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nature of mathematics

Questions and Answers of Nature Of Mathematics

A researcher chooses three leaves from a target environment and classifies each sample as fungus free or contaminated. Suppose that a leaf has a probability of 0.2 of being infected. In Problems
The probability that children in a specific family will have blond hair is \(\frac{3}{4}\). If there are four children in the family, what is the probability that two of them are blond?
The probability that the children in a specific family will have brown eyes is \(\frac{3}{8}\). If there are four children in the family, what is the probability that at least two of them have brown
What is the probability that if a pair of dice is rolled six times, exactly one sum of seven is rolled?
What is the probability that if a pair of dice is rolled twelve times, exactly two sums of seven are rolled?
If Marcy can make \(70 \%\) of free throws in a basketball game, what is the probability that she makes five of the next six free throws?
If Bart can make only \(40 \%\) of free throws in a basketball game, what is the probability that he will make exactly one of the next three free throws?
Lymnozyme cures most infections in Koi fish caused by bacteria; in fact, it has been shown to be \(96 \%\) effective if used according to the directions. If five Koi with a bacterial infection are
Lymnozyme cures most infections in Koi fish caused by bacteria; in fact, it has been shown to be \(96 \%\) effective if used according to the directions. If 15 Koi with a bacterial infection are
It is known that \(85 \%\) of the graduates of Foley's School of Motel Management are placed in a job within 6 months of graduation. If a class has 20 graduates, what is the probability that 15 will
If a graduating class from Problem 47 has 10 graduates, what is the probability that at least 9 will be placed within 6 months?
Suppose the National League team has a probability of \(\frac{3}{5}\) of winning the World Series and the American League team has a probability of \(\frac{2}{5}\). The series is over as soon as one
Suppose the National League team has a probability of \(\frac{3}{5}\) of winning a World Series game and the American League team has a probability of \(\frac{2}{5}\). The series is over as soon as
The batting average of the star baseball player Mike Thompson is 0.300 [that is, \(P(\) hit \()=0.3\) ]. What is the probability that Thompson will get at least three hits in four times at bat?
Eighty percent of the widgets of the Ampex Widget Company meet the specifications of its customers. If a sample of six widgets is tested, what is the probability that three or more of them would fail
Suppose that research has shown that the probability that a missile penetrates enemy defenses and reaches its target is 0.1 . Find the smallest number of identical missiles that are necessary in
Suppose a person claims to have extrasensory perception (ESP) and says she can read mental images \(75 \%\) of the time.We set up an experiment where she must determine whether we are looking at a
Repeat Problem 54, except that the person claims to read mental images \(90 \%\) of the time.
Fire frequency has a great impact on national parks. If the fire frequency is too severe, generally species that occur in later successional habitats will be excluded. Likewise, the absence of fire
In a certain office, three men determine who will pay for coffee by each flipping a coin. If one of them has an outcome that is different from the other two, he must pay for the coffee. What is the
In the game described in Problem 57, what is the probability that there will be an odd man out in a particular play if there are four players?Data from Problem 57In a certain office, three men
In the game of Problem 57, what is the probability that there will be an odd man out in a particular play if there are five players?Data from Problem 57In a certain office, three men determine who
Generalize Problem 57 for \(n\) people playing the game of "odd man out."Data from Problem 57In a certain office, three men determine who will pay for coffee by each flipping a coin. If one of them
If a sample from an assembly line reveals four defective items out of 1,000 sampled items, what is the probability that any one item is defective?
What is the probability of obtaining a prime in a single roll of a die?
A pair of dice is rolled. What is the probability that the resulting sum is eight?
A card is selected from an ordinary deck of cards. What is the probability that it is a jack or better? (A jack or better is a jack, queen, king, or ace.)
A single card is drawn from a standard deck of cards. What is the probability that it is an ace, if you know that one ace has already been removed from the deck?
