FINITE MATH.F/BUS,ECON,LIFE..-ACCESS
14th Edition
ISBN: 9780134984209
Author: Barnett
Publisher: PEARSON
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Textbook Question
Chapter 10, Problem 5RE
If a
(A) How many standard deviations is
(B) What is the area under the normal curve between the mean and
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5. (a) State the Residue Theorem. Your answer should include all the conditions required
for the theorem to hold.
(4 marks)
(b) Let y be the square contour with vertices at -3, -3i, 3 and 3i, described in the
anti-clockwise direction. Evaluate
に
dz.
You must check all of the conditions of any results that you use.
(5 marks)
(c) Evaluate
L
You must check all of the conditions of any results that you use.
ཙ
x sin(Tx)
x²+2x+5
da.
(11 marks)
3. (a) Lety: [a, b] C be a contour. Let L(y) denote the length of y. Give a formula
for L(y).
(1 mark)
(b) Let UCC be open. Let f: U→C be continuous. Let y: [a,b] → U be a
contour. Suppose there exists a finite real number M such that |f(z)| < M for
all z in the image of y. Prove that
<
||, f(z)dz| ≤ ML(y).
(3 marks)
(c) State and prove Liouville's theorem. You may use Cauchy's integral formula without
proof.
(d) Let R0. Let w € C. Let
(10 marks)
U = { z Є C : | z − w| < R} .
Let f UC be a holomorphic function such that
0 < |ƒ(w)| < |f(z)|
for all z Є U. Show, using the local maximum modulus principle, that f is constant.
(6 marks)
3. (a) Let A be an algebra. Define the notion of an A-module M. When is a module M
a simple module?
(b) State and prove Schur's Lemma for simple modules.
(c) Let AM(K) and M = K" the natural A-module.
(i) Show that M is a simple K-module.
(ii) Prove that if ƒ € Endд(M) then ƒ can be written as f(m) = am, where a
is a matrix in the centre of M, (K).
[Recall that the centre, Z(M,(K)) == {a Mn(K) | ab
M,,(K)}.]
= ba for all bЄ
(iii) Explain briefly why this means End₁(M) K, assuming that Z(M,,(K))~
K as K-algebras.
Is this consistent with Schur's lemma?
Chapter 10 Solutions
FINITE MATH.F/BUS,ECON,LIFE..-ACCESS
Ch. 10.1 - (A) Using Figure 3, estimate the median annual...Ch. 10.1 - (A) Using Figure 6 estimate the revenue and costs...Ch. 10.1 - Repeat Example 1 for the following intervals: (A)...Ch. 10.1 - The weights (in pounds) were recorded for 20...Ch. 10.1 - (A) Construct a frequency table and histogram for...Ch. 10.1 - (A) Construct a frequency table and histogram for...Ch. 10.1 - Gross domestic product. Graph the data in the...Ch. 10.1 - Corporation revenues. Graph the data in the...Ch. 10.1 - Gold production. Use the double bar graph on world...Ch. 10.1 - Gasoline prices .Graph the data in the following...
