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College Mathematics for Business Economics Life Sciences and Social Sciences 12th edition Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen - Solutions
In Problem ,(1) Introduce slack, surplus, and artificial variables and form the modified problem.(2) Write the preliminary simplex tableau for the modified problem and find the initial simplex tableau.(3) Find the optimal solution of the modified problem by applying the simplex method to the
In Problem ,(1) Introduce slack, surplus, and artificial variables and form the modified problem.(2) Write the preliminary simplex tableau for the modified problem and find the initial simplex tableau.(3) Find the optimal solution of the modified problem by applying the simplex method to the
In Problem, state the converse and the contra positive of the given proposition.If triangle ABC is isosceles, then the base angles of triangle ABC are congruent.
In Problem, state the converse and the contra positive of the given proposition.If g(x) is a quadratic function, then g(x) is a function that is neither increasing nor decreasing.
In Problem, state the converse and the contra positive of the given proposition.If n is an integer that is a multiple of 6, then n is an integer that is a multiple of 2 and a multiple of 3.
In Problem, construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.
In Problem, construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.
In Problem, construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.
In Problem, construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.
In Problem, construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.
In Problem, construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.
In Problem, construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.
In Problem, construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.
In Problem, construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction.
In problem, construct a truth table to verify each implication.
In problem, construct a truth table to verify each implication.
In problem, construct a truth table to verify each implication.
In Problem construct a truth table to verify each equivalence.
In Problem construct a truth table to verify each equivalence.
In Problem construct a truth table to verify each equivalence. P → (p ⋀ q)= p →7
In Problem, verify each equivalence using formulas form table2.¬(¬p → ¬q) = p V q
Can a conditional proposition be false if its converse is true? Explain.
If R = {1,3,4 } and T = {2,4,6}, find (A) {x|x∈ R and x ∈ T } (B) R ∩ T
For P,Q, and R in Problem 39, find P ∩ (Q ∪ R).
In Problem, discuss the validity of each statement. Venn diagrams may be helpful. If the statement is true, explain why. If not. Give a counterexample. If A ∩ B = A, then A C B
Let A be a set that contains exactly n elements. Find a formula in terms of n for the number of subsets of A
How many 2-letter code words can be formed from the first 3 letters of the alphabet if no letter can be used more than once? Solve Problem two ways: (A) Using a tree diagram, and (B) Using the multiplication principle.
In how many ways can 3 coins turn up heads H, or tails T if combined outcomes such as (H,T, H), (H, H,T), and (T, H, H) are considered as different? Solve Problem two ways: (A) Using a tree diagram, and (B) Using the multiplication principle.
A college offers 2 introductory courses in history, 3 in science, 2 in mathematics, 2 in philosophy, and 1 in English.(A) If a freshman takes one course in each area during her first semester, how many course selections are possible?(B) If a part-time student can afford to take only one
The 14 colleges of interest to a high school senior include 6 that are expensive (tuition more than $30,000 per year), 7 that are far from home (more than 200 miles away), and 2 that are both expensive and far from home. (A) If the student decides to select a college that is not expensive and
In Problem, use the given information to determine the number of elements in each of the four disjoint subsets in the following Venn diagram.n(A)=45, n(B)=35, n(A ˆ© B)=15, n(U)=100
In Problem, use the given information to determine the number of elements in each of the four disjoint subsets in the following Venn diagram.n(A)= 70, n(B)=90, n(AU B)=120, n(U)= 200
In Problem, use the given information to determine the number of elements in each of the four disjoint subsets in the following Venn diagram.
In Problem, use the given information to complete the following table.n(A)=55, n(B)= 65, n(AD B)=35, n(U)=100
In Problem, use the given information to complete the following table.n(A)=80, n(B)=70, n(AUB)=110, n(U)=200
In Problem, use the given information to complete the following table.n(A')=81, n(B')=90, n(A'ˆ©B')=63, n(U)= 180
(A) If A and B are disjoint, then n(A∩B)=n(A) + n(B). (B) If n(AUB)=n(A) + n(B),then A and Bare disjoint. In Problem, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.
A delicatessen serves meat sandwiches with the following options: 3 kinds of bread, 5 kinds of meat, and lettuce or sprouts. How many different sandwiches are possible, assuming that one item is used out of each category?
How many 5-letter code words are possible from the first 7 letters of the alphabet if no letter is repeated? If letters can be repeated? If adjacent letters must be different?
A small combination lock has 3 wheels, each labeled with the 10 digits from 0 to 9. How many 3-digit combinations are possible if no digit is repeated? If digits can be repeated? If successive digits must be different?
How many 5-digit ZIP code numbers are possible? How many of these numbers contain no repeated digits?
