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mathematics
college algebra
College Algebra 12th edition Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels - Solutions
Evaluate the expression.C(8, 3)
Evaluate the expression.P(6, 0)
Evaluate each expression.P(9, 2)
Let Sn represent the statement, and use mathematical induction to prove that Sn is true for every positive integer n.13 + 33 + 53 +g+ (2n - 1)3 = n2(2n2 - 1)
Let Sn represent the statement, and use mathematical induction to prove that Sn is true for every positive integer n.2 + 22 + 23 + · · · + 2n = 2(2n - 1)
Let Sn represent the statement, and use mathematical induction to prove that Sn is true for every positive integer n.2 + 6 + 10 + 14 + · · · + (4n - 2) = 2n2
Let Sn represent the statement, and use mathematical induction to prove that Sn is true for every positive integer n.1 + 3 + 5 + 7 + · · · + (2n - 1) = n2
Find the indicated term or terms of the expansion.Last three terms of (2a + 5b)16
Find the indicated term or terms of the expansion.First four terms of (x + 2)12
Find the indicated term or terms of the expansion.Seventh term of (m - 3n)14
Find the indicated term or terms of the expansion.Sixth term of (4x - y)8
Write the binomial expansion of the expression.(m3 - m-2)4
Write the binomial expansion of the expression. (sv5-) 31 Vx.
Write the binomial expansion of the expression.(3z - 5w)3
Write the binomial expansion of the expression.(x + 2y)4
Write the sum using summation notation. 5 6 6 12 6. 13
Write the sum using summation notation.4 + 12 + 36 + · · · + 972
Write the sum using summation notation.10 + 14 + 18 + · · · + 86
Write the sum using summation notation.4 - 1 - 6 - · · · - 66
Evaluate each sum where x1 = 0, x2 = 1, x3 = 2, x4 = 3, x5 = 4, and x6 = 5. Ef(x;)Ax; f(x) = (x – 2)³, Ax=0.1 i=1
Evaluate each sum where x1 = 0, x2 = 1, x3 = 2, x4 = 3, x5 = 4, and x6 = 5. 6) (x² i=1
Evaluate the series that converges. Identify any that diverge.0.9 + 0.09 + 0.009 + 0.0009 + · · ·
Evaluate the series that converges. Identify any that diverge. 12 -16
Evaluate the series that converges. Identify any that diverge. 3 1|3
Evaluate each series that converges. Identify any that diverge. 24 + 8 +-+ 3 9.
Evaluate each sum that exists.Find an infinite geometric series having common ratio 3/4 and sum 6.
Evaluate the sum that exists. Σ 3 i=1
Evaluate the sum that exists. -21 Σ i=1
Evaluate the sum that exists. i=1 4.
Evaluate the sum that exists. E4· 2 i=1
Evaluate the sum that exists. 2500 Σ j=1
Evaluate the sum that exists. 10 (3j – 4) j=1
Evaluate the sum that exists. i + 1 i i=1
Evaluate the sum that exists. + i) i=1
Evaluate the sum that exists. –1)- i=1
Determine S4 for the geometric sequence. 3 2'3 4)
Determine S4 for the geometric sequence.a1 = -1, r = 3
Determine S4 for the geometric sequence.a1 = 3, r = 2
Determine a5 for the geometric sequence.a3 = 4, r = 1/5
Determine a5 for the geometric sequence.a1 = -2, r = 3
Determine S12 for the arithmetic sequence.a2 = 6, d = 10
Determine S12 for the arithmetic sequence.a1 = 2, d = 3
Determine a8 for the arithmetic sequence.a1 = 6x - 9, a2 = 5x + 1
Determine a8 for the arithmetic sequence.a1 = 6, d = 2
Determine the indicated terms for the sequence described.A geometric sequence has a1 = -8 and a7 = - 1/8. Find a4 and an.
Determine the indicated terms for the sequence described.An arithmetic sequence has a5 = -3 and a15 = 17. Find a1 and an.
Write the first five terms of the sequence described.Geometric; a1 = -5, a2 = -1
Write the first five terms of the sequence described.Geometric; a1 = 6, r = 2
Write the first five terms of the sequence described.Arithmetic; a3 = π, a4 = 1
Write the first five terms of the sequence described.Arithmetic; a2 = 10, d = -2
Write an arithmetic sequence that consists of five terms, with first term 4, having the sum of the five terms equal to 25.
