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mathematics
precalculus 1st
Precalculus 1st Edition Jay Abramson - Solutions
For the following exercises, find the indicated term of each binomial without fully expanding the binomial.The tenth term of (x − 1)12
In a group of 5 freshman, 10 sophomores, 3 juniors, and 2 seniors, how many ways can a president, vice president, and treasurer be elected?
For the following exercises, two dice are rolled, and the results are summed.Find the probability of rolling a sum greater than or equal to 15.
For the following exercises, find the indicated term of each binomial without fully expanding the binomial.The ninth term of (a − 3b2)11
For the following exercises, two dice are rolled, and the results are summed.Find the probability of rolling a sum less than 15.
Calculate C(15, 6).
For the following exercises, find the indicated term of each binomial without fully expanding the binomial.The fourth term of (x3 − 1/2 )10
A coffee shop has 7 Guatemalan roasts, 4 Cuban roasts, and 10 Costa Rican roasts. How many ways can the shop choose 2 Guatemalan, 2 Cuban, and 3 Costa Rican roasts for a coffee tasting event?
For the following exercises, two dice are rolled, and the results are summed.Find the probability of rolling a sum less than 6 or greater than 9.
For the following exercises, find the indicated term of each binomial without fully expanding the binomial.The eighth term of (y/2 + 2/x)9
How many subsets does the set {1, 3, 5, … , 99} have?
For the following exercises, two dice are rolled, and the results are summed.Find the probability of rolling a sum between 6 and 9, inclusive.
For the following exercises, use the Binomial Theorem to expand the binomial f(x) = (x + 3)4 .Then find and graph each indicated sum on one set of axes.Find and graph f1 (x), such that f1 (x) is the first term of the expansion.
A day spa charges a basic day rate that includes use of a sauna, pool, and showers. For an extra charge, guests can choose from the following additional services: massage, body scrub, manicure, pedicure, facial, and straight-razor shave. How many ways are there to order additional services at the
For the following exercises, two dice are rolled, and the results are summed.Find the probability of rolling a sum of 5 or 6.
For the following exercises, use the Binomial Theorem to expand the binomial f(x) = (x + 3)4 .Then find and graph each indicated sum on one set of axes.Find and graph f2 (x), such that f2 (x) is the sum of the first two terms of the expansion.
How many distinct ways can the word DEADWOOD be arranged?
For the following exercises, two dice are rolled, and the results are summed.Find the probability of rolling any sum other than 5 or 6.
For the following exercises, use the Binomial Theorem to expand the binomial f(x) = (x + 3)4 .Then find and graph each indicated sum on one set of axes.Find and graph f3 (x), such that f3 (x) is the sum of the first three terms of the expansion.
For the following exercises, a coin is tossed, and a card is pulled from a standard deck. Find the probability of the following: A head on the coin or a club
For the following exercises, use the Binomial Theorem to expand the binomial f(x) = (x + 3)4 .Then find and graph each indicated sum on one set of axes.Find and graph f4 (x), such that f4 (x) is the sum of the first four terms of the expansion.
Evaluate the binomial coefficient (23/8).
For the following exercises, a coin is tossed, and a card is pulled from a standard deck. Find the probability of the following:A tail on the coin or red ace
For the following exercises, use the Binomial Theorem to expand the binomial f(x) = (x + 3)4 .Then find and graph each indicated sum on one set of axes.Find and graph f5 (x), such that f5 (x) is the sum of the first five terms of the expansion.
Use the Binomial Theorem to expand (3x + 1/2 y)6 .
For the following exercises, a coin is tossed, and a card is pulled from a standard deck. Find the probability of the following:A head on the coin or a face card
Use the Binomial Theorem to write the first three terms of (2a + b)17.
For the following exercises, a coin is tossed, and a card is pulled from a standard deck. Find the probability of the following:No aces
For the following exercises, use the Binomial Theorem to expand the binomial f(x) = (x + 3)4 .Then find and graph each indicated sum on one set of axes.Findand write the answer as a binomial coefficient in the form (n/k). Prove it. Hint: Use the fact that, for any integer p, such that p ≥ 1, p! =
For the following exercises, use the Binomial Theorem to expand the binomial f(x) = (x + 3)4 .Then find and graph each indicated sum on one set of axes.In the expansion of (a + b)n , the coefficient of an − k bk is the same as the coefficient of which other term?
Find the fourth term of (3a2 − 2b)11 without fully expanding the binomial.
For the following exercises, use this scenario: a bag of M&Ms contains 12 blue, 6 brown, 10 orange, 8 yellow, 8 red, and 4 green M&Ms. Reaching into the bag, a person grabs 5 M&Ms. What is the probability of getting all blue M&Ms?
