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mathematics
mathematical applications for the management
Mathematical Applications For The Management, Life And Social Sciences 12th Edition Ronald J. Harshbarger, James J. Reynolds - Solutions
Compute 10P6.
In Problems, one card is drawn from a deck of 12 cards numbered 1 through 12. In each case, find the probability that the card is(a) Odd and divisible by 4.(b) Odd or divisible by 4.
Eight horses in a racewear numbers 1, 2, 3, 4, 5, 6, 7, and 8. What is the probability that the first three horses to finish the race will be numbered 1, 2, and 3, respectively?
A bag contains three white balls numbered 1, 2, 3 and four black balls numbered 4, 5, 6, 7. If one ball is drawn at random, find the probability of each event described in Problems.(a) The ball is black and even-numbered.(b) The ball is white or even-numbered.
Compute 8P5.
In Problems, one card is drawn from a deck of 12 cards numbered 1 through 12. In each case, find the probability that the card is(a) Even and divisible by 5.(b) Even or divisible by 5.
Suppose a ball is drawn from a bag containing 9 red balls numbered 1 through 9 and 3 white balls numbered 10 through 12. Two possible sample spaces for this event are S1 = {1, 2, 3, . . . . . . 12} and S2 = {R, W}.(a) Which of these sample spaces is equiprobable? What is the probability that(b) The
A bag contains three white balls numbered 1, 2, 3 and four black balls numbered 4, 5, 6, 7. If one ball is drawn at random, find the probability of each event described in Problems.(a) The ball is odd-numbered.(b) The ball is white.
Compute 6P4.
In Problems, one card is drawn from a deck of 12 cards numbered 1 through 12. In each case, find the probability that the card is(a) Even and divisible by 3.(b) Even or divisible by 3.
In Problems, use probability trees to find the probabilities of the indicated outcomes.A bag contains 5 coins, 4 of which are fair and 1 that has a head on each side. If a coin is selected from the bag and tossed twice, what is the probability of obtaining(a) 2 heads?(b) 2 tails?
A couple bought some stock for $30 per share that pays an annual dividend of $0.90 per share. After 2 years, the price of the stock was $33.(a) What is the return on investment?(b) Find the simple interest rate on the growth of their investment.
The amount of money that needs to be deposited into an account to reach some future goal is called the present value. The following table gives the present value (to the nearest dollar) for an account that earns 10% compounded annually so that the account value will be $50,000 after intervals
A recent college graduate buys a new car by borrowing $18,000 at 8.4% compounded monthly for 5 years. She decides to pay $384 instead of the monthly payment required by the loan.(a) What is the monthly payment required by the loan, and how much extra did she pay per month?(b) How many $384 payments
If changing market conditions cause a company earning $8,000,000 in 2018 to project a loss of 2% of its profit in each of the next 5 years, what profit does it project in 2023?
Suppose a country is so devastated by the AIDS epidemic that its population decreases by 0.5% each year for a 4-year period. If the population was originally 10 million, what is the population at the end of the 4-year period?
A house that 20 years ago was worth $160,000 has increased in value by 4% each year because of inflation. What is its worth today?
The sum of the first 31 terms of the geometric sequence 9, 26, 4, . . .Write an expression that gives the requested term or sum.
The sum of the first 18 terms of the geometric sequence 6, 4, 8/3, . . .Write an expression that gives the requested term or sum.
The sum of the first 14 terms of the geometric sequence 16, 64, 256, . . .In Problems, write an expression that gives the requested term or sum.
The sum of the first 35 terms of the geometric sequence 1, 3, 9, . . .In Problems, write an expression that gives the requested term or sum.
The sum of the first 14 terms of the geometric sequence with first term 3 and common ratio 4In Problems, write an expression that gives the requested term or sum.
The sum of the first 17 terms of the geometric sequence with first term 6 and common ratio 3In Problems, write an expression that gives the requested term or sum.
Identify which of the following formulas applies to each situation in Problems.
For each geometric sequence given in Problems, write the next three terms.(a) 4, 12, 36, . . .(b) 32, 40, 50, . . .(c) –400, 40, –4, . . .
Identify which of the following formulas applies to each situation in Problems.
For each geometric sequence given in Problems, write the next three terms.(a) 3, 6, 12, . . .(b) 81, 54, 36, . . .(c) –0.5, 2, –8, . . .
Identify which of the following formulas applies to each situation in Problems.
Identify which of the following formulas applies to each situation in Problems.