Explain how three sets, A, B, and C, can be related to each other in order for the following equation to hold true (Venn diagrams may be helpful): n(AUBUC) = n(A) + n(B) + n(C) -n(AnC) -n (BnC)
A class of 30 music students includes 13 who play the piano, 16 who play the guitar, and 5 who play both the piano and the guitar. How many students in the class play neither instrument?
A high school football team with 40 players includes 16 players who played offense last year, 17 who played defense, and 12 who were not on last year's team. How many players from last year played both offense and defense?
A corporation plans to fill 2 different positions for vice-president, V1 and V2, from administrative officers in 2 of its manufacturing plants. Plant A has 6 officers and plant B has 8. How many ways can these 2 positions be filled if the V1 position is to be filled from plant A and the V2position
A manufacturing company in city A wishes to truck its product to 4 different cities: P, C, D, and E. If roads interconnect all 4 cities, how many different route plans can be constructed so that a single truck, starting from A, will visit each city exactly once, then return home?
A survey of 800 small businesses indicates that 250 own a video conferencing system, 420 own projection equipment, and 180 own a video conferencing system and projection equipment. (A) How many businesses in the survey own either a video conferencing system or projection equipment? (B) How many own
A cable company offers its 10,000 customers two special services: high-speed internet and digital phone. If 3,770 customers use high-speed internet, 3,250 use digital phone, and 4,530 do not use either of these services, how many customers use both high-speed internet and digital phone?
Refer to the table in Problem 61.(A) How many females are of age 16-19 and earn mini mum wage?(B) How many males are of age 16-24 and earn below minimum wage?(C) How many workers are of age 20-24 or females earning below minimum wage?(D) How many workers earn minimum wage?
A couple is planning to have 3 children. How many boy-girl combinations are possible? Distinguish between combined outcomes such as (B,B,G),(B,G,B), and (G,B,B).(A) Solve using a tree diagram.(B) Solve using the multiplication principle.
If 12,457 people voted for a politician in his first election, 15,322 voted for him in his second election, and 9,345 voted for him in the first and second elections, how many people voted for this politician in the first or second election
In Problem, evaluate the expression/ if the answer is not an integer, round to four decimal places,
In a long-distance foot race, how many different finishes among the first 5 places are possible if 50 people are running? (Exclude ties.)
Nine cards are numbered with the digits from 1 to 9. A 3-card hand is dealt, 1 card at a time. How many hands are possible in which (A) Order is taken into consideration? (B) Order is not taken into consideration?
Discuss the relative growth rates of x!,2x,and x2.
From a standard 52-card deck, how many 5-card hands have all face cards? All face cards, but no kings?
From a standard 52-card deck, how many 5-card hands have 2 clubs and 3 hearts?
Three departments have 12, 15, and 18 members, respectively. If each department selects a delegate and an alternate to represent the department at a conference, how many ways can this be done?
In Problem, discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample.If n is a positive integer greater than 3, then n! >2n.
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
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
Five distinct points are selected on the circumference of a circle. (A) How many line segments can be drawn by joining the points in all possible ways? (B) How many triangles can be drawn using these 5 points as vertices?
Each of 2 countries sends 5 delegates to a negotiating conference. A rectangular table is used with 5 chairs on each long side. If each country is assigned a long side of the table (operation 1), how many seating arrangements are possible?
How many 4-person committees are possible from a group of 9 people if (A) There are no restrictions? (B) Both Jim and Mary must be on the committee? (C) Either Jim or Mary (but not both) must be on the committee?
An electronics store receives a shipment of 30 graphing calculators, including 6 that are defective. Four of these calculators are selected for a local high school. (A) How many selections can be made? (B) How many of these selections will contain no defective calculators?
A real estate company with 14 employees in their central office, 8 in their north office, and 6 in their south office is planning to lay off 12 employees. (A) How many ways can this be done? (B) The company decides to lay off 5 employees from the central office, 4 from the north office, and 3 from
A 4-person grievance committee is selected out of 2 departments A and B, with 15 and 20 people, respectively. In how many ways can the following committees be selected? (A) 3 from A and 1 from B (B) 2 from A and 2 from B (C) All from A (D) 4 PEOPLE REGARDLESS OF DEPARTMENT (E) At least 3 from
A six or club Refer to the description of a standard deck of 52 cards and Figure 4 on page 363. An experiment consists of drawing 1 card from a standard 52-card deck. In Problem, what is the probability of drawing.
In a family with 2 children, excluding multiple births, what is the probability of having 2 girls? Assume that a girl is as likely as a boy at each birth.
Using the probability assignments in Problem 23C, what is the probability that a random customer will not choose brand J or brand P?
In a family with 3 children, excluding multiple births, what is the probability of having 2 boys and 1 girl, in any order? Assume that a boy is as likely as a girl at each birth.
A combination lock has 5 wheels, each labeled with the 10 digits from 0 to 9. If an opening combination is a particular sequence of 5 digits with no repeats, what is the probability of a person guessing the right combination?