For a roll of a pair of dice, find the following.a. \(P(5\) on at least one of the dice )b. \(P(5\) on one die or 4 on the other)c. \(P(5\) on one die and 4 on the other)
a. If the probability of dropping an egg is 0.01 , what is the probability of not dropping the egg?b. If \(P(E)=0.9\), what are the odds in favor of \(E\) ?c. If the odds against an event are 1,000
A game consists of rolling a die and receiving \(\$ 12\) if a one is rolled and nothing otherwise. What is the mathematical expectation?
A box contains three orange balls and two purple balls, and two are selected at random. What is the probability of the second ball being orange if we know that the first draw was orange and we draw
If \(A\) and \(B\) are independent events with \(P(A)=\frac{2}{3}\) and \(P(B)=\frac{3}{5}\), what is \(P(\overline{A \cup B}\) ?
A manufacturer of water test kits knows that about \(0.1 \%\) of the test strips in the kits are defective. Write the binomial probability formula that would be used to determine the probability that
The Weather Channel makes accurate predictions about \(85 \%\) of the time. Use this information to answer the questions in Problems 12-13.What is the probability that Weather Channel meteorologists
The Weather Channel makes accurate predictions about \(85 \%\) of the time. Use this information to answer the questions in Problems 12-13.What is the probability that they are accurate exactly 4 of
A friend says she has two new baby cats to show you, but she doesn't know whether they're both male, both female, or a pair. You tell her that you want only a male, and she telephones the vet and
The probability that an individual who is selected at random from a population has blue eyes has been estimated to be 0.35 . Find the probability that at least one of four people selected at random
An armored car transports money between two locations and travels along one of three routes: \(A_{1}, B_{1}, C_{1}\). On one day, the route is randomly selected according to the probabilities
Suppose a test for hypoglycemia is given. If a person has hypoglycemia, the test will detect it in \(90 \%\) of the cases; if the person does not have hypoglycemia, the test will show a positive
Consider the set of octahedral dice shown in Figure 13.11. Suppose your opponent chooses die \(D\). Which die would you choose, and why, if the game consists of each player rolling his or her chosen
The following problem appeared in an "Ask Marilyn" column, by Marilyn Vos Savant:There are five cars on display as prizes, and their five ignition keys are in a box. You get to pick one key out of
Answer the question in Problem 19 assuming that you are in the audience and want the probability that the contestant will win the car you have selected.Data from Problem 19The following problem
Devise a fair scheme for eliminating coins in this country.
Find the probability that the 13th day of a randomly chosen month will be a Friday.
You have five alternatives from which to choose. List your preferences for the alternatives from best to worst.I. Sure win of \(\$ 5\) and no chance of loss II. \(6.92 \%\) chance to win \(\$ 20\)
a. Choose between \(\mathrm{A}\) and \(\mathrm{B}\) :A. A sure gain of \(\$ 240\)B. \(25 \%\) chance to gain \(\$ 1,000\) and \(75 \%\) chance to gain \(\$ 0\)b. Choose between \(\mathrm{C}\) and
Do some research on Keno probabilities. Write a paper on playing Keno.
Consider the following classroom activity. Suppose the floor consists of square tiles 9 in. on each side. The players will toss a circular disk onto the floor. If the disk comes to rest on the edge
In Problems 5–30,a. Classify the sequences as arithmetic, geometric, Fibonacci, or none of these.b. If arithmetic, give d; if geometric, give r; if Fibonacci, give the first two terms; and if none
What is add-on interest?
What is APR?
Compare and contrast open-end and closed-end credit.
Discuss the methods of calculating credit card interest.
If you have a credit card, describe the method of calculating interest on your card. Name the bank issuing the credit card. If you do not have a credit card, contact a bank and obtain an application
Describe a good procedure for saving money with the purchase of an automobile.