Track the future values of two investments of $5000, one at 6.3% compounded quarterly and another at 6.3% compounded monthly for each interest payment period for 10 years.(a) How long does it take each investment to be worth more than $7500?(b) What are the values of each investment after 3 years,
Identify which of the following formulas applies to each situation in Problems.
Identify which of the following formulas applies to each situation in Problems.
Jane Adele deposits $1500 in an account at the beginning of each 3-month period for 9 years. If the account pays interest at the rate of 8% compounded quarterly, how much will she have in her account after 9 years?In Problems,(a) State whether the problem relates to an ordinary annuity or an
What difference does 0.5% make on a loan? To explore this question, find (to the nearest dollar) the monthly payment and total interest paid over the life of the loan for each of the following.(a) An auto loan of $15,000 at 8.0% versus 8.5%, both compounded monthly for 4 years.(b) A mortgage loan
For 3 years, $4000 is placed in a savings account at the beginning of each 6-month period. If the account pays interest at 10% compounded semiannually, how much will be in the account at the end of the 3 years?In Problems,(a) State whether the problem relates to an ordinary annuity or an annuity
If $10,000 had been invested in the Sagamore Capital Opportunity Fund on September 30, 2008, it would have been worth $46,649.55 on September 30, 2018. What interest rate compounded annually did this investment earn?
A woman makes $3000 contributions at the end of each half-year to a retirement account for a period of 8 years. For the next 20 years, she makes no additional contributions and no withdrawals.(a) If the account earns 7.5% compounded semiannually, find the value of the account after the 28 years.(b)
A couple would like to have $50,000 at the end of 412 years. They can invest $10,000 now and make additional contributions at the end of each quarter over the 412 years. If the investment earns 7.7% compounded quarterly, what size payments will enable them to reach their goal?
If you took a home mortgage loan of $150,000 for 30 years at 8.4% compounded monthly, your monthly payments would be $1142.76. Suppose after 2 years you had an additional $2000. Would you save more over the life of the loan by paying an extra $2000 with your 24th payment or by paying $1160 per
A 400-mg dose of heart medicine is taken daily. During each 24-hour period, the body eliminates 40% of this drug (so that 60% remains in the body). Thus the amount of drug in the bloodstream just after the 31st dose is given by400 + 400(0.6) + 400(0.6)2 + 400(0.6)3 + ........ + 400(0.6)29 +
The following sequence is arithmetic: 298.8, 293.3, 287.8, 282.3, . . . .(a) If you were not told that this sequence was arithmetic, how could you tell that it was?(b) Find the 51st term of this sequence.(c) Find the sum of the first 51 terms.
A house is rented for $7200 per quarter, with each quarter’s rent payable in advance. If money is worth 8% compounded quarterly and the rent is deposited in an account, what is the future value of the rent for one year?
Suppose that a 10-year corporate bond has a maturity value of $10,000 and a coupon rate of 10%, with coupons paid semiannually. Find the market price of the bond if the current yield rate is 6% compounded semiannually. Is this bond selling at a discount or at a premium?
If you want to earn 2% annual simple interest on an investment, how much should you pay for a note that will be worth $13,500 in 10 months?
What is the compound interest if $41,000 is invested for 10 years at 8% compounded continuously?
Find the future value of an annuity due of $2000 paid at the beginning of each 6-month period for 8 years if the interest rate is 6% compounded semiannually.
A couple borrows $180,000 at 5.4% compounded monthly for 30 years. After making 80 payments of $1010.76, they refinance at 4.8% compounded monthly for 25 years, with refinancing costs of $550 added to the new loan.(a) Find the amount refinanced.(b) Find the new monthly payment.(c) How much is saved
Is there any difference between the present values in parts (a) and (b)? Explain.(a) An annuity due that pays $1000 at the beginning of each year for 10 years(b) Taking $1000 now and establishing an ordinary annuity that pays $1000 at the end of each year for 9 years
Grandparents plan to establish a college trust for their youngest grandchild. How much is needed now so that the trust, which earns 6.4% compounded quarterly, will provide $4000 at the end of each quarter for 4 years after being deferred for 10 years?
A firm buys 12 file cabinets at $140 each, with payment in full due in 90 days. How much must the firm deposit now to have enough to pay the bill if money is worth 3% simple interest per year? Use 360 days in a year.
Maxine deposited $400 at the beginning of each month for 15 years in an account that earned 6% compounded monthly. Find the value of the account after the 15 years.
If $1500 is deposited at the end of each half-year in a retirement account that earns 8.2% compounded semiannually, how long will it be before the account contains $500,000?
