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college mathematics for business

Questions and Answers of College Mathematics For Business

Three fair coins are tossed 1,000 times with the following frequencies of outcomes:(A) What is the empirical probability of obtaining 2 heads?(B) What is the theoretical probability of obtaining 2
If 3 people are selected from a group of 7 men and 3 women, what is the probability that at least 1 woman is selected?
A new lie-detector test has been devised and must be tested before it is used. One hundred people are selected at random, and each person draws a card from a box of 100 cards. Half the cards instruct
Two fair (not weighted) dice are each numbered with a 3 on one side, a 2 on two sides, and a 1 on three sides. The dice are rolled, and the numbers on the two up faces are added. If X is the random
If you pay $3.50 to play the game in Problem 62 (the dice are rolled once) and you are returned the dollar amount corresponding to the sum on the faces, what is the expected value of the game? Is the
If each of 5 people is asked to identify his or her favorite book from a list of 10 best-sellers, what is the probability that at least 2 of them identify the same book?
A clothing company selected 1,000 persons at random and surveyed them to determine a relationship between the age of the purchaser and the annual purchases of jeans. The results are given in the
A market research firm has determined that 40% of the people in a certain area have seen the advertising for a new product and that 85% of those who have seen the advertising have purchased the
Explain how the three events A, B, and C from a sample space S are related to each other in order for the following equation to hold true:P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∩ B)
A $2,000 bicycle is insured against theft for an annual premium of $170. If the probability that the bicycle will be stolen during the year is .08 (empirically determined), what is the expected value
Explain how the three events A, B, and C from a sample space S are related to each other in order for the following equation to hold true:P(A ∪ B ∪ C) = P(A) + P(B) + P(C)
A company sales manager, after careful analysis, presents two sales plans. It is estimated that plan A will net $10 million if successful (probability .8) and lose $2 million if not (probability .2);
Many (but not all) calculators experience an overflow error when computing 365Pn for n > 39 and when computing 365n. Explain how you would evaluate P(E) for any n > 39 on such a calculator.
Twelve precision parts, including 2 that are substandard, are sent to an assembly plant. The plant will select 4 at random and will return the entire shipment if 1 or more of the sample are found to
An urn contains 2 one-dollar bills, 1 five-dollar bill, and 1 ten-dollar bill. A player draws bills one at a time without replacement from the urn until a ten-dollar bill is drawn. Then the game
If the odds in favor of an event E occurring are a to b, show that a P(E) %3D a + b
A dozen tablet computers, including 2 that are defective, are sent to a computer service center. A random sample of 3 is selected and tested. Let X be the random variable associated with the number
By testing a large number of individuals, it has been determined that 82% of the population have normal hearts, 11% have some minor heart problems, and 7% have severe heart problems. Ninety-five
In a straw poll, 30 students in a mathematics class are asked to indicate their preference for president of student government. Approximate empirical probabilities are assigned on the basis of the
By examining the past driving records of city drivers, an insurance company has determined the following (empirical) probabilities:If a city driver is selected at random, what is the probability
If a salesperson has gross sales of over $600,000 in a year, then he or she is eligible to play the company’s bonus game: A black box contains 1 twenty-dollar bill, 2 five-dollar bills, and 1
An ice cream company wishes to use a new red dye to enhance the color in its strawberry ice cream. The U.S. Food and Drug Administration (FDA) requires the dye to be tested for cancer-producing
In order to test a new drug for adverse reactions, the drug was administered to 1,000 test subjects with the following results: 60 subjects reported that their only adverse reaction was a loss of
Problem refer to the data in the following table, obtained in a study to determine the frequency and dependency of IQ ranges relative to males and females. 1,000 people were chosen at random and the
Problems 87 and 88 refer to the data in the following table, obtained from a random survey of 1,000 residents of a state. The participants were asked their political affiliations and their
Problems 87 and 88 refer to the data in the following table, obtained from a random survey of 1,000 residents of a state. The participants were asked their political affiliations and their
Problem refer to the data in the following table, obtained in a study to determine the frequency and dependency of IQ ranges relative to males and females. 1,000 people were chosen at random and the
A survey of a precinct’s residents revealed that 55% of the residents were members of the Democratic party and 60% of the Democratic party members voted in the last election. What is the
In Problem find the indicated number of elements by referring to the following table of enrollments in a finite mathematics class:Let the universal set U be the set of all 120 students in the class,
In Problem find the indicated number of elements by referring to the following table of enrollments in a finite mathematics class:Let the universal set U be the set of all 120 students in the class,
In Problem use the Venn diagram to indicate which of the eight blood types are included in each set.(A ∪ B)′When receiving a blood transfusion, a recipient must have all the antigens of the
In Problem use the Venn diagram to indicate which of the eight blood types are included in each set.(A ∪ B ∪ Rh)′When receiving a blood transfusion, a recipient must have all the antigens of
In Problem use the Venn diagram to indicate which of the eight blood types are included in each set.A′ ∩ BWhen receiving a blood transfusion, a recipient must have all the antigens of the donor.
