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Questions and Answers of Mathematics Economics Business

Refer to the partially completed table of the six basic solutions to the e-systemFind basic solution (F). (A) (B) (C) (D) (E) (F) 2x1 + 5x2 + S₁ = 32 x₁ + 2x₂ + $₂ =
Refer to Table 5. For the basic solution (x1, x2, s1, s2, s3) = (27, 6, 9, 0, 0) of row 10, classify the variables as basic or nonbasic. Table 5 The Table
Evaluate the expression.7!/4!3!
A computer manufacturing company has two assembly plants, plant A and plant B, and two distribution outlets, outlet I and outlet II. Plant A can assemble at most 700 computers a month, and plant B
A shipment box contains 12 graphing calculators, out of which 2 are defective. A calculator is drawn at random from the box and then, without replacement, a second calculator is drawn. Discuss
From Example 1 we can conclude that the probability is 0 that a single roll of a fair die will equal the expected value for a roll of a die (the number of dots facing up is never 3.5). What is the
Find the average (mean) of the exam scores 73, 89, 45, 82, and 66.
Consider the sample space of equally likely events for the rolling of a single fair die:(A) What is the probability of rolling a number that is odd and exactly divisible by 3?(B) What is the
Refer to Example 1.(A) What is the probability of the pointer landing on a number greater than 4?(B) What is the probability of the pointer landing on a number greater than 4, given that it landed on
In a single deal of 5 cards from a standard 52-card deck, what is the probability of being dealt 5 clubs?
One urn has 3 blue and 2 white balls; a second urn has 1 blue and 3 white balls (Fig. 1). A single fair die is rolled and if 1 or 2 comes up, a ball is drawn out of the first urn; otherwise, a ball
Repeat Example 1, but find P(U1|W) and P(U2|W).Data from Example 1One urn has 3 blue and 2 white balls; a second urn has 1 blue and 3 white balls (Fig. 1). A single fair die is rolled and if 1 or 2
(A) Suppose that E and F are complementary events. Are E and F necessarily mutually exclusive? Explain why or why not.(B) Suppose that E and F are mutually exclusive events. Are E and F necessarily
Use the sample space in Example 1 to answer the following:(A) What is the probability of rolling an odd number and a prime number?(B) What is the probability of rolling an odd number or a prime
Relative to the number wheel experiment (Fig. 1) and the sample spacewhat is the event E (subset of the sample space S) that corresponds to each of the following outcomes? Indicate whether the event
Refer to Example 8. If a person from Springfield is selected at random, what is the (empirical) probability that(A) He or she has not tried either cola? What are the (empirical) odds for this
The board of regents of a university is made up of 12 men and 16 women. If a committee of 6 is chosen at random, what is the probability that it will contain 3 men and 3 women?
What is the probability that the committee in Example 8 will have 4 men and 2 women?
A circular spinner is divided into 15 sectors of equal area: 6 red sectors, 5 blue, 3 yellow, and 1 green. In Problem consider the experiment of spinning the spinner once. Find the probability that
A circular spinner is divided into 15 sectors of equal area: 6 red sectors, 5 blue, 3 yellow, and 1 green. In Problem consider the experiment of spinning the spinner once. Find the probability that
A circular spinner is divided into 15 sectors of equal area: 6 red sectors, 5 blue, 3 yellow, and 1 green. In Problem consider the experiment of spinning the spinner once. Find the probability that
A circular spinner is divided into 15 sectors of equal area: 6 red sectors, 5 blue, 3 yellow, and 1 green. In Problem consider the experiment of spinning the spinner once. Find the probability that
A circular spinner is divided into 15 sectors of equal area: 6 red sectors, 5 blue, 3 yellow, and 1 green. In Problem consider the experiment of spinning the spinner once. Find the probability that
A circular spinner is divided into 15 sectors of equal area: 6 red sectors, 5 blue, 3 yellow, and 1 green. In Problem consider the experiment of spinning the spinner once. Find the probability that
A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a diamond, and let F be the event that the card drawn is a face card. In Problem, find the indicated
A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a diamond, and let F be the event that the card drawn is a face card. In Problem, find the indicated
A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a diamond, and let F be the event that the card drawn is a face card. In Problem, find the indicated
A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a diamond, and let F be the event that the card drawn is a face card. In Problem, find the indicated
A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a diamond, and let F be the event that the card drawn is a face card. In Problem, find the indicated
In Problem compute each probability using formula (1) on page 423 and appropriate table values.P(D|B)Formula 1 P(A/B) = P(ANB) P(B) P(B) = 0 (1)
Repeat Problem 19 with the same game costing $3.50 for each play.Data from Problem 19After paying $4 to play, a single fair die is rolled, and you are paid back the number of dollars corresponding to
In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25. In Problem, use equation (1) to compute the probability that the
In Problem compute each probability using formula (1) on page 423 and appropriate table values.P(C|E)Formula 1 P(A|B) = P(ANB) P(B) P(B) = 0 (1)
In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25. In Problem, use equation (1) to compute the probability that the
In Problem compute each probability using formula (1) on page 423 and appropriate table values.P(B|D)Formula 1 P(A|B) = P(ANB) P(B) P(B) = 0 (1)
In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25. In Problem, use equation (1) to compute the probability that the
In Problem compute each probability using formula (1) on page 423 and appropriate table values.P(E|C)Formula 1 P(A|B) = P(ANB) P(B) P(B) = 0 (1)
In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25. In Problem, use equation (1) to compute the probability that the
In Problem compute each probability using formula (1) on page 423 and appropriate table values.P(D|C)Formula 1 P(A/B) = P(ANB) P(B) P(B) = 0 (1)
In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25. In Problem, use equation (1) to compute the probability that the
In Problem compute each probability using formula (1) on page 423 and appropriate table values.P(E|A)Formula 1 P(A|B) = P(ANB) P(B) P(B) = 0 (1)
In Problem compute each probability using formula (1) on page 423 and appropriate table values.P(A|C)Formula 1 P(A/B) = P(ANB) P(B) P(B) = 0 (1)
In Problem compute each probability using formula (1) on page 423 and appropriate table values.P(B|B)Formula 1 P(A|B) = P(ANB) P(B) P(B) = 0 (1)
A fair coin is tossed 10 times. On each of the first 9 tosses the outcome is heads. Discuss the probability of a head on the 10th toss.