Write the first five terms of each sequence. State whether the sequence is arithmetic, geometric, or neither.a1 = 1, a2 = 3,an = an-2 + an-1, if n ≥ 3
Write the first five terms of the sequence. State whether the sequence is arithmetic, geometric, or neither.a1 = 5an = an-1 - 3, if n ≥ 2
Write the first five terms of the sequence. State whether the sequence is arithmetic, geometric, or neither.an = n(n + 1)
Write the first five terms of the sequence. State whether the sequence is arithmetic, geometric, or neither.an = 2(n + 3)
Write the first five terms of the sequence. State whether the sequence is arithmetic, geometric, or neither.an = (-2)n
Write the first five terms of the sequence. State whether the sequence is arithmetic, geometric, or neither. п an п+1
Suppose that in a family I = 2 and S = 4. If the probability P is 0.25 of there being k = 2 uninfected members after 1 week, find the possible values of p to the nearest thousandth. Write P as a function of p.
Solve the problem.What will happen when an infectious disease is introduced into a family? Suppose a family has I infected members and S members who are not infected but are susceptible to contracting the disease. The probability P of exactly k people not contracting the disease during a 1-week
Solve the problem.The screens illustrate how the table feature of a graphing calculator can be used to find the probabilities of having 0, 1, 2, 3, or 4 girls in a family of 4 children. That 0 appears for values of x greater than 4 because these events are impossible.
Solve the problem.The probability that a male will be color-blind is 0.042. Find the probabilities that in a group of 53 men, the following are true.(a) Exactly 5 are color-blind. (b) No more than 5 are color-blind.(c) None are color-blind. (d) At least 1 is color-blind.
The table gives the results of a survey of 153,015 first-year students from the class of 2018 at 227 of the nation’s four-year colleges and universities.Using the percents as probabilities, find the probability of each event for a randomly selected student.The student applied to no colleges.
The table gives the results of a survey of 153,015 first-year students from the class of 2018 at 227 of the nation’s four-year colleges and universities.Using the percents as probabilities, find the probability of each event for a randomly selected student.The student applied to more than 3
The table gives the results of a survey of 153,015 first-year students from the class of 2018 at 227 of the nation’s four-year colleges and universities.Using the percents as probabilities, find the probability of each event for a randomly selected student.The student applied to at least 2
The table gives the results of a survey of 153,015 first-year students from the class of 2018 at 227 of the nation’s four-year colleges and universities.Using the percents as probabilities, find the probability of each event for a randomly selected student.The student applied to fewer than 4
In the U.S. House of Representatives, the number of representatives from each state is proportional to the state’s population. California (the most populous state) has 53 representatives, whereas Wyoming (the least populous state) has just 1 representative. The table gives the percentage of
In the U.S. House of Representatives, the number of representatives from each state is proportional to the state’s population. California (the most populous state) has 53 representatives, whereas Wyoming (the least populous state) has just 1 representative. The table gives the percentage of
In the U.S. House of Representatives, the number of representatives from each state is proportional to the state’s population. California (the most populous state) has 53 representatives, whereas Wyoming (the least populous state) has just 1 representative. The table gives the percentage of
In the U.S. House of Representatives, the number of representatives from each state is proportional to the state’s population. California (the most populous state) has 53 representatives, whereas Wyoming (the least populous state) has just 1 representative. The table gives the percentage of
Work each problem.Refer to Exercise 31. Suppose the percents and probabilities in the table are estimates of annual growth during the next 3 yr. What is the probability that an investment of $10,000 will grow in value to at least $15,000 during the next 3 yr?Exercise 31.Percent Growth
A financial analyst has determined the possibilities (and their probabilities) for the growth in value of a certain stock during the next year. (Assume these are the only possibilities.) See the table. For instance, the probability of a 5% growth is 0.15. If you invest $10,000 in the stock, what is
The management of a firm wishes to survey the opinions of its workers, classified as follows for the purpose of an interview: 30% have worked for the company 5 or more years, 28% are female, 65% contribute to a voluntary retirement plan, and 50% of the female workers contribute to the retirement
The table is an abbreviated version of the 2010 period life table used by the Office of the Chief Actuary of the Social Security Administration. (The actual table includes every age, not just every tenth age.) Theoretically, this table follows a group of 100,000 males at birth and gives the number
If three of the four selections in Exercise 27 are correct, the player wins $200. Find the probability of this occurring.Exercise 27One game in a state lottery requires you to pick 1 heart, 1 club, 1 diamond, and 1 spade, in that order, from the 13 cards in each suit. What is the probability of
One game in a state lottery requires you to pick 1 heart, 1 club, 1 diamond, and 1 spade, in that order, from the 13 cards in each suit. What is the probability of getting all four picks correct and winning $5000?
