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Questions and Answers of College Algebra

Find the indicated term of each binomial expansion. (k-1); third term
Find the indicated term of each binomial expansion. (r4)¹¹; fourth term
Write each series using summation notation.7 + 8 + 9 + 10 + 11
Find the sum, if it exists, of the terms of each infinite geometric sequence. a₁ = 6, r = 1 3
At the end of each quarter, a 50-year-old woman puts $1200 in a retirement account that pays 2% interest compounded quarterly. When she reaches age 60, she withdraws the entire amount and places it
Evaluate S6 for each arithmetic sequence.a1 = 6, d = 3
Write each series using summation notation.-2 + 4 - 8 + 16 - 32
Solve each problem. Evaluate. (a) 9! (b) 0! (c) 10C4
At the end of each quarter, a 45-year-old man puts $1500 in a retirement account that pays 1.5% interest compounded quarterly. When he reaches age 55, he withdraws the entire amount and places it in
Evaluate S6 for each arithmetic sequence.a1 = 5, d = 4
Write each series using summation notation.-1 + 2 - 3 + 4 - 5 + 6
Evaluate S6 for each arithmetic sequence.a1 = 7, d = -3
Find the indicated term of each binomial expansion. The middle term of (x² + 2y)6
Find the indicated term of each binomial expansion. The middle term of (m³ + 2y)8
Find the sum, if it exists, of the terms of each infinite geometric sequence. a₁ 10, r = 1 5
Find the sum, if it exists, of the terms of each infinite geometric sequence. a₁ = 1000, r = 1 10
When asked to write the series -1 - 4 - 9 - 16 - 25 using summation notation, a student incorrectly wrote the following.Give the correct summation notation. 5 Σ(-1) t=1
Find the indicated term of each binomial expansion. The term with x³y²4 in (3x³-4y²)5
Find the indicated term of each binomial expansion. The term with x³y² in (2x² + 3y)6
Write each series using summation notation.1 + 4 + 9 + 16
Find the sum, if it exists, of the terms of each infinite geometric sequence. a₁ = 8800, r: 3 5
Evaluate S6 for each arithmetic sequence.a1 = -5, d = -4
Find the sum, if it exists, of the terms of each infinite geometric sequence. 2/3 a 100
Write each series using summation notation.1 + 16 + 81 + 256
Use a formula for Sn to evaluate each series. 10 Σ (8i – 5) i=1
Evaluate S6 for each arithmetic sequence.a = 0.9, d = -0.5
Find the sum, if it exists, of the terms of each infinite geometric sequence. 00 i=1 3 6
Use a formula for Sn to evaluate each series. +?= | 2
Use a formula for Sn to evaluate each series. 17 Σ (31 − 1) i=1
Find the sum, if it exists, of the terms of each infinite geometric sequence. i=1 16 (-¹) (-²)' 3 8
Find the sum, if it exists, of the terms of each infinite geometric sequence.
Evaluate S6 for each arithmetic sequence.a1 = 2.4, d = 0.7
The number of mutual funds operating in the United States each year during the period 2012 through 2016 is given in the table. To the nearest whole number, what was the average number of mutual funds
When dropped from a certain height, a ball rebounds to 3/5 of the original height. How high will the ball rebound after the fourth bounce if it was dropped from a height of 10 ft? Round to the
When asked to write the first five terms of the sequence defined by an = 5n - 1, a student incorrectly wrote the following.4 + 9 + 14 + 19 + 24Give the correct answer.
Find the arithmetic mean for each set of values.8, 11, 14, 9, 7, 6, 8
Use a formula for Sn to evaluate each series. (1-4)3 i=1
Find the arithmetic mean for each set of values.10, 12, 8, 19, 23, 12
Find the arithmetic mean for each set of values.55. 5, 9, 8, 2, 4, 7, 3, 2, 0
Find the arithmetic mean for each set of values.2, 1, 4, 8, 3, 7, 10, 8, 0
A seating section in a theater-in-the-round has 20 seats in the first row, 22 in the second row, 24 in the third row, and so on for 25 rows. How many seats are there in the last row? How many seats
Use the remainder theorem to evaluate ƒ(k). f(x) = 2x³ 4x² + 5x - 3; k= 2 -
Find the fourth term in the expansion of (3x+ - zv²).
Use synthetic division to divide. x5x² + x³x²+x-2 x-1
Use synthetic division to divide. x² + x² + x³ + x² + x + 3 x + 1
Use synthetic division to divide. -3x5+2x4 - 5x³ - 6x² - 1 x + 2
Use synthetic division to divide. 2x52x³ + 3x² - 24x - 2 x 2
Use synthetic division to divide. x3 3x² + 5x - 1 x-5
Use synthetic division to divide. -3x5 - 3x4 + 5x³ - 6x² + 3 x + 1
Use synthetic division to divide. 3x5x4 84x² 12x + 3 x - 3
Use synthetic division to divide. 5x36x² + 3x + 14 x + 1
Use synthetic division to divide. x3 + 2x² - 4x + 3 x - 4
Use synthetic division to divide. 4x²5x20 x - 4
Use synthetic division to divide. 4x³ 3x²+2x - 3 x-1
Use synthetic division to divide. x² + 4x 6 x-5
Use synthetic division to divide. x² - 3x + 5 x+1
Use synthetic division to divide. 3x² + 5x - 12 x + 3
Use synthetic division to divide. 2x² + 8x + 13 x + 2
Use synthetic division to divide. 4x² + 19x5 x + 5
A student attempted to dividesynthetically by setting up the division as follows.This is incorrect. Give the correct setup and the answer. 4x³ + 2x² + 6x by x + 2
Use synthetic division to divide. x² + 4x - 21 x-3
A student attempted to dividesynthetically by setting up the division as follows.This is incorrect. Give the correct setup and the answer. 4x³ + 2x² + 6 by x+2
Use synthetic division to divide. x² - 6x + 5 x-1
Fill in each blank with the appropriate response.In arithmetic, the result of the division can be written 19 = 5. 3 5) 19 15 4 +
Fill in each blank with the appropriate response.In algebra, the result of the division x + 3 x - 1)x² + 2x + 3 x² X 3x + 3 3x - 3 6 can be written x² + 2x + 3 = (x-1)()+.
