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mathematics
calculus

Questions and Answers of Calculus

1. A homeowner planning a kitchen remodeling can afford a $600 monthly payment. How much can the homeowner borrow for 5 years at 6%, compounded monthly, and still stay within the budget? 2. AdriAnne
Develop an amortization schedule for the loan described. 1. $100,000 for 3 years at 9% compounded annually 2. $30,000 for 5 years at 7% compounded annually 3. $20,000 for 1 year at 12% compounded
1. How much summer earnings must a college student deposit on August 31 in order to have $3000 for tuition and fees on December 31 of the same year, if the investment earns 6% simple interest? 2.
Suppose you are offered two identical jobs: one paying a starting salary of $40,000 with yearly raises of $2000 and one paying a starting salary of $36,000 with yearly raises of $2500. Which job will
1. An investment is made at 8%, compounded quarterly, for 10 years.(a) Find the number of periods.(b) Find the interest rate per period.2. Write the formula for the future value of a compound
1. Which compounding method, at 6%, earns more money? (a) Semiannually (b) Monthly 2. If $1000 is invested for 4 years at 8%, compounded quarterly, how much interest will be earned? 3. How much must
1. A couple received an inheritance and plan to invest some of it for their grandchild's college education. How much must they invest if they would like the fund to have $100,000 after 15 years, and
If $15,000 is invested at 6%, compounded quarterly, how long will it be before it grows to $25,000?
(a) If an initial investment of $35,000 grows to $257,000 in 15 years, what annual interest rate, continuously compounded, was earned?(b) What is the annual percentage yield on this investment?
Find the annual percentage yield equivalent to a nominal rate of 7.2% (a) Compounded quarterly and (b) Compounded continuously.
1. Legend has it that when the king of Persia wanted to reward the inventor of chess with whatever he desired, the inventor asked for one grain of wheat on the first square of the chessboard, with
1. Find the future value of an ordinary annuity of $800 paid at the end of every 6-month period for 10 years, if it earns interest at 12%, compounded semiannually?2. How much would have to be
1. Find the future value of an annuity due of $800 paid at the beginning of every 6-month period for 10 years, if it earns interest at 12%, compounded semiannually? 2. A company wants to have
1. Find the 80th term of the arithmetic sequence with first term - 2 and common difference 3? 2. Find the 36th term of the arithmetic sequence with third term 10 and eighth term 25?
If $1200 is deposited at the end of each quarter in an account that earns 7.2%, compounded quarterly, how long will it be until the account is worth $60,000?
1. A couple wish to set up an annuity that will provide 6 monthly payments of $3000 while they take an extended cruise. How much of a $15,000 inheritance must be set aside if they plan to leave in 5
Winners of lotteries receive the jackpot distributed over a period of years, usually 20 or 25 years. The winners of a Powerball lottery elected to take a one-time cash payout rather than receive the
1. A recent college graduate's gift from her grandparents is $20,000. How much will this provide at the end of each month for the next 12 months while the graduate travels? Assume that money is worth
Suppose that a 30-year municipal bond has a maturity value of $5000 and a coupon rate of 8%, with coupons paid semiannually. Find the market price of the bond if the current yield rate is 10%
A retirement account that earns 6.8%, compounded semiannually, contains $488,000. How long can $40,000 be withdrawn at the end of each half-year until the account balance is $0?
1. A debt of $1000 with interest at 12%, compounded monthly, is amortized by 12 monthly payments (of equal size). What is the size of each payment? 2. A debt of $8000 is amortized with eight
A woman paid $90,000 down for a house and agreed to pay 18 quarterly payments of $4500 each. If money is worth 4%, compounded quarterly, how much would the house have cost if she had paid cash?
Complete the amortization schedule for the next two payments of a loan for 30 years at 7.5%, compounded monthly, with monthly payments of $699.22. Payment Number...........56 Payment Amount
A corporation borrowed $750,000 for 15 years at 5.4% compounded semiannually. After making 17 payments of $36,795.60, it refinances at 4.8% compounded semiannually for 5 years, with refinancing costs
1. The future value of a series of payments, with interest compounded when the payments are made?2. The simple interest earned on an investment3. The present value of a series of payments, with
If an initial investment of $2500 grows to $38,000 in 18 years, what annual interest rate, compounded annually, did this investment earn?