Ch. 10.1 - Postal service. Graph the data in the following...Ch. 10.1 - Postal service. Refer to Problem 9. If the data...Ch. 10.1 - Federal income. Graph the data in the following...Ch. 10.1 - Gasoline prices. In April 2017 the average price...Ch. 10.1 - Starting salaries. The starting salaries (in...Ch. 10.1 - Commute times. Thirty-two people were chosen at...Ch. 10.1 - Common stocks. The following table shows...Ch. 10.1 - Mouse weights. One hundred healthy mice were...Ch. 10.1 - Population growth. Graph the data in the following...Ch. 10.1 - Aims epidemic. One way to gauge the toll of the...Ch. 10.1 - Nutrition. Graph the data in the following table...Ch. 10.1 - Greenhouse gases. The U.S. Environmental...Ch. 10.1 - Nutrition. Graph the nutritional information in...Ch. 10.1 - Nutrition. Refer to Problem 21. Suppose that you...Ch. 10.1 - Education. For statistical studies, U.S. states...Ch. 10.1 - Study abroad. Would a pie graph be more effective...Ch. 10.1 - Median age. Use the broken-line graph shown to...Ch. 10.1 - State prisoners. In 1980 in the United States, 6...Ch. 10.1 - Grade point Averages. One hundred seniors were...Ch. 10.2 - For many sets of measurements the median lies...Ch. 10.2 - Find the mean for the sample measurements...Ch. 10.2 - Compute the mean for the grouped sample data...Ch. 10.2 - Add the salary $100,000 to those in Example 3 and...Ch. 10.2 - Find the median for the grouped data in the...Ch. 10.2 - Compute the mode(s), median, and mean for each...Ch. 10.2 - In Problems 1-4, find the mean of the data set....Ch. 10.2 - In Problems 1-4, find the mean of the data set....Ch. 10.2 - In Problems 1-4, find the mean of the data set....Ch. 10.2 - In Problems 1-4, find the mean of the data set....Ch. 10.2 - In Problems 5-8, find the indicated sum. (If...Ch. 10.2 - In Problems 5-8, find the indicated sum. (If...Ch. 10.2 - In Problems 5-8, find the indicated sum. (If...Ch. 10.2 - In Problems 5-8, find the indicated sum. (If...Ch. 10.2 - Find the mean, median, and mode for the sets of...Ch. 10.2 - Find the mean, median, and mode for the sets of...Ch. 10.2 - Find the mean, median, and/or mode, whichever are...Ch. 10.2 - Find the mean, median, and/or mode, whichever are...Ch. 10.2 - Find the mean for the sets of grouped data in...Ch. 10.2 - Find the mean for the sets of grouped data in...Ch. 10.2 - Which single measure of central tendency-mean,...Ch. 10.2 - Which single measure of central tendency mean,...Ch. 10.2 - A data set is formed by recording the results of...Ch. 10.2 - A data set is formed by recording the sums on 200...Ch. 10.2 - (A) Construct a set of four numbers that has mean...Ch. 10.2 - (A) Construct a set of five numbers that has mean...Ch. 10.2 - Price earnings ratios. Find the mean, median, and...Ch. 10.2 - Gasoline tax. Find the mean, median, and mode for...Ch. 10.2 - Light bulb lifetime. Find the mean and median for...Ch. 10.2 - Price earnings ratios. Find the mean and median...Ch. 10.2 - Student loan debt. Find the mean median, and mode...Ch. 10.2 - Tourism Find the mean, median, and mode for the...Ch. 10.2 - Mouse weights. Find the mean and median for the...Ch. 10.2 - Blood cholesterol levels. Find the mean and median...Ch. 10.2 - Immigration Find the mean, median, and mode for...Ch. 10.2 - Grade point averages. Find the mean and median for...Ch. 10.2 - Entrance examination scores. Compute the median...Ch. 10.2 - Presidents. Find the mean and median for the...Ch. 10.3 - (A) When is the sample standard deviation of a set...Ch. 10.3 - Find the standard deviation for the sample...Ch. 10.3 - Find the standard deviation for the grouped sample...Ch. 10.3 - Prob. 1ECh. 10.3 - In Problems 1-8, find the indicated sum. (If...Ch. 10.3 - In Problems 1-8, find the indicated sum. (If...Ch. 10.3 - In Problems 1-8, find the indicated sum. (If...Ch. 10.3 - In Problems 1-8, find the indicated sum. (If...Ch. 10.3 - In