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mathematics
college algebra
Intermediate Algebra 13th Edition Margaret Lial, John Hornsby, Terry McGinnis - Solutions
In Problems 13–16, find each sum. 10 Σ(-2)* k=1
In Problems 9–18, show that each sequence is geometric. Then find the common ratio and list the first four terms 3n-1 2⁰² :}
In Problems 9–18, show that each sequence is geometric. Then find the common ratio and list the first four terms. {Un} 2² 3"-1
In Problems 19–26, find the fifth term and the nth term of the geometric sequence whose first term a1 and common ratio r are given. a₁ = 0; 7
In Problems 17–19, find the indicated term in each sequence. 9th term of √2, 2√2, 3√2, ...
In Problems 23–27, prove each statement. If 0 < x < 1, then 0 < x < 1.
In Problems 23–27, prove each statement. If x 1, then x"> 1. >
In Problems 22–25, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 8 k=1 k-1
In Problems 19–26, find the fifth term and the nth term of the geometric sequence whose first term a1 and common ratio r are given. a₁ 1; r = 1 3
In Problems 19–26, find the fifth term and the nth term of the geometric sequence whose first term a1 and common ratio r are given. a₁ = √3; r = √3 a1
In Problems 19–26, find the fifth term and the nth term of the geometric sequence whose first term a1 and common ratio r are given. a₁ = 0; r = 1 TT
In Problems 1–22, use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.n3 + 2n is divisible by 3.
Use the Principle of Mathematical Induction to prove that for all natural numbers n. 5 [2 8]" = [₁ -8 -3] 4n+ 1 2n -8n 1 4n. -
In Problems 33–40, find the nth term an of each geometric sequence. When given, r is the common ratio. -3, 1, 1 1 3'9''
In Problems 33–40, find the nth term an of each geometric sequence. When given, r is the common ratio. 4, 1, 1 1 4' 16'
In Problems 23–27, prove each statement.a + b is a factor of a2n+1 + b2n+1 .
In Problems 27–32, find the indicated term of each geometric sequence.15th term of 1, -1, 1, ...
Problems 37–43 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Solve: log₂ Vx+ 5 = 4
Find the coefficient of x7 in the expansion of (x + 2)9 .
In Problems 33–40, find the nth term an of each geometric sequence. When given, r is the common ratio. 6, 18, 54, 162, . . .
In Problems 33–40, find the nth term an of each geometric sequence. When given, r is the common ratio.5, 10, 20, 40, . . .
In Problems 33–40, find the nth term an of each geometric sequence. When given, r is the common ratio. a₂ = 7; az 1 3
In Problems 33–40, find the nth term an of each geometric sequence. When given, r is the common ratio. 43 || 46 || -la 81
Problems 37–43 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Solve the system: (4x + 3y = -7 2x - 5y = 16
Chris gets paid once a month and contributes $350 each pay period into his 401(k). If Chris plans on retiring in 20 years, what will be the value of his 401(k) if the per annum rate of return of the 401(k) is 6.5% compounded monthly?
In Problems 41–46, find each sum. + + + 3″ । 9
In Problems 33–40, find the nth term an of each geometric sequence. When given, r is the common ratio.a6 = 243; r = -3
In Problems 41–46, find each sum. n k=1 3, k
In Problems 41–46, find each sum. + + 4 + + + 2"-1 4
In Problems 41–46, find each sum. -1-2-4-8 (2"-1)
In Problems 41–46, find each sum. 2 + 6/5 + + ... +21 3/5 n-1
For Problems 47–52, use a graphing utility to find the sum of each geometric sequence. 15 1й n=1 4.3"-1
In Problems 41–46, find each sum. M Σ 4-34-1 k=1
For Problems 47–52, use a graphing utility to find the sum of each geometric sequence. -1-2-4-8-... - 2¹4
For Problems 47–52, use a graphing utility to find the sum of each geometric sequence. 2 + + + ... +20 3/5 15
Problems 53–60 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. If f(x) = x² - 6 and g(x)=√x + 2, find g(f(x)) and state its domain.
In Problems 53–68, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 6 +2+ 2-3 +
In Problems 33–40, find the nth term an of each geometric sequence. When given, r is the common ratio.a2 = 7; a4 = 1575
Problems 53–60 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Simplify: (x³ +1)=x2/3 - x¹/³ (3x²) (x³ + 1)²
In Problems 53–68, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 1 3 9 + 4 16 27 64 +
Problems 53–60 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. 5 If y = x³ + 2x + C and y = 5 when x = 3, find the value of C.
Problems 37–43 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Solve: e3x-7 = 4
In Problems 53–68, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 9 + 12 + 16 + 64 3
Problems 53–60 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Find the vertical asymptotes, if any, of the graph of f(x) = 3x² (x − 3)(x + 1)
Problems 53–60 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. If f(x) x² + 1 2x + 5' point on the graph of f? find f(-2). What is the corresponding
In Problems 53–68, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. k=1 5 4 k-1
In Problems 53–68, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. IN k-1
In Problems 53–68, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. Σ *%( k=1 2/3 k−1 -1 3/
In Problems 53–68, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 8 k−1 Σ 80 k=1 (-3)*
Problems 53–60 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Solve 6x = 5x+1. Express the answer both in exact form and as a decimal rounded to three decimal
In Problems 53–68, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 00 k=1 1|2 •3k-1
In Problems 53–68, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 8 Σ 3/ k=1 IN Κ k−1
In Problems 53–68, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 18 Σ2 k=1 4 k
In Problems 69–82, determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. 2 (3 - ²/{n} 3
In Problems 53–68, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 00 k=1 3 2 3, k
In Problems 69–82, determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. 8 3 4 n
In Problems 69–82, determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. {(3)"}
In Problems 69–82, determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. {3″/2}
In Problems 69–82, determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. n {({})"}
In Problems 69–82, determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. {(-1)"}
If you have been hired at an annual salary of $42,000 and expect to receive annual increases of 3%, what will your salary be when you begin your fifth year?