1. How much must be deposited at the end of each month in an account that earns 8.4%, compounded monthly, if the goal is to have $40,000 after 10 years? 2. What is the future value if $1000 is
1. Quarterly payments of $500 are deposited in an account that pays 8%, compounded quarterly. How much will have accrued in the account at the end of 4 years if each payment is made at the end of
1. An investment broker bought some stock at $87.89 per share and sold it after 3 months for $105.34 per share. What was the annual simple interest rate earned on this transaction?2. A couple feels
A $5000 Mauranol, Inc., corporate bond matures in 10 years and has a coupon rate of 7.2% paid semiannually.(a) If the yield rate is 8% compounded semiannually, find the bond's market price.(b) Three
Kevin Patrick paid off the loan he took out to buy his car, but once the loan was paid, he continued to deposit $400 on the first of each month in an account that paid 5.4%, compounded monthly. After
A young couple receive an inheritance of $72,000 that they want to set aside for a college fund for their two children. How much will this provide at the end of each half-year for a period of 9 years
A bank is trying to decide whether to advertise some new 18-month certificates of deposit (CDs) at 6.52%, compounded quarterly, or at 6.48%, compounded continuously. Which rate is a better investment
To purchase a home, a couple borrowed $280,000 at 5.1% compounded monthly for 25 years. After making 70 payments of $1653.21, they plan to refinance at 4.2% compounded monthly for 15 years, with
1. A divorce settlement of $40,000 is paid in $1000 payments at the end of each of 40 months. What is the present value of this settlement if money is worth 12%, compounded monthly? 2. If $8000 is
A couple borrowed $184,000 to buy a condominium. Their loan was for 25 years and money is worth 6%, compounded monthly. (a) Find their monthly payment size. (b) Find the total amount they would pay
Suppose a salesman invests his $12,500 bonus in a fund that earns 10.8%, compounded monthly. Suppose also that he makes contributions of $150 at the end of each month to this fund. (a) Find the
Three years from now, a couple plan to spend 4 months traveling in China, Japan, and Southeast Asia. When they take their trip, they would like to withdraw $10,000 at the beginning of each month to
At age 22, Aruam Sdlonyer receives a $4000 IRA from her parents. At age 30, she decides that at age 67 she'd like to have a retirement fund that would pay $20,000 at the end of each month for 20
A company borrows $2.6 million for 15 years at 5.6%, compounded quarterly. After 2 years of regular payments, the company's profits are such that management feels it can increase the quarterly
1. Find the fourth term of the geometric sequence with first term 64 and eighth term ½?2. Find the sum of the first 16 terms of the geometric sequence 1/9, 1/3, 1, ....?
1. If $8000 is borrowed at 12% simple interest for 3 years, what is the future value of the loan at the end of the 3 years?2. Mary Toy borrowed $2000 from her parents and repaid them $2100 after 9
One ball is drawn at random from a bag containing 4 red balls and 6 white balls. What is the probability that the ball is (a) Red? (b) Green? (c) Red or white?
From a deck of 52 ordinary playing cards, one card is drawn. Find the probability that it is (a) A red king. (b) A king or a black card.
Suppose a fair coin is tossed two times. Construct an equiprobable sample space for the experiment, and determine each of the following probabilities. (a) Pr(0 heads) (b) Pr(1 head) (c) Pr(2 heads)
Suppose a fair coin is tossed four times. Construct an equiprobable sample space for the experiment, and determine each of the following probabilities. (a) Pr(2 heads) (b) Pr(3 heads) (c) Pr(4 heads)
Use Table 7.1 to determine the following probabilities if a distinguishable pair of dice is rolled. (a) Pr(sum is 4) (b) Pr(sum is 10) (c) Pr(sum is 12)
(a) When a pair of distinguishable dice is rolled, what sum is most likely to occur? (b) When a pair of distinguishable dice is rolled, what is Pr(4 ≤ S ≤ 8), where S represents the sum rolled?