Problems 1-8, find the indicated sum. (If...Ch. 10.3 - In Problems 1-8, find the indicated sum. (If...Ch. 10.3 - In Problems 1-8, find the indicated sum. (If...Ch. 10.3 - (A) Find set of the ungrouped mean and sample...Ch. 10.3 - (A) Find the mean and standard deviation of the...Ch. 10.3 - In Problems 11 and 12, find the standard deviation...Ch. 10.3 - In Problems 11 and 12, find the standard deviation...Ch. 10.3 - In Problems 13-18, discuss the validity of each...Ch. 10.3 - In Problems 13-18, discuss the validity of each...Ch. 10.3 - In Problems 13-18, discuss the validity of each...Ch. 10.3 - In Problems 13-18, discuss the validity of each...Ch. 10.3 - In Problems 13-18, discuss the validity of each...Ch. 10.3 - In Problems 13-18, discuss the validity of each...Ch. 10.3 - A data set is formed by recording the sums in 100...Ch. 10.3 - A data set is formed by recording the results of...Ch. 10.3 - Find the mean and standard deviation for each of...Ch. 10.3 - Find the mean and standard deviation for each of...Ch. 10.3 - Find the mean and standard deviation for each of...Ch. 10.3 - Find the mean and standard deviation for each of...Ch. 10.3 - Find the mean and standard deviation for each of...Ch. 10.3 - Find the mean and standard deviation for each of...Ch. 10.3 - Find the mean and standard deviation for each of...Ch. 10.3 - Find the mean and standard deviation for each of...Ch. 10.4 - Find p and q for a single roll of a fair die,...Ch. 10.4 - In Example 2, find the probability of the outcome...Ch. 10.4 - Using the same die experiment as in Example 3,...Ch. 10.4 - Use the binomial formula to expand q+p4.Ch. 10.4 - Repeat Example 5, where the binomial experiment...Ch. 10.4 - Compute the mean and standard deviation for the...Ch. 10.4 - Repeat Example 7 for four patients. The...Ch. 10.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 10.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 10.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 10.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 10.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 10.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 10.4 - In Problems 7-12, a fair coin is tossed four...Ch. 10.4 - In Problems 7-12, a fair coin is tossed four...Ch. 10.4 - In Problems 7-12, a fair coin is tossed four...Ch. 10.4 - In Problems 7-12, a fair coin is tossed four...Ch. 10.4 - In Problems 7-12, a fair coin is tossed four...Ch. 10.4 - In Problems 7-12, a fair coin is tossed four...Ch. 10.4 - In Problems 13-18 construct a histogram for the...Ch. 10.4 - In Problems 13-18 construct a histogram for the...Ch. 10.4 - In Problems 13-18 construct a histogram for the...Ch. 10.4 - In Problems 13-18 construct a histogram for the...Ch. 10.4 - In Problems 13-18 construct a histogram for the...Ch. 10.4 - In Problems 13-18 construct a histogram for the...Ch. 10.4 - In Problems 19-24, round answers to four decimal...Ch. 10.4 - In Problems 19-24, round answers to four decimal...Ch. 10.4 - In Problems 19-24, round answers to four decimal...Ch. 10.4 - In Problems 19-24, round answers to four decimal...Ch. 10.4 - In Problems 19-24, round answers to four decimal...Ch. 10.4 - In Problems 19-24, round answers to four decimal...Ch. 10.4 - If a baseball player has a batting average of 350...Ch. 10.4 - If a true-false test with 10 questions is given,...Ch. 10.4 - A multiple-choice test consists of 10 questions,...Ch. 10.4 - If 60 of the electorate supports the mayor, what...Ch. 10.4 - Construct a histogram for each of the binomial...Ch. 10.4 - Construct a histogram for each of the binomial...Ch. 10.4 - Construct a histogram for each of the binomial...Ch. 10.4 - Construct a histogram for each of the binomial...Ch. 10.4 - A random variable represents the number of...Ch. 10.4 - A random variable represents the number of...Ch. 10.4 - In Problems 35 and 36 a coin is loaded so that the...Ch. 10.4 - In Problems 35 and 36 a coin is loaded so that the...Ch. 10.4 - Find conditions on p that guarantee the histogram...Ch. 10.4 - Consider two binomial distributions for 1,000...Ch. 10.4 - A random variable represents the number of heads...Ch. 10.4 - A random variable represents the number of times a...Ch. 10.4 - Management training each year a company selects a...Ch. 10.4 - Employee turnover. If the probability of a new...Ch. 10.4 - Quality control A manufacturing process produces,...Ch. 10.4 - Guarantees. A manufacturing process produces, on...Ch. 10.4 - Quality control. A manufacturing process produces,...Ch. 10.4 - Management training. Each year a company selects 5...Ch. 10.4 - Medical diagnosis A tuberculosis patient is given...Ch. 10.4 - Harmful drug side effect. A pharmaceutical...Ch. 10.4 - Genetics. The probability that brown-eyed parents,...Ch. 10.4 - Gene mutation the probability of gene mutation...Ch. 10.4 - Epidemics. If the probability of a person...Ch. 10.4 - Drug side effect the probability that a given drug...Ch. 10.4 - Testing A multiple-choice test is given with 5...Ch. 10.4 - Opinion polls. An opinion poll based on a small...Ch. 10.4 - Testing. A multiple-choice test is given with 5...Ch. 10.4 - Sociology. The probability that a marriage will...Ch. 10.4 - Sociology. If the probability is .55 that a...Ch. 10.5 - What percentage of the light bulbs in Example 1...Ch. 10.5 - Refer to Example 1. What is the probability that a...Ch. 10.5 - In Example 3, Use the normal curve to approximate...Ch. 10.5 - Suppose in Example 4 that the manufacturing...Ch. 10.5 - In Problems 1-6, use Appendix C to find the area...Ch. 10.5 - In Problems 1-6, use Appendix C to find the area...Ch. 10.5 - In Problems 1-6, use Appendix C to find the area...Ch. 10.5 - In Problems 1-6, use Appendix C to find the area...Ch. 10.5 - In Problems 1-6, use Appendix C to find the area...Ch. 10.5 - In Problems 1-6, use Appendix C to find the area...Ch. 10.5 - In Problems 7-14, use Appendix C to find the area...Ch. 10.5 - In Problems 7-14, use Appendix C to find the area...Ch. 10.5 - In Problems 7-14, use Appendix C to find the area...Ch. 10.5 - Prob. 10ECh. 10.5 - In Problems 7-14, use Appendix C to find the area...Ch. 10.5 - In Problems 7-14, use Appendix C to find the area...Ch. 10.5 - In Problems 7-14, use Appendix C to find the area...Ch. 10.5 - In Problems 7-14, use Appendix C to find the area...Ch. 10.5 - In Problems 15-20, given a normal distribution...Ch. 10.5 - In Problems 15-20, given a normal distribution...Ch. 10.5 - In Problems 15-20, given a normal distribution...Ch. 10.5 - In Problems 15-20, given a normal distribution...Ch. 10.5 - In Problems 15-20, given a normal distribution...Ch. 10.5 - In Problems 15-20, given a normal distribution...Ch. 10.5 - In Problems 21.26, given a normal distribution...Ch. 10.5 - In Problems 21.26, given a normal distribution...Ch. 10.5 - In Problems 21.26, given a normal distribution...Ch. 10.5 - In Problems 21.26, given a normal distribution...Ch. 10.5 - In Problems 21.26, given a normal distribution...Ch. 10.5 - In Problems 21.26, given a normal distribution...Ch. 10.5 - In Problems 27-34, consider the normal...Ch. 10.5 - In Problems 27-34, consider the normal...Ch. 10.5 - Consider the normal distribution with mean 60 and...Ch. 10.5 - In Problems 27-34, consider the normal...Ch. 10.5 - In Problems 27-34, consider the normal...Ch. 10.5 - In Problems 27-34, consider the normal...Ch. 10.5 - In Problems 27-34, consider the normal...Ch. 10.5 - In Problems 27-34, consider the normal...Ch. 10.5 - In Problems 35-40, discuss the validity of each...Ch. 10.5 - In Problems 35-40, discuss the validity of each...Ch. 10.5 - In Problems 35-40, discuss the validity of each...Ch. 10.5 - In Problems 35-40, discuss the validity of each...Ch. 10.5 - In Problems 35-40, discuss the validity of each...Ch. 10.5 - In Problems 35-40, discuss the validity of each...Ch. 10.