EBK FINITE MATHEMATICS & ITS APPLICATIO
12th Edition
ISBN: 9780134464053
Author: HAIR
Publisher: YUZU
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Chapter 7.1, Problem 21E
To determine
To calculate: The five-number summary and draw the box plot and also find interquartile range for the
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Q1) Classify the following statements as a true or false statements
a. Any ring with identity is a finitely generated right R module.-
b. An ideal 22 is small ideal in Z
c. A nontrivial direct summand of a module cannot be large or small submodule
d. The sum of a finite family of small submodules of a module M is small in M
A module M 0 is called directly indecomposable if and only if 0 and M are
the only direct summands of M
f. A monomorphism a: M-N is said to split if and only if Ker(a) is a direct-
summand in M
& Z₂ contains no minimal submodules
h. Qz is a finitely generated module
i. Every divisible Z-module is injective
j. Every free module is a projective module
Q4) Give an example and explain your claim in each case
a) A module M which has two composition senes 7
b) A free subset of a modale
c) A free module
24
d) A module contains a direct summand submodule 7,
e) A short exact sequence of modules 74.
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Q.1) Classify the following statements as a true or false statements:
a. If M is a module, then every proper submodule of M is contained in a maximal
submodule of M.
b. The sum of a finite family of small submodules of a module M is small in M.
c. Zz is directly indecomposable.
d. An epimorphism a: M→ N is called solit iff Ker(a) is a direct summand in M.
e. The Z-module has two composition series.
Z
6Z
f. Zz does not have a composition series.
g. Any finitely generated module is a free module.
h. If O→A MW→ 0 is short exact sequence then f is epimorphism.
i. If f is a homomorphism then f-1 is also a homomorphism.
Maximal C≤A if and only if is simple.
Sup
Q.4) Give an example and explain your claim in each case:
Monomorphism not split.
b) A finite free module.
c) Semisimple module.
d) A small submodule A of a module N and a homomorphism op: MN, but
(A) is not small in M.
Prove that
Σ
prime p≤x
p=3 (mod 10)
1
Ρ
=
for some constant A.
log log x + A+O
1
log x
"
Chapter 7 Solutions
EBK FINITE MATHEMATICS & ITS APPLICATIO
Ch. 7.1 - Suppose that a list consists of 17 numbers in...Ch. 7.1 - Prob. 2CYUCh. 7.1 - Prob. 3CYUCh. 7.1 - In Exercise 1–4, display the data in a bar chart...Ch. 7.1 - In Exercise 1–4, display the data in a bar chart...Ch. 7.1 - In Exercise 1–4, display the data in a bar chart...Ch. 7.1 - In Exercise 1–4, display the data in a bar chart...Ch. 7.1 - 5. School Enrollments Display the data from the...Ch. 7.1 - 6. U.S. Defense Employees Display the data from...Ch. 7.1 - 7. Interest on Public Debt In 2015, the interest...
Ch. 7.1 - 8. U.S. Defense Employees Display the data from...Ch. 7.1 - Great Lakes Display the data from the table in...Ch. 7.1 - Bachelors Degrees Display the data from the table...Ch. 7.1 - Freshman Aspirations Exercises 11 and 12 refer to...Ch. 7.1 - Freshman Aspirations Exercises 11 and 12 refer to...Ch. 7.1 - 13. Vice Presidential Tie Breakers The number of...Ch. 7.1 - 14. Presidential Ages The ages at inauguration of...Ch. 7.1 - Quiz Scores The bar charts in Exercises 15 and 16...Ch. 7.1 - Quiz Scores The bar charts in Exercises 15 and 16...Ch. 7.1 - In Exercises 17 and 18, draw the box plot...Ch. 7.1 - In Exercises 17 and 18, draw the box plot...Ch. 7.1 - In Exercises 19–22, find the five-number summary...Ch. 7.1 - In Exercises 1922, find the five-number summary...Ch. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - 23. Match each of the histograms in column I with...Ch. 7.1 - Food Cost The box plot for the price (in cents) of...Ch. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Batting Averages On April 16, 2016, the Toronto...Ch. 7.1 - In Exercises 28–31, use technology to produce...Ch. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - In Exercises 28–31, use technology to produce...Ch. 7.2 - 1. Carnival Game In a certain carnival game, a...Ch. 7.2 - Carnival Game Refer to the carnival game of...Ch. 7.2 - 1. Final Grades Table 11 gives the frequency...Ch. 7.2 - 2. Gas Queue The number of cars waiting to be...Ch. 7.2 - Weather Reports A local news website counted the...Ch. 7.2 - Production Level A production manager counted the...Ch. 7.2 - Coin Tosses A fair coin is tossed three times, and...Ch. 7.2 - 6. Archery An archer can hit the bull’s-eye of the...Ch. 7.2 - 7. Selecting Balls from an Urn An urn contains...Ch. 7.2 - 8. Rolling a Die A die is rolled, and the number...Ch. 7.2 - Carnival Game In a certain carnival game, the...Ch. 7.2 - 10. Carnival Game In a certain carnival game, a...Ch. 7.2 - 11. Figure 9 is the histogram for a probability...Ch. 7.2 - Figure 10 on the next page is the histogram for a...Ch. 7.2 - Let the random variables X and Y have the...Ch. 7.2 - Let the random variables X and Y have the...Ch. 7.2 - Let the random variables X and Y have the...Ch. 7.2 - Let the random variables X and Y have the...Ch. 7.2 - Let the random variables X and Y have the...Ch. 7.2 - Let the random variables X and Y have the...Ch. 7.2 - Let the random variables X and Y have the...Ch. 7.2 - Let the random variables X and Y have the...Ch. 7.2 - 21. Grade Distributions Two classes take the same...Ch. 7.2 - 22. Grade Distributions Use Table 16 to answer the...Ch. 7.2 - Exercises 23–26 refer to the tables and relative...Ch. 7.2 - Exercises 2326 refer to the tables and relative...Ch. 7.2 - Exercises 2326 refer to the tables and relative...Ch. 7.2 - Exercises 23–26 refer to the tables and relative...Ch. 7.2 - 27. Table 17 gives the probability distribution of...Ch. 7.2 - Table 18 gives the probability distribution of the...Ch. 7.2 - Table 19 gives the probability distribution of the...Ch. 7.2 - Prob. 30ECh. 7.3 - A number is selected at random from the numbers 0...Ch. 7.3 - 2. If the experiment in Problem 1 is repeated 20...Ch. 7.3 - Prob. 3CYUCh. 7.3 - In Exercises 14, calculate (kn)pkqnk for the given...Ch. 7.3 - In Exercises 1–4, calculate for the given values...Ch. 7.3 - In Exercises 14, calculate (kn)pkqnk for the given...Ch. 7.3 - In Exercises 1–4, calculate for the given values...Ch. 7.3 - Coin Tosses A coin is tossed 10 times. In...Ch. 7.3 - Coin Tosses A coin is tossed 10 times. In...Ch. 7.3 - Coin Tosses A coin is tossed 10 times. In...Ch. 7.3 - Coin Tosses A coin is tossed 10 times. In...Ch. 7.3 - Coin Tosses A coin is tossed 10 times. In...Ch. 7.3 - Coin Tosses A coin is tossed 10 times. In...Ch. 7.3 - Rolling a Die A single die is rolled four times....Ch. 7.3 - Rolling a Die A single die is rolled four times....Ch. 7.3 - Rolling a Die A single die is rolled four times....Ch. 7.3 - Rolling a Die A single die is rolled four times....Ch. 7.3 - Rolling a Die A single die is rolled four times....Ch. 7.3 - Rolling a Die A single die is rolled four times....Ch. 7.3 - Twenty-Somethings Fourteen percent of U.S....Ch. 7.3 - Twenty-Somethings Fourteen percent of U.S....Ch. 7.3 - Twenty-Somethings Fourteen percent of U.S....Ch. 7.3 - Twenty-Somethings Fourteen percent of U.S....Ch. 7.3 - Twenty-Somethings Fourteen percent of U.S....Ch. 7.3 - Twenty-Somethings Fourteen percent of U.S....Ch. 7.3 - Career Training According to the study The...Ch. 7.3 - Prob. 24ECh. 7.3 - Career Training According to the study The...Ch. 7.3 - Career Training According to the study The...Ch. 7.3 - 27. Children A family chosen at random has four...Ch. 7.3 - 28. New Employees A manager at a call center...Ch. 7.3 - College Acceptances Exercises 29 and 30 refer to...Ch. