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mathematics
college mathematics for business
Questions and Answers of
College Mathematics For Business
In Problem use interval notation to specify the given interval.{x| x2 ≥16}
In Problem factor each polynomial into the product of first-degree factors with integer coefficients.x3 + 15x2 + 50x
In Problem find an equation of the form Ax + By = C for the given line.The line through (-2, 9) that has slope 2
In Problem use interval notation to specify the given interval.{x| x2 > 25}
In Problem factor each polynomial into the product of first-degree factors with integer coefficients.x3 - 7x2 + 12x
In Problem find the slope of the line through the given points. Write the slope as a reduced fraction, and also give its decimal form.(-12, -3) and (4, 3)
In Problem find an equation of the form Ax + By = C for the given line.The horizontal line through (7, 1)
In Problem use interval notation to specify the given interval.{x| 0.1 ≤ x ≤ 0.3}
In Problem factor each polynomial into the product of first-degree factors with integer coefficients.x2 + 5x - 36
In Problem find the slope of the line through the given points. Write the slope as a reduced fraction, and also give its decimal form.(10, 14) and (0, 68)
In Problem find an equation of the form Ax + By = C for the given line.The vertical line through (-6, 3)
In Problem use interval notation to specify the given interval.{x| -10 < x < 100}
In Problem find the slope of the line through the given points. Write the slope as a reduced fraction, and also give its decimal form.(-1, 11) and (1, 8)
In Problem find an equation of the form Ax + By = C for the given line.The vertical line through (5, 0)
In Problem use interval notation to specify the given interval.The set of all real numbers from -8 to -4, excluding -8 but including -4
In Problem factor each polynomial into the product of first-degree factors with integer coefficients.x2 - 64
In Problem factor each polynomial into the product of first-degree factors with integer coefficients.x2 - 81
In Problem find the slope of the line through the given points. Write the slope as a reduced fraction, and also give its decimal form.(2, 7) and (6, 16)
In Problem find an equation of the form Ax + By = C for the given line.The horizontal line through (0, 4)
In a study to determine employee voting patterns in a recent strike election, 1,000 employees were selected at random and the following tabulation was made:(A) Convert this table to a probability
In Problem use interval notation to specify the given interval.The set of all real numbers from -3 to 5, including -3 and 5
Show that P(A|B) + P(A′|B) = 1.
Show that P(A|A) = 1 when P(A) ≠ 0.
If P(E) = c/d, show that odds in favor of E occurring are c to d - c.
Six men in 100 and 1 woman in 100 are colorblind. A person is selected at random and is found to be color-blind. What is the probability that this person is a man? (Assume that the total population
From a survey of 100 city residents, it was found that 40 read the daily newspaper, 70 watch the evening news, and 30 do both. What is the (empirical) probability that a resident selected at
Problem refer to the following experiment: 2 balls are drawn in succession out of a box containing 2 red and 5 white balls. Let Ri be the event that the ith ball is red, and let Wi be the event that
In Problem compute the odds against obtainingA 3 or an even number in a single roll of a die
In Problem compute the odds against obtainingA number greater than 4 in a single roll of a die
The management of a company finds that 30% of the administrative assistants hired are unsatisfactory. The personnel director is instructed to devise a test that will improve the situation. One
Show that P(U1 |R) + P(U1′ |R) = 1.
A fair coin is tossed 8 times.(A) What is the probability of tossing a head on the 8th toss, given that the preceding 7 tosses were heads?(B) What is the probability of getting 8 heads or 8 tails?
In Problem use the table below. Events A, B, and C are mutually exclusive; so are D, E, and F.In Problem test each pair of events for independence.A and D
In Problem use the table below. Events A, B, and C are mutually exclusive; so are D, E, and F.In Problem find each probability directly from the table.P(C ∩ E)
(A) If 10 out of 32 students in a class were born in June, July, or August, what is the approximate empirical probability of any student being born in June, July, or August?(B) If one is as likely to
Using the following probability tree:P(A | B′) .2 B .4 .8 B' Start .3 B .6 .7 B'
Find the probabilities in Problem by referring to the tree diagram below.P(C) -C A D Start - C 3 D 5
Using the following probability tree:P(A |B) .2 B .4 .8 B' Start .3 B .6 .7 B'
In Problem use the table below. Events A, B, and C are mutually exclusive; so are D, E, and F.In Problem find each probability directly from the table.P(E)
Find the probabilities in Problem by referring to the tree diagram below.P(B) -C A D Start - C 3 D 5
Using the following probability tree:P(B) .2 B .4 .8 B' Start .3 B .6 .7 B'
Find the probabilities in Problem by referring to the tree diagram below.P(A) -C A D Start - C 3 D 5
Using the following probability tree:P(A′ ∩ B) .2 B .4 .8 B' Start .3 B .6 .7 B'
Using the following probability tree:P(A ∩ B) .2 B .4 .8 B' Start .3 B .6 .7 B'
In Problem find the conditional probability, in a single roll of two fair dice, thatAt least one die is a six, given that the sum is odd.
