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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

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.
For the following exercises, two coins are tossed.Find the probability of tossing at least one tail.
For the following exercises, express each geometric sum using summation notation.−1/6 + 1/12 − 1/24 + … + 1/768
To allocate annual bonuses, a manager must choose his top four employees and rank them first to fourth. In how many ways can he create the “Top-Four” list out of the 32 employees?
For the following exercises, find the specified term for the geometric sequence, given the first term and common ratio. The first term is 2, and the common ratio is 3. Find the 5th term.
For the following exercises, use the Binomial Theorem to expand each binomial.(3x − 2y)4
For the following exercises, four coins are tossed.Find the probability of tossing exactly two heads.
For the following exercises, determine whether the infinite series has a sum. If so, write the formula for the sum. If not, state the reason. 8 Σ m= m = 1 4m-1
For the following exercises, find the specified term for the geometric sequence, given the first four terms. an = {−1, 2, −4, 8, ...}. Find a12.
For the following exercises, write an explicit formula for each sequence. 4 1,,2, 1, 1, 16 5
For the following exercises, use the spinner in Figure 1.Construct a probability model showing each possible outcome and its associated probability. (Use the first letter for colors.)
For the following exercises, write an explicit formula for each sequence. 4, 7, 12, 19, 28, …
For the following exercises, write the first five terms of the geometric sequence.a1 = 7, an = 0.2an − 1
For the following exercises, use the Binomial Theorem to write the first three terms of each binomial. (a + b)17
For the following exercises, compute the value of the expression.C(7, 6)
For the following exercises, write an explicit formula for each sequence. 1-e¹ 1-e² 1-e³ 1-e4 0, 1+e²¹ 1+e³¹1+ e¹' 1 + es'
Use the formula for the sum of the first n terms of an arithmetic series to find the sum of the first eleven terms of the arithmetic series 2.5, 4, 5.5, … .
For the following exercises, four coins are tossed.Find the probability of tossing exactly two heads or at least two tails.
For the following exercises, determine whether the infinite series has a sum. If so, write the formula for the sum. If not, state the reason. Σ+(-2) k=1 k−1
For the following exercises, compute the value of the expression.C(10, 3)
For the following exercises, find the specified term given two terms from an arithmetic sequence. a1 = 33 and a7 = −15. Find a4 .
For the following exercises, four coins are tossed.Find the probability of tossing either two heads or three heads.
For the following exercises, write a recursive formula for each geometric sequence.an = {−32, −16, −8, −4, ...}
For the following exercises, use the Binomial Theorem to write the first three terms of each binomial.(a − 2b)15
Use the formula for the sum of the first n terms of a geometric series to find S9 for the series 12, 6, 3, 3/2 , …
For the following exercises, one card is drawn from a standard deck of 52 cards. Find the probability of drawing the following: A club
For the following exercises, use the spinner in Figure 1. What is the probability of landing on blue or an odd number? 6 5 7 4 Figure 1 1 3 2
The fees for the first three years of a hunting club membership are given in Table 1. If fees continue to rise at the same rate, how much will the total cost be for the first ten years of
For the following exercises, write a recursive formula for each geometric sequence.an = {14, 56, 224, 896, ...}
For the following exercises, use the Binomial Theorem to write the first three terms of each binomial.(x − 2y)8
For the following exercises, find the number of subsets in each given set.{a, b, c, … , z}
For the following exercises, use the recursive formula to write the first five terms of the arithmetic sequence. a1 = 39; an = an − 1 −3
For the following exercises, write the first five terms of the sequence. a1 = 9, an = an − 1 + n
For the following exercises, one card is drawn from a standard deck of 52 cards. Find the probability of drawing the following: A two
For the following exercises, use the following scenario. Javier makes monthly deposits into a savings account. He opened the account with an initial deposit of $50. Each month thereafter he increased
For the following exercises, write a recursive formula for each geometric sequence.an = {10, −3, 0.9, −0.27, ...}
For the following exercises, use the Binomial Theorem to write the first three terms of each binomial.(3a + b)20
For the following exercises, find the number of subsets in each given set.A set containing 5 distinct numbers, 4 distinct letters, and 3 distinct symbols
For the following exercises, use the recursive formula to write the first five terms of the arithmetic sequence.a1 = −19; an = an − 1 −1.4
For the following exercises, write the first five terms of the sequence.a1 = 3, an = (−3)an − 1
For the following exercises, one card is drawn from a standard deck of 52 cards. Find the probability of drawing the following:Six or seven
For the following exercises, use the geometric series Graph the first 7 partial sums of the series. ∞ k = 1 1 2 k
For the following exercises, use the spinner in Figure 1.What is the probability of landing on anything other than blue or an odd number? 6 5 7 4 Figure 1 1 3 2
For the following exercises, use the spinner in Figure 1.What is the probability of landing on blue? 5 7 4 Figure 1 1 3 2
For the following exercises, use the spinner in Figure 1.What is the probability of landing on an odd number? 6 5 7 4 Figure 1 1 3 2
A ladder has 15 tapered rungs, the lengths of which increase by a common difference. The first rung is 5 inches long, and the last rung is 20 inches long. What is the sum of the lengths of the rungs?
For the following exercises, find the number of subsets in each given set. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
For the following exercises, find the specified term given two terms from an arithmetic sequence.a3 = −17.1 and a10 = −15.7. Find a21.
