College Algebra 1st Edition
ISBN: 9781938168383
Author: Jay Abramson
Publisher: Jay Abramson
1 Prerequisites 2 Equations And Inequalities 3 Functions 4 Linear Functions 5 Polynomial And Rational Functions 6 Exponential And Logarithmic Functions 7 Systems Of Equations And Inequalities 8 Analytic Geometry 9 Sequences, Probability And Counting Theory Chapter9: Sequences, Probability And Counting Theory
9.1 Sequences And Their Notations 9.2 Arithmetic Sequences 9.3 Geometric Sequences 9.4 Series And Their Notations 9.5 Counting Principles 9.6 Binomial Theorem 9.7 Probability Chapter Questions Section: Chapter Questions
Problem 1RE: Write the first four terms of the sequence defined by the recursive formula a1=2,an=an1+n. Problem 2RE: Evaluate 6!(53)!3! Problem 3RE: Write the first four terms of the sequence defined by the explicit formula a an=10n+3 . Problem 4RE: Write the first four terms of the sequence defined by the explicit formula an=n!n(n+1). Problem 5RE: Is the sequence 47,4721,8221,397,... arithmetic? If so, find the common difference. Problem 6RE: Is the sequence 2,4,8,16,... arithmetic? If so, find the common difference. Problem 7RE: An arithmetic sequence has the first term a1=18 and common difference d=8 . What are the first five... Problem 8RE: An arithmetic sequence has terms a3=11.7 and a8=14.6 . What is the first term? Problem 9RE: Write a recursive formula for the arithmetic sequence 20,10,0,10,... Problem 10RE: Write a recursive formula for the arithmetic sequence 0,12,1,32,... , and then find the 31stterm. Problem 11RE: Write an explicit formula for the arithmetic sequence 78,2924,3724,158,... Problem 12RE: How many terms are in the finite arithmetic sequence 12,20,28,...,172 ? Problem 13RE: Find the common ratio for the geometric sequence 2.5,5,10,20,... Problem 14RE: Is the sequence 4,16,28,40,... geometric? If so find the common ratio. If not, explain why. Problem 15RE: A geometric sequence has terms a7=16,384 and a9=262,144 . What are the first five terms? Problem 16RE: A geometric sequence has the first term a1=3 and common ratio r=12 What is the 8thterm? Problem 17RE: What are the first five terms of the geometric sequence a1=3,an=4an1 Problem 18RE: Write a recursive formula for the geometric sequence 1,13,19,127,... Problem 19RE: Write an explicit formula for the geometric sequence 15,115,145,1135,... Problem 20RE: How many terms are in the finite geometric sequence 5,53,59,...,559,049 Problem 21RE: Use summation notation to write the sum of terms 12m+5 from m=0 to m=5 . Problem 22RE: Use summation notation to write the sum that results from adding the number 13 twenty times. Problem 23RE: Use the formula for the sum of the first ii terms of an arithmetic series to find the sum of the... Problem 24RE: A ladder has 15 tapered rungs, the lengths of which increase by a common difference. The first rung... Problem 25RE: Use the formula for the sum of the first nterms of a geometric series to find S9 , for the series... Problem 26RE: The fees for the first three years of a hunting club membership are given in Table 1. If fees... Problem 27RE: Find the sum of the infinite geometric series k145(13)k=1. Problem 28RE: A ball has a bounce-back ratio 35 . of the height of the previous bounce. Write a series... Problem 29RE: Alejandro deposits $80 of his monthly earnings into an annuity that earns 6.25% annual interest,... Problem 30RE: The twins Sarah and Scott both opened retirement accounts on their 2lst birthday. Sarah deposits... Problem 31RE: How many ways are there to choose a number from the set 10,6,4,10,12,18,24,32 that is divisible by... Problem 32RE: In a group of 20 musicians, 12 play piano, 7 play trumpet, and 2 play both piano and trumpet. How... Problem 33RE: How many ways are there to construct a 4-digit code if numbers can be repeated? Problem 34RE: A palette of water color paints has 3 shades of green, 3 shades of blue, 2 shades of red, 2 shades... Problem 35RE: Calculate P(18,4) . Problem 36RE: In a group of 5 freshman, 10 sophomores, 3 juniors, and 2 seniors, how many ways can a president,... Problem 37RE: Calculate C(15,6) Problem 38RE: A coffee shop has 7 Guatemalan roasts, 4 Cuban roasts, and 10 Costa Rican roasts. How many ways can... Problem 39RE: How many subsets does the set 1,3,5,...,99 have? Problem 40RE: A day spa charges a basic day rate that includes use of a sauna, pool, and showers. For an extra... Problem 41RE: How many distinct ways can the word DEADWOOD be arranged? Problem 42RE: How many distinct rearrangements of the letters of the word DEADWOOD are there if the arrangement... Problem 43RE: Evaluate the binomial coefficient (823) . Problem 44RE: Use the Binomial Theorem to expand (3x+12y)6 Problem 45RE: Use the Binomial Theorem to write the first three terms of (2a+b)17. Problem 46RE: Find the fourth term of (3a22b)11 without fully expanding the binomial. Problem 47RE: For the following exercises, assume two die are rolled. 