In Problem find the conditional probability, in a single roll of two fair dice, thatNeither die is a six, given that the sum is greater than 7.
Using the following probability tree:P(B |A′) .2 B .4 .8 B' Start .3 B .6 .7 B'
Two coins are flipped. You win $2 if either 2 heads or 2 tails turn up; you lose $3 if a head and a tail turn up. What is the expected value of the game?
In Problem find the conditional probability, in a single roll of two fair dice, thatThe sum is odd, given that at least one die is a six.
Using the following probability tree:P(B |A) .2 B .4 .8 B' Start .3 B .6 .7 B'
In Problem find the conditional probability, in a single roll of two fair dice, thatThe sum is greater than 7, given that neither die is a six.
Using the following probability tree:P(A) .2 B .4 .8 B' Start .3 B .6 .7 B'
After paying $4 to play, a single fair die is rolled, and you are paid back the number of dollars corresponding to the number of dots facing up. For example, if a 5 turns up, $5 is returned to you
In Problem find the conditional probability, in a single roll of two fair dice, thatThe roll is doubles, given that the sum is 10.
Using the table of probabilities shownAre S and X independent? X Y Z Totals S .10 .25 .15 .50 T .05 .20 .02 .27 R .05 .15 .03 .23 Totals .20 .60 .20 1.00
In Problem find the conditional probability, in a single roll of two fair dice, thatThe sum is even, given that the sum is less than 6.
Using the table of probabilities shownAre T and Z independent? X Y Z Totals S .10 .25 .15 .50 T .05 .20 .02 .27 R .05 .15 .03 .23 Totals .20 .60 .20 1.00
A fair coin is flipped. If a head turns up, you win $1. If a tail turns up, you lose $1. What is the expected value of the game? Is the game fair?
In Problem find the conditional probability, in a single roll of two fair dice, thatThe sum is 10, given that the roll is doubles.
Using the table of probabilities shownFind P(T| Z) X Y Z Totals S .10 .25 .15 .50 T .05 .20 .02 .27 R .05 .15 .03 .23 Totals .20 .60 .20 1.00
In Problem find the conditional probability, in a single roll of two fair dice, thatThe sum is less than 6, given that the sum is even.
In tossing 2 fair coins, what is the expected number of heads?
Using the table of probabilities shownFind P(Z |R) X Y Z Totals S .10 .25 .15 .50 T .05 .20 .02 .27 R .05 .15 .03 .23 Totals .20 .60 .20 1.00
In Problem use the table below. Events A, B, and C are mutually exclusive; so are D, E, and F.In Problem find each probability directly from the table.P(B ∩ D)
Find the probabilities in Problem by referring to the tree diagram below.P(D) -C A D Start - C 3 D 5
Find the probabilities in Problem by referring to the tree diagram below.P(A|C) -C A D Start - C 3 D 5
Find the probabilities in Problem by referring to the tree diagram below.P(B|D) -C A D Start - C 3 D 5
A pair of dice is rolled once. Suppose you lose $10 if a 7 turns up and win $11 if an 11 or 12 turns up. How much should you win or lose if any other number turns up in order for the game to be fair?
A store carries four brands of DVD players: J, G, P, and S. From past records, the manager found that the relative frequency of brand choice among customers varied. Which of the following probability
A player tosses two coins and receives $5 if 2 heads turn up, loses $4 if 1 head turns up, and wins $2 if 0 heads turn up. Compute the expected value of the game. Is the game fair?