For the following exercises, write an explicit formula for each sequence. 1, 1 1 1 1 2'4' 8 16
For the following exercises, use the following scenario. Javier makes monthly deposits into a savings account. He opened the account with an initial deposit of $50. Each month thereafter he increased
For the following exercises, write the first eight terms of the piecewise sequence. a = 11 (2n + 1)² if n is divisible by 4 2 if n is not divisible by 4 n
Write a recursive formula for the geometric sequence 1, 1/3 , 1/9 , 1/27 , …
For the following exercises, write the first eight terms of the piecewise sequence. a = 11 1 -0.6 5-¹ if n is prime or 1 2.5 (-2)-¹ if n is composite .
For the following exercises, four coins are tossed. What is the sample space?
For the following exercises, use the formula for the sum of the first n terms of each geometric sequence, and then state the indicated sum. 9 + 3 + 1 + 1/3 + 1/9
A rock group needs to choose 3 songs to play at the annual Battle of the Bands. How many ways can they choose their set if have 15 songs to pick from?
For the following exercises, use the Binomial Theorem to expand each binomial.(4x − 3y)5
For the following exercises, compute the value of the expression.P(11,5)
For the following exercises, find the specified term for the geometric sequence, given the first term and common ratio.The first term is 16 and the common ratio is − 1/3. Find the 4th term.
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 a6 = 12 and a14 = 28.
For the following exercises, use the formula for the sum of the first n terms of each geometric sequence, and then state the indicated sum. Σ5.2"-1 n=1
For the following exercises, write the first eight terms of the piecewise sequence. a = n 4(n² 2) if n ≤3 or n > 6 n²-2 4 if3
Write an explicit formula for the geometric sequence −1/5 , −1/15 , −1/45 , −1/135 , …
A self-serve frozen yogurt shop has 8 candy toppings and 4 fruit toppings to choose from. How many ways are there to top a frozen yogurt?
For the following exercises, use the Binomial Theorem to expand each binomial.(1/x + 3y)5
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 a7 = 21 and a15 = 42.
For the following exercises, use the formula for the sum of the first n terms of each geometric sequence, and then state the indicated sum. Σ64. 0.20 - 1 a=1
For the following exercises, compute the value of the expression.C(8, 5)
How many terms are in the finite geometric sequence −5, −5/3 , −5/9 , …, − 5/59,049 ?
For the following exercises, four coins are tossed.Find the probability of tossing exactly three heads.
How many distinct ways can the word EVANESCENCE be arranged if the anagram must end with the letter E?
For the following exercises, use the Binomial Theorem to expand each binomial.(x−1 + 2y−1)4
For the following exercises, find the specified term for the geometric sequence, given the first four terms. 2 2 a. = {-2, 3, -3, 2. Find a,. {-2₂ n 9' 27
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 a8 = 40 and a23 = 115.
For the following exercises, compute the value of the expression.C(12, 4)
Use summation notation to write the sum of terms 1/2 m + 5 from m = 0 to m = 5.
For the following exercises, four coins are tossed.Find the probability of tossing four heads or four tails.
For the following exercises, determine whether the infinite series has a sum. If so, write the formula for the sum. If not, state the reason. 12 + 18 + 24 + 30 + ...
Use the Binomial Theorem to expand (3/2 x − 1/2 y)5
For the following exercises, use the Binomial Theorem to expand each binomial.(√ x − √ y )5
For the following exercises, write the first five terms of the geometric sequence. a1 = −486, an = −1/3 an − 1
For the following exercises, compute the value of the expression.C(26, 3)
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 a9 = 54 and a17 = 102.
For the following exercises, write an explicit formula for each sequence.−4, 2, − 10, 14, − 34, …
For the following exercises, four coins are tossed.Find the probability of tossing all tails.
For the following exercises, four coins are tossed.Find the probability of tossing not all tails.
For the following exercises, determine whether the infinite series has a sum. If so, write the formula for the sum. If not, state the reason.2 + 1.6 + 1.28 + 1.024 + ...
For the following exercises, write the first four terms of the sequence. a = 11 2n + 1 n³
For the following exercises, use the spinner shown in Figure 3 to find the probabilities indicated.Landing on blue or a vowel O C F E Figure 3 A D B I
For the following exercises, evaluate the binomial coefficient. 200 199
For the following exercises, use the spinner shown in Figure 3 to find the probabilities indicated.Landing on yellow or a consonant O C F E Figure 3 A D B I
For the following exercises, write the first four terms of the sequence. a n n² 2n + 1
For the following exercises, write the first five terms of the arithmetic sequence given the first term and common difference.a1 = 0, d = 2/3
For the following exercises, write the first four terms of the sequence.an = −4 ⋅ (−6)n − 1
For the following exercises, use the spinner shown in Figure 3 to find the probabilities indicated.Not landing on yellow or a consonant O C F E Figure 3 A D B I
How many terms are in the finite arithmetic sequence 12, 20, 28, … , 172?
For the following exercises, express each arithmetic sum using summation notation.1/2 + 1 + 3/2 + 2 + … + 4
For the following exercises, determine whether the sequence is geometric. If so, find the common ratio.0.8, 4, 20, 100, 500, ...
For the following exercises, write the first five terms of the arithmetic series given two terms.a13 = −60, a33 = −160
For the following exercises, determine whether to use the Addition Principle or the Multiplication Principle. Then perform the calculations.How many ways are there to construct a string of 3 digits

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