5 hearts? Refer to the description of a standard deck of 52 cards and Figure 4 on page 363. An experiment consists of dealing 5 cards from a standard 52-card deck. In Problem, what is the probability of being dealt
5 non face cards? Refer to the description of a standard deck of 52 cards and Figure 4 on page 363. An experiment consists of dealing 5 cards from a standard 52-card deck. In Problem, what is the probability of being dealt
In a three-way race for the U.S. Senate, polls indicate that the two leading candidates are running neck-and-neck, while the third candidate is receiving half the support of either of the others. Registered voters are chosen at random and asked which of the three will get their vote. Describe an
Suppose that 6 people check their coats in a checkroom. If all claim checks are lost and the 6 coats are randomly returned, what is the probability that all the people will get their own coats back?
Sum is 10. 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, find the probability of the sum of the dots indicated in Problem.
Sum is greater than 8. 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, find the probability of the sum of the dots indicated in Problem.
Sum is not 2, 4, or 6 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, find the probability of the sum of the dots indicated in Problem.
Sum is divisible by 4 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, find the probability of the sum of the dots indicated in Problem.
Sum is 2, 3, or 12 ("craps") 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, find the probability of the sum of the dots indicated in Problem.
Sum is divisible by 2 and 3 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, find the probability of the sum of the dots indicated in Problem.
Red or blue A circular spinner is divided into 12 sectors of equal area: 5 red sectors, 4 blue, 2 yellow, and 1 green. In Problem, consider the experiment of spinning the spinner once. Find the probability that the spinner lands on:
In Problem, a sample space S is described. Would it be reasonable to make the equally likely assumption? Explain. A nickel and dime are tossed. We are interested in the number of heads that appear, so an appropriate sample space is S = {0,1,2}.
(A) Is it possible to get 7 double 6's in 10 rolls of a pair of fair dice? Explain. (B) If you rolled a pair of dice 36 times and got 11 double 6's, would you suspect that the dice were unfair? Why or why not? If you suspect loaded dice, what empirical probability would you assign to the event of
Yellow, red or green A circular spinner is divided into 12 sectors of equal area: 5 red sectors, 4 blue, 2 yellow, and 1 green. In Problem, consider the experiment of spinning the spinner once. Find the probability that the spinner lands on:
Refer to the description of a standard deck of 52 cards on page 363. An experiment consists of dealing 5 cards from a standard 52-card deck. In Problem, what is the probability of being dealt. Four of a kind (4 queens, 4 kings, and so on)?
Refer to the description of a standard deck of 52 cards on page 363. An experiment consists of dealing 5 cards from a standard 52-card deck. In Problem, what is the probability of being dealt. A 2,3,4,5, and 6, all in the same suit?
Refer to the description of a standard deck of 52 cards on page 363. An experiment consists of dealing 5 cards from a standard 52-card deck. In Problem, what is the probability of being dealt. 2 kings and 3 aces?
From a box containing 12 balls numbered 1 through 12. one ball is drawn at random. (A) Explain how a graphing calculator can be used to simulate 400 repetitions of this experiment. (B) Carry out the simulation and find the empirical probability of drawing the 8 ball. (C) What is the probability of
Six popular brands of cola are to be used in a blind taste study for consumer recognition. (A) If 3 distinct brands are chosen at random from the 6 and if a consumer is not allowed to repeat any answers, what is the probability that all 3 brands could be identified by just guessing? (B) If repeats
A 4-person grievance committee is to include employees in 2 departments, A and B, with 15 and 20 employees, respectively. If the 4 people are selected at random from the 35 employees, what is the probability of selecting (A) 3 from A and 1 from B7 (B) 2 from A and 2 from Bl (C) All 4 from .4? (D)
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 probabilities. P(D'U F)
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 probabilities. P(D'U F')
Divisible by 4 or divisible by 7 In a lottery game, a single ball is drawn at random from a container contains 25 identical balls numbered from 1 through 25. In problem, use equation (1) or (2), indicating which is used, to compute the probability that the number drawn is:
Odd or greater than 15 In a lottery game, a single ball is drawn at random from a container contains 25 identical balls numbered from 1 through 25. In problem, use equation (1) or (2), indicating which is used, to compute the probability that the number drawn is:
Less than 12 or greater than13 In a lottery game, a single ball is drawn at random from a container contains 25 identical balls numbered from 1 through 25. In problem, use equation (1) or (2), indicating which is used, to compute the probability that the number drawn is:
If the probability is .03 that an automobile tire fails in less than 50,000 miles, what is the probability that the tire does not fail in 50,000 miles? In a lottery game, a single ball is drawn at random from a container contains 25 identical balls numbered from 1 through 25. In problem, use
Compute the probability of event E if the odds in favor of E are (A) 3/5 (B) 1/7 (C) .6 (D) .35
Compute the probability of event E if the odds in favor of E are (A) 5/9 (B) 4/3 (C) 3/7 (D) 23/77
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