An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space shown in Figure 2 and, assuming each simple event is as likely as any other,
Suppose that 5 thank-you notes are written and 5 envelopes are addressed. Accidentally, the notes are randomly inserted into the envelopes and mailed without checking the addresses. What is the
Compute the probability of event E if the odds in favor of E are(A) 3/8(B) 11/7(C) 4/1(D) 49/51
An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space shown in Figure 2 and, assuming each simple event is as likely as any other,
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If the odds for E equal the odds against E′, then P(E) = 1/2.
To simulate roulette on a graphing calculator, a random integer between -1 and 36 is selected (-1 represents 00; see Problem 35). The command in Figure A simulates 200 games.(A) Use the statistical
In Problem a player is dealt two cards from a 52-card deck. If the first card is black, the player returns it to the deck before drawing the second card. If the first card is red, the player sets it
An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space shown in Figure 2 and, assuming each simple event is as likely as any other,
In Problem a player is dealt two cards from a 52-card deck. If the first card is black, the player returns it to the deck before drawing the second card. If the first card is red, the player sets it
Use a graphing calculator to simulate the results of placing a $1 bet on black in each of 400 games of roulette (see Problems 36 and 45) and compare the simulated and expected gains or losses.Data
An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space shown in Figure 2 and, assuming each simple event is as likely as any other,
In Problem a player is dealt two cards from a 52-card deck. If the first card is black, the player returns it to the deck before drawing the second card. If the first card is red, the player sets it
A 3-card hand is dealt from a standard deck. You win $20 for each diamond in the hand. If the game is fair, how much should you lose if the hand contains no diamonds?
An insurance company found that on average, over a period of 10 years, 23% of the drivers in a particular community who were involved in an accident one year were also involved in an accident the
Identify any absorbing states for the following transition matrices: (A) A в A 1 0 P= B.5 с 0 .5 0 .5 .5 CLO (B) A в с A 0 0 1 1 0 0 P= BO C 10
An insurance company classifies drivers as low-risk if they are accident-free for one year. Past records indicate that 98% of the drivers in the low-risk category (L) one year will remain in that
(A) Refer to the transition diagram in Figure 1. What is the probability that a person using brand A will switch to another brand when he or she runs out of toothpaste?(B) Refer to transition
Identify any absorbing states for the following transition matrices: (A) A P = B C A B C .5 0 .5 0 1 0 0 .5 .5 (B) A A 0 P = B 1 CL0 B C 1 0 0 0 0 1
(A) For the initial-state matrix S0 = [a b c], find the first four state matrices, S1, S2, S3, and S4, in the Markov chain with transition matrix(B) Do the state matrices appear to be approaching a
Which of the following matrices are regular? .8 (A) = AP-[82] .6 -RJ (B) P = (C) P = .5 0 1 .5 .5 0 050
Which of the following matrices are regular? .3 (A) P = [2 .7 (B) P= = 1 [9] (C) P = 0 .5 5 0 1 0 .5 0 .5
Find P4 and use it to find S4 for P= A A' .9 A .1 A' .6 .4 A A' and So [28]
(A) Suppose that the toothpaste company started with only 5% of the market instead of 10%. Write the initial-state matrix and find the next six state matrices. Discuss the behavior of these state
Find P4 and use it to find S4 forIf a graphing calculator or a computer is available for computing matrix products and powers of a matrix, finding state matrices for any number of trials becomes a
Use a transition diagram to determine whether P is the transition matrix for an absorbing Markov chain. (A) A B C 0 .5 0 .5 .5 A 1 0 P=B.5 C0 (B) A A0 0 1 0 B C 1 0 0 P = BO C 1
Use a transition diagram to determine whether P is the transition matrix for an absorbing Markov chain. (A) A B .5 0 1 .5 A P = B 0 C 0 C .5 0 .5 (B) A P = B C A 0 1 0 в 1 0 0 с 0 0 1
Refer to Example 4. States D and G are referred to as absorbing states because a student who enters either one of these states never leaves it. Absorbing states are discussed in detail.(A) How can
The transition matrix for a Markov chain is(A) Find the stationary matrix S.(B) Discuss the long-run behavior of Sk and Pk. P = -[1.2 = .3 .8
Determine whether each statement is true or false. Use examples and verbal arguments to support your conclusions.(A) A Markov chain with two states, one nonabsorbing and one absorbing, is always an