For the following exercises, use the Binomial Theorem to expand the binomial f(x) = (x + 3)4 .Then find and graph each indicated sum on one set of axes.Consider the expansion of (x + b)40. What is the exponent of b in the kth term?
For the following exercises, assume two die are rolled. Construct a table showing the sample space.
For the following exercises, use this scenario: a bag of M&Ms contains 12 blue, 6 brown, 10 orange, 8 yellow, 8 red, and 4 green M&Ms. Reaching into the bag, a person grabs 5 M&Ms.What is the probability of getting 4 blue M&Ms?
For the following exercises, assume two die are rolled. What is the probability that a roll includes a 2?
For the following exercises, use this scenario: a bag of M&Ms contains 12 blue, 6 brown, 10 orange, 8 yellow, 8 red, and 4 green M&Ms. Reaching into the bag, a person grabs 5 M&Ms.What is the probability of getting 3 blue M&Ms?
For the following exercises, use the Binomial Theorem to expand the binomial f(x) = (x + 3)4 .Then find and graph each indicated sum on one set of axes.Which expression cannot be expanded using the Binomial Theorem? Explain. a. (x2 − 2x + 1)b. (√a + 4√a − 5)8 c. (x3 + 2y2 −
For the following exercises, use this scenario: a bag of M&Ms contains 12 blue, 6 brown, 10 orange, 8 yellow, 8 red, and 4 green M&Ms. Reaching into the bag, a person grabs 5 M&Ms.What is the probability of getting no brown M&Ms?
For the following exercises, assume two die are rolled.What is the probability that a roll includes a 2 or results in a pair?
Use the following scenario for the exercises that follow: In the game of Keno, a player starts by selecting 20 numbers from the numbers 1 to 80. After the player makes his selections, 20 winning numbers are randomly selected from numbers 1 to 80. A win occurs if the player has correctly selected 3,
For the following exercises, assume two die are rolled.What is the probability that a roll doesn’t include a 2 or result in a pair?
Use the following scenario for the exercises that follow: In the game of Keno, a player starts by selecting 20 numbers from the numbers 1 to 80. After the player makes his selections, 20 winning numbers are randomly selected from numbers 1 to 80. A win occurs if the player has correctly selected 3,
For the following exercises, assume two die are rolled.What is the probability of rolling a 5 or a 6?
Use the following scenario for the exercises that follow: In the game of Keno, a player starts by selecting 20 numbers from the numbers 1 to 80. After the player makes his selections, 20 winning numbers are randomly selected from numbers 1 to 80. A win occurs if the player has correctly selected 3,
For the following exercises, use the Binomial Theorem to write the first three terms of each binomial.(2a + 4b)7
For the following exercises, use the Binomial Theorem to write the first three terms of each binomial.(x − 1)18
For the following exercises, write a recursive formula for each geometric sequence.an = {0.61, 1.83, 5.49, 16.47, ...}
For the following exercises, write the first five terms of the sequence. a₁ = -4, a a n a 1 +2n - 1 n-1 -
For the following exercises, find the number of subsets in each given set.The set of even numbers from 2 to 28
For the following exercises, use the geometric series What number does Sn seem to be approaching in the graph? Find the sum to explain why this makes sense. ∞ k = 1 1 2 k
For the following exercises, write a recursive formula for each arithmetic sequence. a = {40, 60, 80, ... }
For the following exercises, use the spinner in Figure 1. A bowl of candy holds 16 peppermint, 14 butterscotch, and 10 strawberry flavored candies. Suppose a person grabs a handful of 7 candies. What is the percent chance that exactly 3 are butterscotch? (Show calculations and round to the
A ball has a bounce-back ratio 3/5 of the height of the previous bounce. Write a series representing the total distance traveled by the ball, assuming it was initially dropped from a height of 5 feet. What is the total distance? (Hint: the total distance the ball travels on each bounce is the sum
For the following exercises, one card is drawn from a standard deck of 52 cards. Find the probability of drawing the following:Red six
For the following exercises, write a recursive formula for each geometric sequence. 11 1 1 5' 10' 60' 360'
For the following exercises, use the Binomial Theorem to write the first three terms of each binomial.(x3 − √y)8
For the following exercises, find the number of subsets in each given set.The set of two-digit numbers between 1 and 100 containing the digit 0
For the following exercises, write a recursive formula for each arithmetic sequence.a = {17, 26, 35, ... }
For the following exercises, write the first five terms of the sequence. a₁ = -1, an = (-3) -1 - 2 a n-1
Alejandro deposits $80 of his monthly earnings into an annuity that earns 6.25% annual interest, compounded monthly. How much money will he have saved after 5 years?