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Veterinary Medicine Exercises 31 and 32 refer to...Ch. 7.3 - Car Sales An automotive salesman determines that...Ch. 7.3 - 34. Insurance Claims A homeowner’s insurance...Ch. 7.3 - Coin Tosses When a coin is tossed 100 times, the...Ch. 7.3 - Rolling Dice When a die is rolled 10 times, the...Ch. 7.3 - Figure 6 shows the histogram for a binomial random...Ch. 7.3 - 38. Figure 7 shows the histogram for a binomial...Ch. 7.3 - Prob. 39ECh. 7.3 - Prob. 40ECh. 7.3 - Centenarians The probability that a 20-year-old...Ch. 7.3 - 42. Left-handedness Ten percent of the population...Ch. 7.3 - 43. Drug Reaction Suppose that the probability of...Ch. 7.3 - Prob. 44ECh. 7.3 - Voter Polling Suppose that 60% of the voters in a...Ch. 7.3 - Jury Verdict A jury has 12 jurors. A vote of at...Ch. 7.3 - Quality Control Three percent of the circuit...Ch. 7.3 - Quality Control Refer to Example 1. What is the...Ch. 7.3 - Genetics Every offspring inherits a gene for hair...Ch. 7.3 - Theft of Gold A small country owns 10,000 gold...Ch. 7.3 - Prob. 51ECh. 7.3 - 52. Basketball A basketball player makes free...Ch. 7.3 - Basketball A basketball player makes 82% of her...Ch. 7.3 - 54. Darts The probability is .64 that a dartist...Ch. 7.3 - Tennis A single match at the mens U.S. Open...Ch. 7.3 - 56. Baseball The World Series consists of a...Ch. 7.3 - Prob. 57ECh. 7.3 - Prob. 58ECh. 7.3 - Prob. 59ECh. 7.3 - Prob. 60ECh. 7.3 - Prob. 61ECh. 7.3 - Prob. 62ECh. 7.3 - Prob. 63ECh. 7.3 - Prob. 64ECh. 7.3 - Prob. 66ECh. 7.3 - Prob. 67ECh. 7.3 - 68. Calculate the probability of between 45 and 55...Ch. 7.3 - Prob. 69ECh. 7.4 - Life Insurance A 74-year-old man pays $1000 for a...Ch. 7.4 - Prob. 2CYUCh. 7.4 - In Exercises 14, determine whether the quantity...Ch. 7.4 - In Exercises 14, determine whether the quantity...Ch. 7.4 - In Exercises 1–4, determine whether the quantity...Ch. 7.4 - In Exercises 14, determine whether the quantity...Ch. 7.4 - Find the expected value for the probability...Ch. 7.4 - Find the expected value for the probability...Ch. 7.4 - Grades A college student received the following...Ch. 7.4 - Gymnastic Scores An Olympic gymnast received the...Ch. 7.4 - 9. Comparing Toothpastes Table 12 gives the...Ch. 7.4 - 10. Investments Table 13 gives the possible...Ch. 7.4 - In Exercises 11–14, find the expected value for...Ch. 7.4 - In Exercises 11–14, find the expected value for...Ch. 7.4 - In Exercises 11–14, find the expected value for...Ch. 7.4 - In Exercises 1114, find the expected value for the...Ch. 7.4 - Roulette In American roulette, a bettor may place...Ch. 7.4 - 16. Roulette In American roulette, a dollar may be...Ch. 7.4 - Carnival Game In a carnival game, the player...Ch. 7.4 - Carnival Game In a carnival game, the player...Ch. 7.4 - 19. Life Insurance Using life insurance tables, a...Ch. 7.4 - Life Insurance Using life insurance tables, a...Ch. 7.4 - 21. Batting Averages Five members of a baseball...Ch. 7.4 - 22. Exam Scores Three members of a study group...Ch. 7.4 - Dice A pair of dice is rolled, and the larger of...Ch. 7.4 - Dice A pair of dice is rolled, and the smaller of...Ch. 7.4 - Chuck-a-Luck Redo Example 6, where the player wins...Ch. 7.4 - 26. Chuck-a-Luck Consider Example 6 with six...Ch. 7.4 - Bachelors Degrees According to the National Center...Ch. 7.4 - 28. Faculty Degrees According to the American...Ch. 7.4 - 29. Rolling a Die A die is rolled 30 times. What...Ch. 7.4 - Baseball Ted is a consistent .275 hitter. How many...Ch. 7.4 - Basketball A basketball player makes 40% of their...Ch. 7.4 - 32. Binomial Trials What is the probability of...Ch. 7.4 - Exercises 33–36 require the use of counting...Ch. 