braking e,ciency is 88%. How long might the average skid mark be to the nearest tenth of a foot?

4. Arami’s car left three skid marks on the road after she slammed her foot on the brake pedal to make an emergency stop. The police measured them to be 45 feet, 40 feet, and 44 feet. What skid distance will be used when calculating the skid speed formula?

5. Andrea was traveling down a road at 45 mph when she was forced to immediately apply her brakes in order to come to a complete stop. Her car left two skid marks that averaged 60 feet in length with a di-erence of 6 feet between them. Her brakes were operating at 90% e,ciency at the time of the incident. What was the possible drag factor of this road surface? What were the lengths of each skid mark?

6. The measure of the middle ordinate of a yaw mark is 7 feet. The radius of the arc is determined to be 64 feet. What was the length of the chord used in this situation? Round your answer to the nearest tenth of a foot.

7. Russell was driving on a gravel road that had a 20 mph speed limit posted. A car ahead of him pulled out from a parking lot causing Russell to immediately apply the brakes. His tires left two skid marks of lengths 60 feet and 62 feet. The road had a drag factor of 0.47. His brakes were operating at 95% e,ciency. The police gave Russell a ticket for speeding. Russell insisted that he was driving under the limit. Who is correct (the police or Russell)? Explain.


5-1 Classified Ads - Home - Elgin Local Schools · 2018-01-16 · 22.50 + 5.75( x # 6) when x $ 6...

Documents

Transcript of 5-1 Classified Ads - Home - Elgin Local Schools · 2018-01-16 · 22.50 + 5.75( x # 6) when x $ 6...