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 10.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 10.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 10.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 10.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 10.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 10.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 10.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 10.5 - The probability of success in a Bernoulli trial is...Ch. 10.5 - For a binomial distribution with n=100, explain...Ch. 10.5 - A binomial experiment consists of 500 trials. The...Ch. 10.5 - A binomial experiment consists of 500 trials. The...Ch. 10.5 - A binomial experiment consists of 500 trials. The...Ch. 10.5 - A binomial experiment consists of 500 trials. The...Ch. 10.5 - A binomial experiment consists of 500 trials. The...Ch. 10.5 - A binomial experiment consists of 500 trials. The...Ch. 10.5 - A binomial experiment consists of 500 trials. The...Ch. 10.5 - A binomial experiment consists of 500 trials. The...Ch. 10.5 - To graph Problems 59-62, use a graphing calculator...Ch. 10.5 - To graph Problems 59-62, use a graphing calculator...Ch. 10.5 - To graph Problems 59-62, use a graphing calculator...Ch. 10.5 - To graph Problems 59-62, use a graphing calculator...Ch. 10.5 - (A) If 120 scores are chosen from a normal...Ch. 10.5 - (A) If 250 scores are chosen from a normal...Ch. 10.5 - Sales Salespeople for a solar technology company...Ch. 10.5 - Guarantees. The average lifetime for a car battery...Ch. 10.5 - Quality control. A manufacturing process produces...Ch. 10.5 - Quality control. An automated manufacturing...Ch. 10.5 - Marketing claims. A company claims that 60 of the...Ch. 10.5 - Labor relation A union representative 60 claims of...Ch. 10.5 - Medicine. The average healing time of a certain...Ch. 10.5 - Agriculture. The average height of a hay crop is...Ch. 10.5 - Genetics. In a family with 2 children, the...Ch. 10.5 - Genetics. In Problem 73, what is the approximate...Ch. 10.5 - Testing. Scholastic Aptitude Tests (SATs) are...Ch. 10.5 - Politics. Candidate Harkins claims that she will...Ch. 10.5 - Grading on a curve. An instructor grades on a...Ch. 10.5 - Psychology. A test devised to measure...Ch. 10 - Use a bar graph and a broken-line graph to graph...Ch. 10 - Use a pie graph to graph the data on educational...Ch. 10 - (A) Draw a histogram for the binomial distribution...Ch. 10 - For the set of sample measurements...Ch. 10 - If a normal distribution has a mean of 100 and a...Ch. 10 - Given the sample of 25 quiz scores listed in the...Ch. 10 - For the set of grouped sample data given in the...Ch. 10 - (A) Construct a histogram for the binomial...Ch. 10 - What are the mean and standard deviation for a...Ch. 10 - In Problems 10 and 11, discuss the validity of...Ch. 10 - In Problems 10 and 11, discuss the validity of...Ch. 10 - If the probability of success in a single trial of...Ch. 10 - Given a normal distribution with mean 50 and...Ch. 10 - A data set is formed by recording the sums of 100...Ch. 10 - For the sample quiz scores in Problem 6, find the...Ch. 10 - A fair die is rolled five times. What is the...Ch. 10 - Two dice are rolled three times. What is the...Ch. 10 - Ten students take an exam worth 100 points. (A)...Ch. 10 - In the last presidential election, 39 of a city’s...Ch. 10 - A random variable represents the number of wins in...Ch. 10 - Retail sales. The daily number of bad checks...Ch. 10 - Preference survey. Find the mean, median, and/or...Ch. 10 - Plant safety. The weekly record of reported...Ch. 10 - Personnel screening.The scores on a screening test...Ch. 10 - Market research A newspaper publisher claims that...Ch. 10 - Health care. A small town has three doctors on...
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