For the following exercises, find the indicated sum. [=v I = B Σα FI
For the following exercises, one card is drawn from a standard deck of 52 cards. Find the probability of drawing the following:An ace or a diamond
For the following exercises, write a recursive formula for each geometric sequence. H ={- -2, 4 3' 8 16 9' 27
For the following exercises, find the indicated term of each binomial without fully expanding the binomial. The fourth term of (2x − 3y)4
For the following exercises, find the distinct number of arrangements. The letters in the word “juggernaut”
For the following exercises, write the first five terms of the sequence. n ( 7 ) (¹ ¯ "v + 2) = "v '0ε = = 'v
For the following exercises, write a recursive formula for each arithmetic sequence.a = {−1, 2, 5, ... }
The twins Sarah and Scott both opened retirement accounts on their 21st birthday. Sarah deposits $4,800.00 each year, earning 5.5% annual interest, compounded monthly. Scott deposits $3,600.00 each year, earning 8.5% annual interest, compounded monthly. Which twin will earn the most interest by the
For the following exercises, find the indicated sum. 6 H = l n(n – 2)
For the following exercises, write a recursive formula for each geometric sequence. a₁ 512' 1 1 128' 32'
For the following exercises, one card is drawn from a standard deck of 52 cards. Find the probability of drawing the following:A non-ace
For the following exercises, find the indicated term of each binomial without fully expanding the binomial. The fourth term of (3x − 2y)5
For the following exercises, find the distinct number of arrangements.The letters in the word “academia”
For the following exercises, write the first eight terms of the sequence. 9₁-24¹9,-1,a₁-(2a__) (3a__) = n 71
For the following exercises, write a recursive formula for each arithmetic sequence.a = {12, 17, 22, ... }
How many ways are there to choose a number from the set { −10, −6, 4, 10, 12, 18, 24, 32} that is divisible by either 4 or 6?
For the following exercises, one card is drawn from a standard deck of 52 cards. Find the probability of drawing the following:A heart or a non-jack
For the following exercises, find the indicated sum. 17 Σκ k=1
For the following exercises, write the first five terms of the geometric sequence. an = −4 ⋅ 5n − 1
For the following exercises, find the indicated term of each binomial without fully expanding the binomial.The third term of (6x − 3y)7
For the following exercises, find the distinct number of arrangements.The letters in the word “academia” that begin and end in “a”
For the following exercises, write the first eight terms of the sequence. a, = -1, 0, = 5, 0, = 0,m_2(3 - am_i) 1 a, n-2 n-1
For the following exercises, write a recursive formula for each arithmetic sequence.a = {−15, −7, 1, ... }
In a group of 20 musicians, 12 play piano, 7 play trumpet, and 2 play both piano and trumpet. How many musicians play either piano or trumpet?
For the following exercises, two dice are rolled, and the results are summed. Construct a table showing the sample space of outcomes and sums.
For the following exercises, find the indicated sum. 2k k=1
For the following exercises, write the first five terms of the geometric sequence. a₁ n n-1 12. • (-/-) 2
For the following exercises, write the first eight terms of the sequence. a₁ = 2, a₂ = 10, a 11 2(a + 2) a n-2
For the following exercises, find the indicated term of each binomial without fully expanding the binomial.The eighth term of (7 + 5y)14
For the following exercises, two dice are rolled, and the results are summed.Find the probability of rolling a sum of 3.
For the following exercises, find the indicated term of each binomial without fully expanding the binomial.The seventh term of (a + b)11
For the following exercises, two dice are rolled, and the results are summed.Find the probability of rolling at least one four or a sum of 8.
A palette of water color paints has 3 shades of green, 3 shades of blue, 2 shades of red, 2 shades of yellow, and 1 shade of black. How many ways are there to choose one shade of each color?
For the following exercises, find the specified term for the arithmetic sequence given the first term and common difference.First term is 7, common difference is 8, find the 7th term.
For the following exercises, compute the value of the expression.P(9, 6)
For the following exercises, find the first term given two terms from an arithmetic sequence.Find the first term or a1 of an arithmetic sequence if a11 = 11 and a21 = 16.
For the following exercises, write a recursive formula for each geometric sequence. an = {−1, 5, −25, 125, ...}
For the following exercises, write the first eight terms of the piecewise sequence. a n n² 2n + 1 n²5 ifn> 5 if n < 5
For the following exercises, find the specified term for the arithmetic sequence given the first term and common difference.First term is 4, common difference is 5, find the 4th term.
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