In Problem use the Venn diagram to indicate which of the eight blood types are included in each set.Rh′ ∩ AWhen receiving a blood transfusion, a recipient must have all the antigens of the donor.
In Problem use a tree diagram to represent a factorization of the given integer into primes, so that there are two branches at each number that is not prime. For example, the factorization 24 = 4 . 6
In Problem without using a calculator, determine which event, E or F, is more likely to occur. P(E) = : P(F) = 4 6.
In Problem write each expression as a quotient of integers, reduced to lowest terms. 3 1 1 3
In Problem write the expression as a quotient of integers, reduced to lowest terms. 5 12 7 12
In Problem use a tree diagram to represent a factorization of the given integer into primes, so that there are two branches at each number that is not prime. For example, the factorization 24 = 4 . 6
In Problem without using a calculator, determine which event, E or F, is more likely to occur. P(E) = 2 P(F) 3
In Problem write each expression as a quotient of integers, reduced to lowest terms. 7 1 2 4 7
In Problem use a tree diagram to represent a factorization of the given integer into primes, so that there are two branches at each number that is not prime. For example, the factorization 24 = 4 . 6
In Problem write the expression as a quotient of integers, reduced to lowest terms. 3
Each of the first 10 letters of the alphabet is printed on a separate card. What is the probability of drawing 3 cards and getting the code word dig by drawing d on the first draw, i on the second
In Problem without using a calculator, determine which event, E or F, is more likely to occur. P(E) = ;P(F) = 4 8
In Problem write each expression as a quotient of integers, reduced to lowest terms. 3 3 1-
In Problem write the expression as a quotient of integers, reduced to lowest terms. 4 6
In Problem use a tree diagram to represent a factorization of the given integer into primes, so that there are two branches at each number that is not prime. For example, the factorization 24 = 4 . 6
A drug has side effects for 50 out of 1,000 people in a test. What is the approximate empirical probability that a person using the drug will have side effects?
In Problem without using a calculator, determine which event, E or F, is more likely to occur. 7 P(E) = .9;P(F) 8
In Problem write each expression as a quotient of integers, reduced to lowest terms. 4 7 2/7
In Problem use a tree diagram to represent a factorization of the given integer into primes, so that there are two branches at each number that is not prime. For example, the factorization 24 = 4 . 6
In Problem write the expression as a quotient of integers, reduced to lowest terms. 2 9. 2 1 9.
In Problem without using a calculator, determine which event, E or F, is more likely to occur. 1 P(E) = .15;P(F) 6. %3D
In Problem write each expression as a quotient of integers, reduced to lowest terms. 4 3 5 4 1 1 4 3 5 3 5 4
In Problem write the expression as a quotient of integers, reduced to lowest terms. 3 16 3 1 16
In Problem use a tree diagram to represent a factorization of the given integer into primes, so that there are two branches at each number that is not prime. For example, the factorization 24 = 4 . 6
In Problem without using a calculator, determine which event, E or F, is more likely to occur. 6. 5 P(E) =:P(F) 11
In Problem write each expression as a quotient of integers, reduced to lowest terms. 1 2 5 3 1 2 4 1 5 3 5 4
Problem refer to the Venn diagram below for events A and B in an equally likely sample space S. Find each of the indicated probabilities.P(A ∩ B) S A B 12 38 23 27
Find the probabilities in Problems by referring to the tree diagram below.P(M ∩ A) = P(M)P(A|M) .7 A M .6 .3 B Start .2 A .4 .8 B
Problem refer to the Venn diagram below for events A and B in an equally likely sample space S. Find each of the indicated probabilities.P(A ∪ B) S A B 12 38 23 27
Find the probabilities in Problems by referring to the tree diagram below.P(N ∩ B) = P(N)P(B|N) .7 A M .6 .3 B Start .2 A .4 .8 B
Problem refer to the Venn diagram below for events A and B in an equally likely sample space S. Find each of the indicated probabilities.P(A′ ∪ B) S A B 12 38 23 27
Find the probabilities in Problems by referring to the tree diagram below.P(A) = P(M ∩ A) + P(N ∩ A) .7 A M .6 .3 B Start .2 A .4 .8 B
Problem refer to the Venn diagram below for events A and B in an equally likely sample space S. Find each of the indicated probabilities.P(A ∩ B′) S A B 12 38 23 27
You draw and keep a single bill from a hat that contains a $1, $10, $20, $50, and $100 bill. What is the expected value of the game to you?