What amount must you invest in an account that earns 6.8% compounded quarterly if you want to have $9500 after 5 years?
Jenny Reed bought SSX stock for $25 per share. The annual dividend was $1.50 per share, and after 4 years, SSX was selling for $34 per share.(a) What is the return on investment?(b) Find the simple interest rate of growth of her money.
A $780,000 IRA is used to supplement a retired couple’s income with payments at the end of each quarter for the next 15 years. If money is worth 8% compounded quarterly, what is the size of each payment?
If $10,000 is invested at 7% compounded continuously, what is the value of the investment after 20 years?
An accountant wants to withdraw $3000 from an investment at the beginning of each quarter for the next 15 years. How much must be deposited originally if the investment earns 6% compounded quarterly? Assume that after the 15 years, the balance is zero.
Find the annual percentage yield (the effective annual rate) for an investment that earns 8.4% compounded monthly.
Find the future value of an ordinary annuity of $3000 paid quarterly for 5 years, if the interest rate is 6% compounded quarterly.
How much must you put aside at the beginning of each half-year if, in 6 years, you want to have $12,000 and the current interest rate is 6.2% compounded semiannually?
If you borrow $800 for 6 months at 6% annual simple interest, how much must you repay at the end of the 6 months?
Find the future value of an ordinary annuity of $8000 paid quarterly for 3 years, if the interest rate is 8% compounded quarterly.
If you borrow $2500 for 15 months at 4% simple interest, how much money must you repay after the 15 months?
Identify any geometric sequences and their common ratios.(a) 1/4, 2, 16, 128, . . . .(b) 16, -12, 9, -27/4, . . . .(c) 4, 16, 36, 64, . . . .
A couple borrowed $97,000 at 7.2% compounded monthly for 25 years to purchase a condominium.(a) Find their monthly payment.(b) Over the 25 years, how much interest will they pay?
$20,000 is invested for 6 months at an annual simple interest rate of 2%.(a) How much interest will be earned?(b) What is the future value of the investment after 6 months?
Find the sum of the first 60 terms of the arithmetic sequence 1/3, 1/2, 2/3, . . . .
If an investment of $1000 grew to $13,500 in 9 years, what interest rate compounded annually did this investment earn?
A debt of $280,000 is amortized with 40 equal semiannual payments of $14,357.78. If interest is 8.2% compounded semiannually, find the unpaid balance of the debt after 25 payments have been made.
$10,000 is invested for 6 years at an annual simple interest rate of 1.6%(a) How much interest will be earned?(b) What is the future value of the investment at the end of the 6 years?.
To buy a municipal bond that matures to $10,000 in 9 months, you must pay $9510. What simple interest rate is earned?
In Problems, find the requested value (to the nearest dollar) and tell what each of the other values represents.(a)(b) 1- (1 + 0.01)-120 Find A,: A, = 2550 0.01
Identify any arithmetic sequences and find the common differences.(a) 12, 7, 2, -3, . . . . .(b) 1, 3, 6, 10, . . . . .(c) 1/6, 1/3, 1/2, 2/3 . . . . .
In Problems, find the requested value (to the nearest dollar) and explain what each of the other values represents.(a)(b) (1 + S = 1000 + 0.03)25 – 1 Find S: 0.03
Suppose you invest $100 at the end of each month in an account that earns 6.9% compounded monthly. What is the future value of the account after 5 1/2 years?
In Problems, find the requested value (to the nearest dollar) and tell what each of the other values represents.(a)(b) -30 Find A,: A, 1- (1 + 0.04) 1300 0.04
Find the first 4 terms of the sequence with the nth terman = 1/n2
In Problems, find the requested value (to the nearest dollar) and explain what each of the other values represents.(a)(b) (1 + 0.02)60 – 1 S = 2500 0.02
If $8000 is invested at 7% compounded continuously, how long will it be before it grows to $47,000?