If a pair of dice, one green and one red, is rolled, what is(a) Pr(4 ≤ S ≤ 7), where S is the sum rolled?(b) Pr(8 ≤ S ≤ 12), where S is the sum rolled?
If a green die and a red die are rolled, find (a) Pr(2 ≤ S ≤ 6), where S is the sum rolled on the two dice. (b) Pr(4 ≤ S), where S is the sum rolled on the two dice.
Suppose a die is tossed 1200 times and a 6 comes up 431 times. (a) Find the empirical probability for a 6 to occur. (b) On the basis of a comparison of the empirical probability and the theoretical
Suppose that a coin is tossed 3000 times and 1800 heads result. What is the empirical probability that a head will occur with this coin? Is there evidence that the coin is a fair coin?
One ball is drawn at random from a bag containing 4 red balls and 6 white balls. What is the probability that the ball is (a) White? (b) White or red? (c) Red and white?
If the odds that a particular horse will win a race are 1:20, what is the probability (a) That the horse will win the race? (b) That the horse will lose the race?
If the odds that an event E will not occur are 23:57, what is the probability (a) That event E will occur? (b) That event E will not occur?
A car rental firm has 425 cars. Sixty-three of these cars have defective turn signals and 32 have defective tires. What is the probability that one of these cars selected at random (a) Has defective
The table gives the average number of voters in Springfield in each of three political parties during the last 12 years, along with the average number that voted in presidential elections during this
In a sales promotion, a clothing store gives its customers a chance to draw a ticket from a box that contains a discount on their next purchase. The box contains 3000 tickets giving a 10% discount,
A dry cleaning firm has 12 employees: 7 women and 5 men. Three of the women and five of the men are 40 years old or older. The remainder are over 20 years old and under 40. If a person is chosen at
The table gives the percents of U.S. residents who participated in the recommended amount of physical activity, who participated in an insufficient amount of physical activity, and who were inactive,
The table gives the percent of U.S. residents who participated in no leisure-time physical activity, categorized by race or origin.(a) What is the probability that a Black person participated in no
Forty percent of a company's total output consists of baseballs, 30% consists of softballs, and 10% consists of tennis balls. Its only remaining product is handballs. If we place balls in a box in
A supply of 500 plasma television displays has 6 defective displays. What is the probability that a display picked at random from the supply is not defective?
A frustrated store manager is asked to make four different yes-no decisions that have no relation to each other. Because he is impatient to leave work, he flips a coin for each decision. If the
A couple plan to have two children and want to know the probability of having one boy and one girl. (a) Does {0, 1, 2} represent an equiprobable sample space for finding the probability of exactly
What is the probability that a couple planning to have two children will have (a) One child of each sex? (b) Two children of the same sex?
In a certain town, citizens' groups have identified three intersections as potentially dangerous. They collected the following data.For each intersection, find the probability that a vehicle entering
The table gives the number of fatal occupational injuries from transportation incidents. If a fatality from this group is chosen at random, what is the probability that it is (a) A highway
Prior to an election, a poll of 1200 citizens is taken. Suppose 557 plan to vote for A, 533 plan to vote for B, and the remainder indicate they will not vote. (a) If the poll is accurate, find the
A die is rolled. What is the probability that (a) A 4 will result? (b) A 7 will result? (c) An odd number will result?
Suppose a county has 800,000 registered voters, 480,000 of whom are Democrats and 290,000 of whom are Republicans. If a registered voter is chosen at random, what is the probability that(a) He or she
Suppose that at a certain hospital the births on a given day consisted of 8 girls and 2 boys. Suppose that at the same hospital, the births in a given year consisted of 1220 girls and 1194 boys.(a)
A traffic survey showed that 5680 cars entered an intersection of the main street of a city and that 1460 of them turned onto the intersecting street at this intersection. (a) What is the empirical
The odds of an American home having at least one container of ice cream in the freezer are 9 to 10. What is the probability that an American home chosen at random will have ice cream in its freezer?