The U.S. resident population by region (in millions) for selected years is given in the table. Find the probability, to the nearest thousandth, that a U.S. resident selected at random satisfied the following in parts (a)–(d).(a) Lived in the West in 2006(b) Lived in the Midwest in 2000(c) Lived
The numbers (in thousands) of foreign-born people who were living in the United States in 2012, according to region of birth, are given in the table. Find the probability, to the nearest thousandth, that a foreign-born U.S. resident in 2012 satisfied the following in parts (a) –(c).(a) Born in
Two fair dice are rolled. Find the probabilities in parts (a)–(d).(a) The sum of the dots is at least 10.(b) The sum of the dots is less than 10.(c) The sum of the dots is either 7 or at least 10.(d) The sum of the dots is 2, or the dice both show the same number.(e) What are the odds against
A card is drawn at random from a standard deck of 52 cards. Find the probabilities in parts (a)–(d).(a) The card is a spade. (b) The card is not a spade.(c) The card is a spade or a heart. (d) The card is a spade or a face card.(e) What are the odds in favor of drawing a spade?
The probability that a bank with assets greater than or equal to $30 billion will make a loan to a small business is 0.002. What are the odds against such a bank making a small business loan?
A baseball player with a batting average of .300 comes to bat. What are the odds in favor of the ball player getting a hit?
Write the event in set notation and give the probability of the event.Associate each probability in parts (a)–(e) with one of the statements in choices A–E.(a) P(E) = 0.01 (b) P(E) = 1(c) P(E) = 0.99(d) P(E) = 0 (e) P(E) = 0.5A. The event is certain. B. The event is impossible.C.
Write the event in set notation and give the probability of the event.If the probability of an event is 0.857, what is the probability that the event will not occur?
Write the event in set notation and give the probability of the event.A student gives the probability of an event in a problem as 6/5. Why must this answer be incorrect?
Write each event in set notation and give the probability of the event.Refer to Exercise 11.(a) The result is a repeated number. (b) The second number is 1 or 3.(c) The first number is even and the second number is odd.Exercise 11.The spinner shown here is spun twice. 3 2.
Write each event in set notation and give the probability of the event.Refer to Exercise 10.(a) Both slips are marked with even numbers.(b) Both slips are marked with odd numbers.(c) Both slips are marked with the same number.(d) One slip is marked with an odd number, the other with an even
Write the event in set notation and give the probability of the event.Refer to Exercise 9.(a) All three coins show the same face.(b) At least two coins are tails.Exercise 9.Three fair coins are tossed.
Write the event in set notation and give the probability of the event.Refer to Exercise 8.(a) The result of the toss is heads. (b) The result of the toss is tails.Exercise 8.A two-headed coin is tossed once.
Write the event in set notation and give the probability of the event.Refer to Exercise 7.(a) Both coins show the same face. (b) At least one coin is a head.Exercise 7.Two fair coins are tossed.
Write a sample space with equally likely outcomes for the experiment.A fair die is rolled and then a fair coin is tossed.
Write a sample space with equally likely outcomes for the experiment.The spinner shown here is spun twice. 3 2.
Write a sample space with equally likely outcomes for each experiment.Slips of paper marked with the numbers 1, 2, 3, and 4 are placed in a box. A slip is drawn and set aside, its number is recorded, and then a second slip is drawn.
Write a sample space with equally likely outcomes for the experiment.Three fair coins are tossed.
Write a sample space with equally likely outcomes for the experiment.A two-headed coin is tossed once.
Write a sample space with equally likely outcomes for the experiment.Two fair coins are tossed.
Fill in the blank(s) to correctly complete each sentence.When a fair coin is tossed and a fair die is rolled, the probability of obtaining a “head” and a “3” is ________.
Fill in the blank(s) to correctly complete each sentence.When a fair coin is tossed 4 times, the probability of obtaining heads on all tosses is ___________.
Fill in the blank(s) to correctly complete each sentence.When two distinct fair dice are rolled, there are _______ possible outcomes, and the probability of each outcome is _______.
Fill in the blank(s) to correctly complete each sentence.When two different denominations of fair coins are tossed, there are ________possible outcomes, and the probability of each outcome is ______.
Fill in the blank(s) to correctly complete each sentence.When a fair die is rolled, there are ________ possible outcomes, and the probability of each outcome is ______.
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