In 2015, 88% of U.S. residents used the Internet, up from 14% in 1995. The table shows the percent who use the Internet for selected years from 2000 and projected to 2025.(a) Find the logarithmic function that models the percent p as a function of x, the number of years after 1990. Report the model
In Example 6 we used data from 1920 and projected to 2050 and found that the expected life span in the United States can be modeled as a function of the year of birth byL(x) = 8.7744 + 14.907 ln xwhere x is the number of years after 1900. Using data from 1920 to 1989, the modelℓ(x) = 11.616 +
The following table gives the U.S. population, ages 20–64, (in millions) for selected years from 1950 and projected to 2050.(a) Find the logistic function that models these data. Use x as the number of years after 1950 and report your model with 3 significant digit coefficients.(b) Use the
The sound level of a military jet taking off has intensity about 1014 times I0. Find the decibel reading for this threshold.In Problems, use the fact that the loudness of sound (in decibels) perceived by the human ear depends on intensity levels according toL = 10 log(I/I0)where I0 is the threshold
Find the loudness when I is 10,000 times I0. This is the intensity level of the average voice.In Problems, use the fact that the loudness of sound (in decibels) perceived by the human ear depends on intensity levels according toL = 10 log(I/I0)where I0 is the threshold of hearing for the average
Use the formula R = log (I/I0) in Problems.The most destructive earthquake in the United States was the 1906 San Francisco quake that measured 7.8 on the Richter scale. The quake and subsequent fires that burned for several days destroyed 80% of the city. This 1906 quake was the seventeenth most
The number of people N(t) in a community who are reached by a particular rumor at time t is given by the equation(a) Find N(0).(b) What is the upper limit on the number of people affected?(c) How long before 75% of the upper limit is reached? 50,500 N(t) 1 + 100e-0.7t
After hiring a new VP for advertising, a company predicts that sales will increase and that the yearly sales will be given by the equationN = 10,000(0.3)0.5twhere t represents the number of years after the hiring of the new VP.(a) What are the sales when the new VP begins?(b) What are the predicted
From 1950 and projected to 2050, the percent of workers who are females can be modeled byw(x) = 9.42 + 8.70 ln xwhere x is the number of years after 1940.(a) Find the expected percent of female workers in 2020.(b) Find the year in which the percent of workers that are females is expected to be
The total cost for x units of a product is given byC(x) = 1200 ln(2x + 5) + 3400 dollars(a) Find the total cost of 40 items (to the nearest dollar).(b) Find the number of units for which total cost is $10,000.
The table shows the total personal income in the United States (in billions of dollars) for selected years from 1960 and projected to 2024.(a) These data can be modeled by an exponential function. Write the equation of this function, with x equal to the number of years after 1960. Report the model
In Problems, use a calculator to determine whether expression(a) is equivalent to expression (b). If they are equivalent, state what properties are being illustrated. If they are not equivalent, rewrite expression (a) so that they are equivalent.(a) log2 34/17(b) log2 34 - log2 17
Severely obese persons (BMI ≥ 40) have a greatly increased risk of diabetes, heart disease, and many other ailments that are very expensive to treat. The table gives the percent of Americans who are severely obese for the years from 1990 and projected to 2030.(a) Find an exponential function that
The revenue (in millions of U.S. dollars) from natural gas extraction in Germany from 2012 and projected through 2020 can be modeled byy = 3895.7 + 4783.3 ln xwhere x is the number of years after 2010.(a) What does the model predict the revenue to be in 2025, assuming the model remains valid?(b)
One of the components of the U.S. real gross domestic product (GDP) is real national consumption. Using U.S. Energy Administration data for selected years from 2014 and projected to 2040, this real consumption (in trillions of dollars) can be modeled by the functionC(t) = 10.2 e0.0227twhere t is
Using Social Security Administration data for selected years from 2012 and projected to 2050, the U.S. consumer price index (CPI) can be modeled by the functionC(t) = 92.7e0.0271twhere t is the number of years past 2010 and C(t) is in 2012 dollars. With the data’s reference year as 2012, a 2018
Use the properties of logarithms to write each expression in Problems as a single logarithm.log (2x + 1) - 1/3 log (x + 1)
Use the following information to answer Problems. World population can be considered as growing according to the equationN = N0(1 + r)twhere N0 is the number of individuals at time t = 0, r is the yearly rate of growth, and t is the number of years.Repeat Problem 42 when the growth rate is 7%.
The graph in the following figure shows the projected federal spending for Medicare as a percent of the gross domestic product. If these expenditures were modeled as a function of time, which of a growth exponential, a decay exponential, or a logarithm would be the best model? Justify your answer.
Use the following information to answer Problems. World population can be considered as growing according to the equationN = N0(1 + r)twhere N0 is the number of individuals at time t = 0, r is the yearly rate of growth, and t is the number of years.Repeat Problem 41 when the growth rate is 5%.
Centers for Disease Control and Prevention data from 2010 and projected to 2050 indicate that adult diabetes in the United States could dramatically increase. With x equal to the number of years after 2000, the percent of U.S. adults with diabetes can be modeled byy = -13.0 + 11.9 ln xUse the model
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