If the odds against dying in an industrial accident are 3992:3, what is the probability of dying in an industrial accident?
The probability of being killed in any sort of non-transportation accident is 1 70. What are the odds against being killed in any sort of non-transportation accident?
An urn contains three red balls numbered 1, 2, 3, four white balls numbered 4, 5, 6, 7, and three black balls numbered 8, 9, 10. A ball is drawn from the urn. What is the probability that (a) It is
An urn contains three red balls numbered 1, 2, 3, four white balls numbered 4, 5, 6, 7, and three black balls numbered 8, 9, 10. A ball is drawn from the urn. What is the probability that the ball
From a deck of 52 ordinary playing cards, one card is drawn. Find the probability that it is (a) A queen. (b) A red card. (c) A spade.
A card is drawn from a deck of 52 playing cards. What is the probability that it is an ace, king, or jack?
In a game where only one player can win, the probability that Jack will win is 1/5 and the probability that Bill will win is 1/4. Find the probability that one of them will win.
A cube has 3 faces painted white, 2 faces painted red, and 1 face painted blue. What is the probability that a roll will result in a red or blue face?
A ball is drawn from a bag containing 13 red balls numbered 1-13 and 5 white balls numbered 14-18. What is the probability that (a) The ball is not even-numbered? (b) The ball is red and
A ball is drawn from a bag containing 13 red balls numbered 1-13 and 5 white balls numbered 14-18. What is the probability that(a) The ball is not red?(b) The ball is white and odd-numbered?(c) The
If you draw one card at random from a deck of 12 cards numbered 1 through 12, what is the probability that the number you draw is even and divisible by 5?
A car rental firm has 425 cars. Sixty-three of these cars have defective turn signals, and 32 have defective tires. What is the probability that one of these cars selected at random (a) Does not have
A company employs 65 people. Eight of the 30 men and 21 of the 35 women work in the business office. What is the probability that an employee picked at random is a woman or works in the business
Sacco and Rosen are among three candidates running for public office, and polls indicate that the probability that Sacco will win is 1 3 and the probability that Rosen will win is 1 2. Only one
Rob Lee knows his camera will take a good picture unless the flash is defective or the batteries are dead. The probability of having a defective flash is 0.05, the probability of the batteries being
The table gives the percent of employees of the Ace Company in each of three salary brackets, categorized by the sex of the employees. An employee is selected at random.(a) What is the probability
At the Baker Engineering Company, 40% of the employees are female and 60% of the employees earn less than $60,000. If 30% of the employees are females who earn less than $60,000, what is the
The table gives the projected number of workers in various categories in Springfield in 2020. If one of the represented workers is chosen at random, use the table to find the probability that the
In the United States in 2011, there were 596,339 deaths from heart disease, 575,313 from cancer, and 128,931 from stroke. If a death is chosen at random from the 2,512,873 deaths that occurred in
The table gives the numbers of new HIV infections in various categories for the United States and six dependent areas in 2011. Use the table to find the probability that a person diagnosed in 2011
In 2012, the death rate from motor vehicle accidents was 10.8 per 100,000 people and the death rate from falls was 8.4 per 100,000 people. What is the probability that an accidental death in 2012 was
The cognitive complexity of a structure was studied by Scott* using a technique in which a person was asked to specify a number of objects and group them into as many groupings as he or she found
A group of 100 people contains 60 Democrats and 35 Republicans. If there are 60 women and if 40 of the Democrats are women, what is the probability that a person selected at random is a Democrat or a
A mathematics class consists of 16 engineering majors, 12 science majors, and 4 liberal arts majors. (a) What is the probability that a student selected at random will be a science or liberal arts
Repairing a copy machine requires that two parts be delivered from two suppliers. The probability that part A will be delivered on Thursday is 0.6, and the probability that part B will be delivered
The table summarizes the opinions of various groups on the issue of oil drilling in national parks.1. Find the probability that an individual chosen at random is a Republican or favors oil drilling

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