Find the probabilities in Problems by referring to the tree diagram below.P(B) = P(M ∩ B) + P(N ∩ B) .7 A M .6 .3 B Start .2 A .4 .8 B
The table gives the number of male and female workers earning at or below the minimum wage for several age categories.(A) How many males are of age 20–24 and earn below minimum wage?(B) How many
A cable television company has 8,000 subscribers in a suburban community. The company offers two premium channels: HBO and Showtime. If 2,450 subscribers receive HBO, 1,940 receive Showtime, and
Let U be the set of all 2-card hands, let K be the set of all 2-card hands that contain exactly 1 king, and let H be the set of all 2-card hands that contain exactly 1 heart. Find n(K ∩ H′), n(K
Let U be the set of all 2-card hands, let K be the set of all 2-card hands that contain exactly 1 king, and let Q be the set of all 2-card hands that contain exactly 1 queen. Find n(K ∩ Q′), n(K
If p is the proposition “I want pickles” and q is the proposition “I want tomatoes,” rewrite the sentence “I want tomatoes, but I do not want pickles” using symbols.
In Problem refer to the Venn diagram below and find the indicated number of elements.n( (A ∪ B)′ ) U A B 21 42 18 19
In Problem refer to the table in the graphing calculator display below, which shows y1 = nPr and y2 = nCr for n = 6.Explain how the table illustrates the formulanPr = r!nCr NORMAL FLOAT AUTO
In Problem construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.p ∨ (p → q)
In Problem draw a Venn diagram for sets A, B, and C and shade the given region.A ∩ B′ ∩ C U A B 21 42 18 19
In Problem construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.¬ p → (p ∨ q)
Problem refer to the following Venn diagram.Which of the numbers x, y, z, or w must equal 0 if A ⊂ B? A B y
In Problem draw a Venn diagram for sets A, B, and C and shade the given region.A′ ∩ B′ ∩ C U A B 21 42 18 19
A group of 150 people includes 52 who play chess, 93 who play checkers, and 28 who play both chess and checkers. How many people in the group play neither game?
In Problem draw a Venn diagram for sets A, B, and C and shade the given region.(A ∪ B)′ U A B 21 42 18 19
Problem refer to the following Venn diagram.Which of the numbers x, y, z, or w must equal 0 if A ∩ B = U? A B y
In Problem draw a Venn diagram for sets A, B, and C and shade the given region.A′ ∪ (B′ ∩ C) U A B 21 42 18 19
In Problem draw a Venn diagram for sets A, B, and C and shade the given region.(A ∩ B)′ ∪ C U A B 21 42 18 19
In Problem construct a truth table to verify each implication.¬ p ∧ q ⇒ p ∨ q
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample.If n and r are positive integers and 1 < r < n, then nCr < nPr .
A survey of 1,200 people indicates that 850 own HDTVs, 740 own DVD players, and 580 own HDTVs and DVD players.(A) How many people in the survey own either an HDTV or a DVD player?(B) How many own
In Problem construct a truth table to verify each implication.¬ p → (q ∧ ¬q) ⇒p
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample.If n and r are positive integers and 1 < r < n, then nPr < n!.
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counter example.If n and r are positive integers and 1 < r < n, then nCr < n!.
Note from the table in the graphing calculator display below that the largest value of nCr when n = 20 is 20C10 = 184,756. Use a similar table to find the largest value of nCr when n = 24. NORMAL
Note from the table in the graphing calculator display that the largest value of nCr when n = 21 is 21C10 = 21C11 = 352,716. Use a similar table to find the largest value of nCr when n = 17. NORMAL
A politician running for a third term is planning to contact all contributors to her first two campaigns. If 1,475 individuals contributed to the first campaign, 2,350 contributed to the second
How many different 5-child families are possible where the gender of the children in the order of their births is taken into consideration [that is, birth sequences such as (B, G, G, B, B) and (G, B,
A survey of 1,000 people indicates that 340 have invested in stocks, 480 have invested in bonds, and 210 have invested in stocks and bonds.(A) How many people in the survey have invested in stocks or
In a study of twins, a sample of 6 pairs of identical twins will be selected for medical tests from a group of 40 pairs of identical twins. In how many ways can this be done?
Let p be the proposition “every politician is honest.” Explain why the statement “every politician is dishonest” is not equivalent to ¬ p. Express ¬ p as an English sentence without using
In Problem find the indicated number of elements by referring to the following table of enrollments in a finite mathematics class:Let the universal set U be the set of all 120 students in the class,
In an unusual recall election, there are 67 candidates to replace the governor of a state. To negate the advantage that might accrue to candidates whose names appear near the top of the ballot, it is

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