Use estimation to select the best response in Problems 7-24.Do not calculate.If you purchase a \(\$ 2,400\) item and pay for it with monthly installments for 2 years, the monthly payment is A. \(\$
Use estimation to select the best response in Problems 7-24.Do not calculate.If you purchase a \(\$ 595.95\) item and pay for it with monthly installments for 1 year, the monthly payment isA. about
Use estimation to select the best response in Problems 7-24.Do not calculate.If I do not pay off my credit card each month, the most important cost factor is A. the annual fee B. the APR C. the grace
Use estimation to select the best response in Problems 7-24.Do not calculate.If I pay off my credit card balance each month, the most important cost factor is A. the annual fee B. the APR C. the
Use estimation to select the best response in Problems 7-24.Do not calculate.The method of calculation most advantageous to the consumer is the A. previous balance method B. adjusted balance method
Use estimation to select the best response in Problems 7-24.Do not calculate.If you purchase an item for \(\$ 1,295\) at an interest rate of \(9.8 \%\), and you finance it for 1 year, then the amount
Use estimation to select the best response in Problems 7-24.Do not calculate.If you purchase an item for \(\$ 1,295\) at an interest rate of \(9.8 \%\), and you finance it for 4 years, then the
Use estimation to select the best response in Problems 7-24.Do not calculate.If you purchase a new car for \(\$ 10,000\) and finance it for 4 years, the amount of interest you would expect to pay is
Use estimation to select the best response in Problems 7-24.Do not calculate.A reasonable APR to pay for a 3 -year installment loan is A. \(1 \%\)B. \(12 \%\)C. \(32 \%\)
Use estimation to select the best response in Problems 7-24.Do not calculate.A reasonable APR to pay for a 3-year automobile loan is A. \(6 \%\)B. \(40 \%\)C. \(\$ 2,000\)
Use estimation to select the best response in Problems 7-24.Do not calculate.If you wish to purchase a car with a sticker price of \(\$ 10,000\), a reasonable offer to make to the dealer is A. \(\$
Use estimation to select the best response in Problems 7-24.Do not calculate.A reasonable APR for a credit card is A. \(1 \%\)B. \(30 \%\)C. \(12 \%\)
Use estimation to select the best response in Problems 7-24.Do not calculate.In an application of the average daily balance method for the month of August, \(t\) is A. \(\frac{1}{12}\)B.
Use estimation to select the best response in Problems 7-24.Do not calculate.When using the average daily balance method for the month of September, \(t\) is A. \(\frac{1}{12}\)B.
Use estimation to select the best response in Problems 7-24.Do not calculate.If your credit card balance is \(\$ 650\) and the interest rate is \(12 \%\) APR, then the credit card interest charge is
Use estimation to select the best response in Problems 7-24.Do not calculate.If your credit card balance is \(\$ 952\), you make a \(\$ 50\) payment, the APR is \(12 \%\), and the interest is
Use estimation to select the best response in Problems 7-24.Do not calculate.If your credit card balance is \(\$ 952\), you make a \(\$ 50\) payment, the APR is \(12 \%\), and the interest is
Use estimation to select the best response in Problems 7-24.Do not calculate.If your credit card balance is \(\$ 952\), you make a \(\$ 50\) payment, the APR is \(12 \%\), and the interest is
Convert each credit card rate in Problems 25-30 to the APR.Oregon, \(1 \frac{1}{4} \%\) per month
Convert each credit card rate in Problems 25-30 to the APR.Arizona, \(1 \frac{1}{3} \%\) per month
Convert each credit card rate in Problems 25-30 to the APR.New York, \(1 \frac{1}{2} \%\) per month
Convert each credit card rate in Problems 25-30 to the APR.Tennessee, \(0.02740 \%\) daily rate
Convert each credit card rate in Problems 25-30 to the APR.Ohio, \(0.02192 \%\) daily rate
Convert each credit card rate in Problems 25-30 to the APR.Nebraska, \(0.03014 \%\) daily rate
Calculate the monthly finance charge for each credit card transaction in Problems 31-34. Assume that it takes 10 days for a payment to be received and recorded, and that the month is 30 days
Calculate the monthly finance charge for each credit card transaction in Problems 31-34. Assume that it takes 10 days for a payment to be received and recorded, and that the month is 30 days
Calculate the monthly finance charge for each credit card transaction in Problems 31-34. Assume that it takes 10 days for a payment to be received and recorded, and that the month is 30 days
Calculate the monthly finance charge for each credit card transaction in Problems 31-34. Assume that it takes 10 days for a payment to be received and recorded, and that the month is 30 days
Round your answers in Problems 35-38 to the nearest dollar.Make a \(6 \%\) offer on a Chevrolet Corsica that has a sticker price of \(\$ 14,385\) and a dealer cost of \(\$ 13,378\).