47. Construct a table showing the sample... Problem 48RE: For the following exercises, assume two die are rolled. 48. What is the probability that a roll... Problem 49RE: For the following exercises, assume two die are rolled. 49. What is the probability of rolling a... Problem 50RE: For the following exercises, assume two die are rolled. 50. What is the probability that a roll... Problem 51RE: For the following exercises, assume two die are rolled. 51.What is the probability that a roll... Problem 52RE: For the following exercises, assume two die are rolled. 52. What is the probability of rolling a 5... Problem 53RE: For the following exercises, assume two die are rolled. 53. What is the probability that a roll... Problem 54RE: For the following exercises, use the following data: An elementary school survey found that 350 of... Problem 55RE: For the following exercises, use the following data: An elementary school survey found that 350 of... Problem 56RE: For the following exercises, use the following data: An elementary school survey found that 350 of... Problem 57RE: For the following exercises, use the following data: An elementary school survey found that 350 of... Problem 1PT: Write the first four terms of the sequence defined by the recursive formula a=14,an=2+an12 Problem 2PT: Write the first four terms of the sequence defined by the explicit formula an=n2n1n! . Problem 3PT: Is the sequence 0.3,1.2,2.1,3,... arithmetic? If sofind the common difference. Problem 4PT: An arithmetic sequence has the first term a1=4 and common difference d=43 .What is the 6thterm? Problem 5PT: Write a recursive formula for the arithmetic sequence 2,72,5,132,... and then find the 22nd term. Problem 6PT: Write an explicit formula for the arithmetic sequence 15.6,15,14.4,13.8,... and then find the 32... Problem 7PT: Is the sequence 2,1,12,14,... . geometric? If sofind the common ratio. If not, explain why. Problem 8PT: What is the 11thterm of the geometric sequence 1.5,3,6,12,... ? Problem 9PT: Write a recursive formula for the geometric sequence 1,12,14,18,.... Problem 10PT: Write an explicit formula for the geometric sequence 4,43,49,427,.... Problem 11PT: Use summation notation to write the sum of terms 3k256k from k=3 to k=15 . Problem 12PT: A community baseball stadium has 10 seats in the first row, 13 seats in the second row, 16 seats in... Problem 13PT: Use the formula for the sum of the first n terms of a geometric series to find k=170.2(5)k1 . Problem 14PT: Find the sum of the infinite geometric series. k=113(15)k1 Problem 15PT: Rachael deposits $3,600 into a retirement fund each year. The fund earns 7.5% annual interest,... Problem 16PT: In a competition of 50 professional ballroom dancers, 22 compete in the fox-trot competition, 18... Problem 17PT: A buyer of a new sedan can custom order the car by choosing from 5 different exterior colors, 3... Problem 18PT: To allocate annual bonuses, a manager must choose his top four employees and rank them first to... Problem 19PT: A rock group needs to choose 3 songs to play at the annual Battle of the Bands. How many ways can... Problem 20PT: A self-serve frozen yogurt shop has 8 candy toppings and 4 fruit toppings to choose from. How many... Problem 21PT: How many distinct ways can the word EVANESCENCE be arranged if the anagram must end with the letter... Problem 22PT: Use the Binomial Theorem to expand (32x12y)5 . Problem 23PT: Find the seventh term of (x212)13 “without fully expanding the binomial. Problem 24PT: For the following exercises, use the spinner in Figure 1. Figure 1 24. Construct a probability model... Problem 25PT: For the following exercises, use the spinner in Figure 1. Figure 1 25. What is the probability of... Problem 26PT: For the following exercises, use the spinner in Figure 1. Figure 1 26. What is the probability of... Problem 27PT: For the following exercises, use the spinner in Figure 1. Figure 1 27. What is the probability of... Problem 28PT: For the following exercises, use the spinner in Figure 1. Figure 1 28. What is the probability of... Problem 29PT: For the following exercises, use the spinner in Figure 1. Figure 1 29. A bowl of candy holds 16... Problem 23RE: Use the formula for the sum of the first ii terms of an arithmetic series to find the sum of the...
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The arithmetic mean of the X series is X̅ = 150. The numbers in the A series were obtained by adding the number 25 to the values in the X series. So what is the arithmetic mean of the A series?
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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