If the result of Exercise 67 seems hard to believe, look at it this way: Use long division to find the repeating decimal representations of 1/3 and 2/3. Then line up the decimals vertically and add
Choose the letter of the correct setup to perform synthetic division on the indicated quotient. x³ 3x² + 2 x-1 A. 11 -3 2 B. -11 -3 2 C. 1)1 -3 02 D. 1)-1 3 0 -2
Choose the letter of the correct setup to perform synthetic division on the indicated quotient. x² + 3x - 6 x-2 A. -2)1 3 -6 B. -2)-1 -3 -3 6 C. 2)1 3 -6 D. 2)-1 -3 6
The repeating decimal 0.99999 . . . can be written as the sum of the terms of a geometric sequence with a1 = 0.9 and r = 0.1.Because |0.1| Use this formula to find a more common way of writing the
A child builds with blocks, placing 35 blocks in the first row, 31 in the second row, 27 in the third row, and so on. Continuing this pattern, can he end with a row containing exactly 1 block? If
A stack of firewood has 28 pieces on the bottom, 24 on top of those, then 20, and so on. If there are 108 pieces of wood, how many rows are there?
A vehicle depreciates by 20% of its value each year. If it cost $35,000 new, what is its value after 6 yr?
A machine depreciates by 1/4 of its value each year. If it cost $50,000 new, what is its value after 8 yr?
Constantin has started on a fitness program. He plans to jog 10 min per day for the first week and then to add 10 min per day each week until he is jogging an hour each day. In which week will this
A growing community increases its consumption of electricity 2% per yr.(a) If the community uses 1.1 billion units of electricity now, how much will it use 5 yr from now? Round to the nearest
In a certain community, the consumption of electricity has increased about 6% per yr.(a) If the community uses 1.1 billion units of electricity now, how much will it use 5 yr from now? Round to the
Malik is offered a job with a starting salary of $2000 per month with a guaranteed increase of $100 every four months for 3 yr. What will Malik’s salary be at the end of that time?
A tracer dye is injected into a system with an ingestion and an excretion. After 1 hr, 2/3 of the dye is left. At the end of the second hour, 2/3 of the remaining dye is left, and so on. If one unit
Nancy’s aunt has promised to deposit $1 in her account on the first day of her birthday month, $2 on the second day, $3 on the third day, and so on for 30 days. How much will this amount to over
Suppose that Cherian is offered a job at $1600 per month with a guaranteed increase of $50 every six months for 5 yr. What will Cherian’s salary be at the end of that time?
A particular substance decays in such a way that it loses half its weight each day. In how many days will 256 g of the substance be reduced to 32 g? How much of the substance is left after 10 days?
Billy’s aunt deposits $2 in his savings account on the first day of February, $4 on the second day, $6 on the third day, and so on for the entire month. How much will this amount to? (Assume that
Use a formula for Sn to evaluate each series. 2000 Στ i=1
A fully wound yo-yo has a string 40 in. long. It is allowed to drop, and on its first rebound it returns to a height 15 in. lower than its original height. Assuming that this “rebound ratio”
The total assets of mutual funds operating in the United States, in billions of dollars, for each year during the period 2012 through 2016 are shown in the table. What were the average assets per
Use a formula for Sn to evaluate each series. 250 Σ: i=1
A fully wound yo-yo is dropped the length of its 30-in. string. Each time it drops, it returns to 1/2 of its original height. How far does it travel before it comes to rest?
Solve each application.A ball is dropped from a height of 20 m, and on each bounce it returns to 3/4 of its previous height. How far will the ball travel before it comes to rest?
Add or subtract as indicated. Write answers in lowest terms as needed. 9 1 3
Find each absolute value and simplify if needed. |9-21|- τι
Find each absolute value and simplify if needed. |-9|- |-3|
Add or subtract as indicated. Write answers in lowest terms as needed. 4 15 + 5
Add or subtract as indicated. Write answers in lowest terms as needed. 7 1 + 12 12
Perform the indicated operations. 3 (14) 6-4
Find each absolute value and simplify if needed. |-16| + |14|
Find each absolute value and simplify if needed. -|10-9|
Perform the indicated operations. 6+[(9-) -ε-] - ｶー
Frank’s grandson was asked to evaluate the following expression.Frank gave the answer as 8, but his grandson gave the answer as 14. The grandson explained that the answer is 14 because of the
Complete each statement so that the indicated property is illustrated. Simplify each answer if possible. 5x + 9y = (commutative property)
Add or subtract as indicated. Write answers in lowest terms as needed. 3 5 + 16 16

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