7.4 - Exercises 3336 require the use of counting...Ch. 7.4 - Exercises 33–36 require the use of counting...Ch. 7.4 - Exercises 33–36 require the use of counting...Ch. 7.4 - Rain Insurance The promoter of a football game is...Ch. 7.4 - Theft Insurance Bob wishes to insure a priceless...Ch. 7.4 - Ticket Sales Last weekend, a movie theater sold x...Ch. 7.4 - 40. Candle Sales A store sold an average...Ch. 7.4 - 41. Weather The average daily temperature during...Ch. 7.4 - Grades Jos wants to earn a 90% overall average in...Ch. 7.4 - 43. Mean If 5, 6, and x have the same average as...Ch. 7.4 - Game of Chance Table 14 gives the probability...Ch. 7.4 - 45. Factory Production An assembly line produces...Ch. 7.4 - 46. Weekly Revenue A small business had an average...Ch. 7.4 - 47. Truck Capacity A truck can carry a maximum of...Ch. 7.4 - Magazine Sales Half of the magazines at a...Ch. 7.5 - 1. (a) Compute the variance of the probability...Ch. 7.5 - 2. Refer to the probability distribution in Table...Ch. 7.5 - 1. Compute the variance of the probability...Ch. 7.5 - 2. Compute the variance of the probability...Ch. 7.5 - Determine by inspection which one of the...Ch. 7.5 - Determine by inspection which one of the...Ch. 7.5 - 5. Investment Returns Table 7 gives the...Ch. 7.5 - Golf Scores Two golfers recorded their scores for...Ch. 7.5 - Weekly Sales Table 8 gives the relative frequency...Ch. 7.5 - Course Grades Student A received the following...Ch. 7.5 - Coin Tosses Suppose that a coin is tossed 10...Ch. 7.5 - 10. Dice Suppose that a pair of dice is rolled 720...Ch. 7.5 - 11. Quality Control A manufacturer produces smart...Ch. 7.5 - 12. Basketball A basketball player makes each free...Ch. 7.5 - Chebychev Inequality Suppose that a probability...Ch. 7.5 - Chebychev Inequality Suppose that a probability...Ch. 7.5 - 15. Bulb Lifetimes For certain types of...Ch. 7.5 - 16. Quality Control An electronics firm determines...Ch. 7.5 - Prob. 17ECh. 7.5 - 18. Chebychev Inequality Suppose that a...Ch. 7.5 - Dice The probability distribution for the sum of...Ch. 7.5 - Dice The probability distribution, rounded to the...Ch. 7.5 - Variance Use the alternative formula for variance...Ch. 7.5 - 22. If X is a random variable, then the variance...Ch. 7.5 - Prob. 23ECh. 7.5 - Prob. 24ECh. 7.5 - 25. College Enrollments Table 12 gives the fall...Ch. 7.5 - Prob. 26ECh. 7.5 - Prob. 27ECh. 7.5 - Prob. 28ECh. 7.6 - Refer to Fig. 35(a). Find the value of z for which...Ch. 7.6 - Refer to the normal curve in Fig. 35(b). Express...Ch. 7.6 - In Exercises 1-8, use the table for A(z) (Table 2)...Ch. 7.6 - In Exercises 1-8, use the table for A(z) (Table 2)...Ch. 7.6 - In Exercises 1-8, use the table for A(z) (Table 2)...Ch. 7.6 - In Exercises 1-8, use the table for A(z) (Table 2)...Ch. 7.6 - In Exercises 1-8, use the table for (Table 2) to...Ch. 7.6 - In Exercises 1-8, use the table for (Table 2) to...Ch. 7.6 - In Exercises 1-8, use the table for (Table 2) to...Ch. 7.6 - In Exercises 1-8, use the table for A(z) (Table 2)...Ch. 7.6 - In Exercises 9-12, find the value of z for which...Ch. 7.6 - In Exercises 9-12, find the value of z for which...Ch. 7.6 - In Exercises 9-12, find the value of z for which...Ch. 7.6 - In Exercises 9-12, find the value of z for which...Ch. 7.6 - What is the 80th percentile of the standard normal...Ch. 7.6 - What is the 40th percentile of the standard normal...Ch. 7.6 - Prob. 15ECh. 7.6 - Prob. 16ECh. 7.6 - Prob. 17ECh. 7.6 - Prob. 18ECh. 7.6 - Exercises 1922 refer to the normal curve with...Ch. 7.6 - Exercises 19–22 refer to the normal curve with...Ch. 7.6 - Exercises 19–22 refer to the normal curve with...Ch. 7.6 - Exercises 1922 refer to the normal curve with...Ch. 7.6 - In Exercises 23-26, find the areas of the shaded...Ch. 7.6 - In Exercises 23-26, find