Two coins are flipped 1,000 times with the following frequencies:(A) Compute the empirical probability for each outcome.(B) Compute the theoretical probability for each outcome.(C) Using the
A spinning device has 3 numbers, 1, 2, and 3, each as likely to turn up as the other. If the device is spun twice, what is the probability that(A) The same number turns up both times?(B) The sum of
In Problem use the table below. Events A, B, and C are mutually exclusive; so are D, E, and F.In Problem test each pair of events for independence.A and E
Roulette wheels in Nevada generally have 38 equally spaced slots numbered 00, 0, 1, 2, . . . , 36. A player who bets $1 on any given number wins $35 (and gets the bet back) if the ball comes to
In Problem use the table below. Events A, B, and C are mutually exclusive; so are D, E, and F.In Problem test each pair of events for independence.B and D
Two dice are rolled. The sample space is chosen as the set of all ordered pairs of integers taken from {1, 2, 3, 4, 5, 6}. What is the event A that corresponds to the sum being divisible by 4? What
In Problem use the table below. Events A, B, and C are mutually exclusive; so are D, E, and F.In Problem test each pair of events for independence.B and E
Given the following probabilities for an event E, find the odds for and against E:
A person tells you that the following approximate empirical probabilities apply to the sample space {e1, e2, e3, e4}: P(e1) ≈ .1, P(e2) ≈ -.2, P(e3) ≈ .6, P(e4) ≈ 2. There are three reasons
A pair of dice are rolled 1,000 times with the following frequencies of outcomes:Use these frequencies to calculate the approximate empirical probabilities and odds for the events in Problem(A) The
In Problem refer to the following probability tree:Suppose that c = e. Discuss the dependence or independence of events U and M. M U c+d = 1 a d N Start a + b = 1 a, b, c, d, e, f+0 M e +f = 1 f
Use the following information to complete the frequency table below: n(B) = 45, n(U) n(A) = 50, %3D n(A U B) = 80, 100 %3D A A' Totals B B' Totals
Given the following probabilities for an event E, find the odds for and against E:
In Problem use the table below. Events A, B, and C are mutually exclusive; so are D, E, and F.In Problem test each pair of events for independence.A and B
In Problem use the table below. Events A, B, and C are mutually exclusive; so are D, E, and F.In Problem test each pair of events for independence.D and F
Five thousand tickets are sold at $1 each for a charity raffle. Tickets will be drawn at random and monetary prizes awarded as follows: 1 prize of $500; 3 prizes of $100, 5 prizes of $20, and 20
In Problem use the table below. Events A, B, and C are mutually exclusive; so are D, E, and F.In Problem test each pair of events for independence.B and F
A pointer is spun on a circular spinner. The probabilities of the pointer landing on the integers from 1 to 5 are given in the table below.(A) What is the probability of the pointer landing on an odd
In Problem refer to the following probability tree:Suppose that c = d = e = f . Discuss the dependence or independence of events M and N. M U c+d = 1 a d N Start a + b = 1 a, b, c, d, e, f+0 M e +f =
In Problem use the table below. Events A, B, and C are mutually exclusive; so are D, E, and F.In Problem test each pair of events for independence.C and F
A group of 10 people includes one married couple. If 4 people are selected at random, what is the probability that the married couple is selected?
A 5-card hand is drawn from a standard deck. Discuss how you can tell that the following two events are dependent without any computation.S = hand consists entirely of spadesH = hand consists
In Problem compute the odds in favor of obtainingA head in a single toss of a coin
The annual premium for a $5,000 insurance policy against the theft of a painting is $150. If the (empirical) probability that the painting will be stolen during the year is .01, what is your expected
A fair coin is tossed twice. Consider the sample space S = {HH, HT, TH, TT} of equally likely simple events. We are interested in the following events:E1 = a head on the first tossE2 = a tail on the
After careful testing and analysis, an oil company is considering drilling in two different sites. It is estimated that site A will net $30 million if successful (probability .2) and lose $3 million
Suppose that at each birth, having a girl is not as likely as having a boy. The probability assignments for the number of boys in a 3-child family are approximated empirically from past records and
A manufacturer obtains GPS systems from three different subcontractors: 20% from A, 40% from B, and 40% from C. The defective rates for these subcontractors are 1%, 3%, and 2%, respectively. If a
A new, simple test has been developed to detect a particular type of cancer. The test must be evaluated before it is used. A medical researcher selects a random sample of 1,000 adults and finds (by
Let A be the event that all of a family’s children are the same gender, and let B be the event that the family has at most 1 boy. Assuming the probability of having a girl is the same as the
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