Don contributes $500 at the end of each quarter to a tax-sheltered annuity (TSA). What will the value of the TSA be after the 80th deposit (20 years) if the per annum rate of return is assumed to be 5% compounded quarterly?
Ray contributes $1000 to an individual retirement account (IRA) semiannually. What will the value of the IRA be when Ray makes his 30th deposit (after 15 years) if the per annum rate of return is assumed to be 7% compounded semiannually?
The following data represent the marital status of males 18 years old and older in the U.S. in 2017. (a) Determine the number of males 18 years old and older who are widowed or divorced. (b) Determine the number of males 18 years old and older who are married, divorced, or separated. Marital
Problems 113–120 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Find the value of the determinant:. 3 1 0 -2 4 -1 0 6 -21
In Problems 15–22, use the information given in the figure.How many are in A and B? 15 A 2 3 сл со 5 15 с 2 B 10 4 U
In Problems 15–22, use the information given in the figure.How many are not in A? A 15 2 355 15 C 2 B 10 4 U
In Problems 15–22, use the information given in the figure.How many are in A and B and C? 15 A 2 35 сл со 15 с 2 B 10 4 U
The following data represent the marital status of females 18 years old and older in the U.S. in 2017 (a) Determine the number of females 18 years old and older who are divorced or separated. (b) Determine the number of females 18 years old and older who are married, widowed, or divorced. Marital
In Problems 15–22, use the information given in the figure.How many are in A or B? 15 A 2 3 сл со 5 15 C 2 В 10 4 U
Scott and Alice want to purchase a vacation home in 10 years and need $50,000 for a down payment. How much should they place in a savings account each month if the per annum rate of return is assumed to be 3.5% compounded monthly?
For a child born in 2018, the cost of a 4-year college education at a public university is projected to be $185,000. Assuming a 4.75% per annum rate of return compounded monthly, how much must be contributed to a college fund every month to have $185,000 in 18 years when the child begins college?
In Problems 15–22, use the information given in the figure.How many are in A or B or C? 15 A с со 3 5 2 2 15 С B 10 4 U
A special section in the end zone of a football stadium has 2 seats in the first row and 14 rows total. Each successive row has 2 seats more than the row before. In this particular section, the first seat is sold for 1 cent, and each following seat sells for 5% more than the previous seat. Find the
Problems 113–120 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Use the Change-of-Base Formula and a calculator to evaluate log7 62. Round the answer to three decimal
Problems 113–120 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Find the equation of the hyperbola with vertices at (-2, 0) and (2, 0), and a focus at (4, 0).
Problems 113–120 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Write the factored form of the polynomial function of smallest degree that touches the x-axis at x = 4,
Problems 113–120 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Factor completely: x4 - 29x2 + 100
Problems 113–120 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Use a graphing utility to determine the interval(s) where g(x) = x3 + 2x2 - 3.59x - 2.9 is decreasing.
Problems 36–44 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Solve the system: √x - y = 5 lx - y² = -1 2
Problems 36–44 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Graph (x - 2)2 + (y + 1)2 = 9.
Problems 36–44 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Find all the real zeros of the function: f(x) = (x - 2) (x2 - 3x - 10)
Problems 36–44 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Solve: log3 x + log3 2 = -2
Problems 36–44 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Solve: x3 = 72x
Problems 36–44 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Determine whether the infinite series converges or diverges. If it converges, find the sum. 4 + 12
Problems 36–44 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Multiply: (2x - 7) (3x2 - 5x + 4)
Problems 36–44 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Find the partial fraction decomposition: 3x2 + 15x+5 x3+2x²+x
Your friend has just been hired at an annual salary of $50,000. If she expects to receive annual increases of 4%, what will be her salary as she begins her 5th year?
Find each product. 9 7 21 36,
Simplify each expression. -12 3 4 (6.5÷3)
Rewrite each statement with > so that it uses < instead. Rewrite each statement with < so that it uses >.-5 > -10
In the decimal number 367.9412, name the digit that has each place value.(a) Tens (b) Tenths (c) Thousandths (d) Ones or units (e) Hundredths
Simplify each expression. (-5+√4)-2² -5-2
Find each product. 3100 8 24 9
Rewrite each statement with > so that it uses < instead. Rewrite each statement with < so that it uses >.-7 > -12
The following problems provide more practice on operations with fractions and decimals. Perform the indicated operations. -2.5 (0.8) (1.5)
Multiply or divide as indicated.8.04 ÷ 10
Multiply or divide as indicated.124.03 ÷ 100
On August 10, 1936, a temperature of 120°F was recorded in Ozark, Arkansas. On February 13, 1905, Gravette, Arkansas, recorded a temperature of -29°F. Express the difference between these two temperatures as a positive number. °F 100% 80% 60° 40%- 20% 0⁰- -20% -40% -60° 120⁰ -29°
The following problems provide more practice on operations with fractions and decimals. Perform the indicated operations. - 100 -0.01
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