The transition matrix for a Markov chain isFind the stationary matrix S and the limiting matrix P̅. P = .6 .1 .4 .9
Use P8 and a graphing calculator to find S8 for P and S0 as given in Example 2. Round values in S8 to six decimal places.Data from Example 2Find P4 and use it to find S4 for P= A A' .9 A .1 A' .6
Use P8 and a graphing calculator to find S8 for P and S0 as given in Matched Problem 2. Round values in S8 to six decimal places.Data from Matched Problem 2Find P4 and use it to find S4 forIf a
Refer to Matched Problem 1 in Section 9.1, where we found the following transition matrix for an insurance company:If these probabilities remain valid for a long period of time, what percentage of
Two competing real estate companies are trying to buy all the farms in a particular area for future housing development. Each year, 20% of the farmers decide to sell to company A, 30% decide to sell
Part-time students in a university MBA program are considered to be entry-level students until they complete 15 credits successfully. Then they are classified as advanced-level students and can take
Refer to Example 4. At the end of each year the faculty examines the progress that each advanced-level student has made on the required thesis. Past records indicate that 30% of advanced-level
(A) Find the limiting matrix P for the standard form P̅ found in Example 3.(B) Use P̅ to find the limit of the successive state matrices for S0 = [0 0 1].(C) Use P̅ to find the limit of the
A company rates every employee as below average, average, or above average. Past performance indicates that each year, 10% of the below-average employees will raise their rating to average, and 25%
The following transition diagram is for part-time students enrolled in a university MBA program:(A) In the long run, what percentage of entry-level students will graduate? What percentage of
Repeat Example 5 for the following transition diagram:Data from Example 5The following transition diagram is for part-time students enrolled in a university MBA program:(A) In the long run, what
A mail-order company classifies its customers as preferred, standard, or infrequent depending on the number of orders placed in a year. Past records indicate that each year, 5% of preferred customers
Compute powers of the transition matrix P to approximate P̅ and S to four decimal places. Check the approximation in the equation SP = S. P = .5 .2 7.1.2 4 .1 .3 .5
Repeat Example 5 forData from Example 5Compute powers of the transition matrix P to approximate P̅ and S to four decimal places. Check the approximation in the equation SP = S. P
In Problem use the transition diagramto find S1 and S2 for the indicated initial state matrix S0.S0 = [.3 .7] A 5 .8 B
In Problem use the transition diagramto find S1 and S2 for the indicated initial state matrix S0.S0 = [.9 .1] A 5 .8 B
In Problem use the transition diagramto find S1 and S2 for the indicated initial state matrix S0.S0 = [.5 .5] A 5 .8 B
In Problem use the transition diagramto find S1 and S2 for the indicated initial state matrix S0.S0 = [.2 .8] A 5 .8 B
The Senate is in the middle of a floor debate, and a filibuster is threatened. Senator Hanks, who is still vacillating, has a probability of .1 of changing his mind during the next 5 minutes. If this
Show that ifis a probability matrix, then P2 is a probability matrix. P = [₁ ² a 1-a] b 1-b
In Problem use the transition diagramto find S1 and S2 for the indicated initial state matrix S0.S0 = [.2 .7 .1] 5 4 .1 C 2 .8
Problem refer to the regular Markov chain with transition matrixFor S = [.2 .5], calculate SP. Is S a stationary matrix? Explain. P = .5 52 5 ∞o in .8
Consumers can choose between three long distance telephone services: GTT, NCJ, and Dash. Aggressive marketing by all three companies results in a continual shift of customers among the three
Solve using the simplex method: Maximize subject to P = 6x₁ + 3x2 2x₁ + 3x₂ = 9 -x₁ + 3x₂ = 12 0 X1, X₂ = X2
Use the table method to solve the following linear programming problem, and explain why one of the rows in the table cannot be completed to a basic solution: Maximize subject to P = 10x₁ +
Graph the feasible region for the linear programming problem in Example 1 and trace the path to the optimal solution determined by the simplex method.Data from Example 1Solve the following linear
Interpret the values of the slack and surplus variables in the computer solution to Example 5.Data from Example 5A refinery produces two grades of gasoline, regular and premium, by blending together

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