the areas of the shaded...Ch. 7.6 - In Exercises 23-26, find the areas of the shaded...Ch. 7.6 - In Exercises 23-26, find the areas of the shaded...Ch. 7.6 - 27. What is the probability that an outcome of a...Ch. 7.6 - 28. What is the probability that an outcome of a...Ch. 7.6 - Find the value of for a normal random variable X...Ch. 7.6 - Find the value of for a normal random variable X...Ch. 7.6 - Elephant Heights Suppose that the height (at the...Ch. 7.6 - 32. Bottling Reliability At a soft-drink bottling...Ch. 7.6 - Manufacturing Reliability Bolts produced by a...Ch. 7.6 - Heights In a certain population, heights (in...Ch. 7.6 - 35. Manufacturing Reliability In a certain...Ch. 7.6 - 36. IQ Scores As measured with the Stanford-Binet...Ch. 7.6 - 37. Production Quotas The number of barrels of oil...Ch. 7.6 - Lightbulb Lifetimes Suppose that the lifetimes of...Ch. 7.6 - SAT Scores Assume that SAT verbal scores for a...Ch. 7.6 - 40. Mailing Bags A mail-order house uses an...Ch. 7.6 - Tire Lifetimes The lifetime of a certain brand of...Ch. 7.6 - Soft-Drink Dispenser Let X be the amount of soda...Ch. 7.6 - (True or False) A normal curve with a large value...Ch. 7.6 - Prob. 44ECh. 7.6 - Prob. 45ECh. 7.6 - Prob. 46ECh. 7.6 - Prob. 47ECh. 7.6 - Prob. 48ECh. 7.7 - 1. Drug Testing A new drug is being tested on...Ch. 7.7 - Prob. 2CYUCh. 7.7 - In Exercises 122, use the normal curve to...Ch. 7.7 - In Exercises 122, use the normal curve to...Ch. 7.7 - In Exercises 122, use the normal curve to...Ch. 7.7 - In Exercises 122, use the normal curve to...Ch. 7.7 - In Exercises 1–22, use the normal curve to ...Ch. 7.7 - In Exercises 122, use the normal curve to...Ch. 7.7 - In Exercises 122, use the normal curve to...Ch. 7.7 - In Exercises 122, use the normal curve to...Ch. 7.7 - In Exercises 122, use the normal curve to...Ch. 7.7 - In Exercises 1–22, use the normal curve to ...Ch. 7.7 - In Exercises 1–22, use the normal curve to ...Ch. 7.7 - In Exercises 1–22, use the normal curve to ...Ch. 7.7 - In Exercises 122, use the normal curve to...Ch. 7.7 - In Exercises 122, use the normal curve to...Ch. 7.7 - In Exercises 1–22, use the normal curve to ...Ch. 7.7 - In Exercises 122, use the normal curve to...Ch. 7.7 - In Exercises 1–22, use the normal curve to ...Ch. 7.7 - In Exercises 1–22, use the normal curve to ...Ch. 7.7 - In Exercises 1–22, use the normal curve to ...Ch. 7.7 - In Exercises 122, use the normal curve to...Ch. 7.7 - In Exercises 122, use the normal curve to...Ch. 7.7 - In Exercises 122, use the normal curve to...Ch. 7.7 - In Exercises 23–26, find the more precise answer...Ch. 7.7 - Prob. 24ECh. 7.7 - In Exercises 23–26, find the more precise answer...Ch. 7.7 - In Exercises 2326, find the more precise answer to...Ch. 7 - What is a bar chart? A pie chart? A histogram? A...Ch. 7 - Prob. 2FCCECh. 7 - What is a frequency distribution? A relative...Ch. 7 - Prob. 4FCCECh. 7 - Prob. 5FCCECh. 7 - What is meant by the probability distribution of a...Ch. 7 - Prob. 7FCCECh. 7 - Prob. 8FCCECh. 7 - Prob. 9FCCECh. 7 - Prob. 10FCCECh. 7 - Prob. 11FCCECh. 7 - Prob. 12FCCECh. 7 - Prob. 13FCCECh. 7 - U.S. Population Display the data from Table 1 in a...Ch. 7 - Find the five-number summary and the interquartile...Ch. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - 6. Archery An archer has probability .3 of hitting...Ch. 7 - 7. Guessing on an Exam A true–false exam consists...Ch. 7 - Dice A pair of fair dice is rolled 12 times. Note:...Ch. 7 - Table 2 gives the probability distribution of the...Ch. 7 - 10. Balls in an Urn An urn contains four red balls...Ch. 7 - The probability distribution of a random variable...Ch. 7 - Dice Game Lucy and Ethel play a game of chance in...Ch. 7 - 13. Suppose that a probability distribution has...Ch. 7 - Prob. 14RECh. 7 - Prob. 15RECh. 7 - Prob. 16RECh. 7 - 17. Heights of Adult Males The height of adult...Ch. 7 - Figure 3(a) is a standard normal curve. Find the...Ch. 7 - Figure 3(b) is a normal curve with =80and=15. Find...Ch. 7 - IQ Scores As measured with the Wechsler Adult...Ch. 7 - 21. Jury Selection In a certain city, 2/5 of the...Ch. 7 - Quality Control In a complicated production...Ch. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - If each number in a set of numbers is increased by...Ch. 7 - 28. If each number in a set of numbers is doubled,...Ch. 7 - Prob. 29RECh. 7 - Prob. 30RECh. 7 - An urn contains four red balls and six white...Ch. 7 - Prob. 2PCh. 7 - An urn contains four red balls and six white...Ch. 7 - An urn contains four red balls and six white...Ch. 7 - An urn contains four red balls and six white...Ch. 7 - An urn contains four red balls and six white...Ch. 7 - An urn contains four red balls and six white...Ch. 7 - An urn contains four red balls and six white...Ch. 7 - An urn contains four red balls and six white...
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- Prove that, for x ≥ 2, d(n) n2 log x = B ― +0 X (금) n≤x where B is a constant that you should determine.arrow_forwardProve that, for x ≥ 2, > narrow_forwardI need diagram with solutionsarrow_forwardT. Determine the least common denominator and the domain for the 2x-3 10 problem: + x²+6x+8 x²+x-12 3 2x 2. Add: + Simplify and 5x+10 x²-2x-8 state the domain. 7 3. Add/Subtract: x+2 1 + x+6 2x+2 4 Simplify and state the domain. x+1 4 4. Subtract: - Simplify 3x-3 x²-3x+2 and state the domain. 1 15 3x-5 5. Add/Subtract: + 2 2x-14 x²-7x Simplify and state the domain.arrow_forwardQ.1) Classify the following statements as a true or false statements: Q a. A simple ring R is simple as a right R-module. b. Every ideal of ZZ is small ideal. very den to is lovaginz c. A nontrivial direct summand of a module cannot be large or small submodule. d. The sum of a finite family of small submodules of a module M is small in M. e. The direct product of a finite family of projective modules is projective f. The sum of a finite family of large submodules of a module M is large in M. g. Zz contains no minimal submodules. h. Qz has no minimal and no maximal submodules. i. Every divisible Z-module is injective. j. Every projective module is a free module. a homomorp cements Q.4) Give an example and explain your claim in each case: a) A module M which has a largest proper submodule, is directly indecomposable. b) A free subset of a module. c) A finite free module. d) A module contains no a direct summand. e) A short split exact sequence of modules.arrow_forward1 2 21. For the matrix A = 3 4 find AT (the transpose of A). 22. Determine whether the vector @ 1 3 2 is perpendicular to -6 3 2 23. If v1 = (2) 3 and v2 = compute V1 V2 (dot product). .arrow_forward7. Find the eigenvalues of the matrix (69) 8. Determine whether the vector (£) 23 is in the span of the vectors -0-0 and 2 2arrow_forward1. Solve for x: 2. Simplify: 2x+5=15. (x+3)² − (x − 2)². - b 3. If a = 3 and 6 = 4, find (a + b)² − (a² + b²). 4. Solve for x in 3x² - 12 = 0. -arrow_forward5. Find the derivative of f(x) = 6. Evaluate the integral: 3x3 2x²+x— 5. - [dz. x² dx.arrow_forward5. Find the greatest common divisor (GCD) of 24 and 36. 6. Is 121 a prime number? If not, find its factors.arrow_forward13. If a fair coin is flipped, what is the probability of getting heads? 14. A bag contains 3 red balls and 2 blue balls. If one ball is picked at random, what is the probability of picking a red ball?arrow_forward24. What is the value of ¿4, where i 25. Simplify log2 (8). = −1? 26. If P(x) = x³- 2x² + 5x - 10, find P(2). 27. Solve for x: e2x = 7.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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