Round your answers in Problems 35-38 to the nearest dollar.Make a \(5 \%\) offer on a Ford Escort that has a sticker price of \(\$ 13,205\) and a dealer cost of \(\$ 12,412.70\).
Round your answers in Problems 35-38 to the nearest dollar.Make a \(10 \%\) offer on a Saturn that has a sticker price of \(\$ 19,895\) and a dealer cost of \(\$ 17,250\).
Round your answers in Problems 35-38 to the nearest dollar.Make a \(10 \%\) offer on a Nissan Pathfinder that has a sticker price of \(\$ 32,129\) and a dealer cost of \(\$ 28,916\).
Find the APR (rounded to the nearest tenth of a percent) for each of the loans described in Problems 39-42.Purchase a living room set for \(\$ 3,600\) at \(12 \%\) add-on interest for 3 years.
Find the APR (rounded to the nearest tenth of a percent) for each of the loans described in Problems 39-42.Purchase a stereo for \(\$ 2,500\) at \(13 \%\) add-on interest for 2 years.
Find the APR (rounded to the nearest tenth of a percent) for each of the loans described in Problems 39-42.Purchase an oven for \(\$ 650\) at \(11 \%\) add-on interest for 2 years.
Find the APR (rounded to the nearest tenth of a percent) for each of the loans described in Problems 39-42.Purchase a refrigerator for \(\$ 2,100\) at \(14 \%\) add-on interest for 3 years.
Assume the cars in Problems 43–46 can be purchased for 0%down for 60 months (in lieu of rebate).A Dodge Ram that has a sticker price of \(\$ 20,650\) with factory and dealer rebates of \(\$ 2,000
Assume the cars in Problems 43-46 can be purchased for 0\% down for 60 months (in lieu of rebate).A BMW that has a sticker price of \(\$ 62,490\) with factory and dealer rebates of \(\$ 6,000 \quad\)
Assume the cars in Problems 43-46 can be purchased for 0\% down for 60 months (in lieu of rebate).A car with a sticker price of \(\$ 42,700\) with factory and dealer rebates of \(\$ 5,100 \quad\)a.
Assume the cars in Problems 43-46 can be purchased for 0\% down for 60 months (in lieu of rebate).A car with a sticker price of \(\$ 36,500\) with factory and dealer rebates of \(\$ 4,200 \quad\)a.
A payday loan provides short-term loans ranging from \(\$ 250\) to \(\$ 2,000\). In Problems 47-50, assume the cost of the loan is \(\$ 1.00\) per day per \(\$ 100\) borrowed until the loan is
A payday loan provides short-term loans ranging from \(\$ 250\) to \(\$ 2,000\). In Problems 47-50, assume the cost of the loan is \(\$ 1.00\) per day per \(\$ 100\) borrowed until the loan is
A payday loan provides short-term loans ranging from \(\$ 250\) to \(\$ 2,000\). In Problems 47-50, assume the cost of the loan is \(\$ 1.00\) per day per \(\$ 100\) borrowed until the loan is
A payday loan provides short-term loans ranging from \(\$ 250\) to \(\$ 2,000\). In Problems 47-50, assume the cost of the loan is \(\$ 1.00\) per day per \(\$ 100\) borrowed until the loan is

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