College Algebra Real Mathematics Real People Edition 7
18th Edition
ISBN: 9781305752368
Author: Ron Larson
Publisher: CENGAGE C
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Chapter 8, Problem 15PS
(a)
To determine
To calculate: The odds in favor and the odds against to choose a blue marble, if a bag has three blue marbles and seven yellow marbles. It is given that the ratio of the probability that the event occurs to the probability that the event doesn’t occur represents the odds in favor for the event to occur and the reciprocal of the ratio represents the odds against for the event to occur.
(b)
To determine
To calculate: The total number of marbles in a bag, given that a bag contains six red marbles and the odds against a red marble are
(c)
To determine
The formula for the probability of an event, in terms of the odds in favor of the event to occur.
(d)
To determine
The formula for the odds in favor of an event in terms of the probability of the event.
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What is the domain and range, thank you !!
Chapter 8 Solutions
College Algebra Real Mathematics Real People Edition 7
Ch. 8.1 - Write the first four terms of the sequence given...Ch. 8.1 - Write the first four terms of the sequence given...Ch. 8.1 - Write an expression for the apparent nth term an...Ch. 8.1 - Write the first five terms of the sequence defined...Ch. 8.1 - Prob. 5ECPCh. 8.1 - Write the first five terms of the sequence given...Ch. 8.1 - Simplify the factorial expression 4!(n+1)!3!n!.Ch. 8.1 - Find the sum i=14(4i+1).Ch. 8.1 - For the series i=1510i find (a) the fourth partial...Ch. 8.1 - Prob. 10ECP
Ch. 8.1 - Prob. 1ECh. 8.1 - Prob. 2ECh. 8.1 - Prob. 3ECh. 8.1 - Prob. 4ECh. 8.1 - Fill in the blanks For the sum i=1nai,1 is the of...Ch. 8.1 - Prob. 6ECh. 8.1 - Writing the Terms of a Sequence In Exercises 7-22,...Ch. 8.1 - Writing the Terms of a Sequence In Exercises 7-22,...Ch. 8.1 - Writing the Terms of a Sequence In Exercises 7-22,...Ch. 8.1 - Writing the Terms of a Sequence In Exercises 7-22,...Ch. 8.1 - Prob. 11ECh. 8.1 - Writing the Terms of a Sequence In Exercises 7-22,...Ch. 8.1 - Writing the Terms of a Sequence In Exercises 7-22,...Ch. 8.1 - Writing the Terms of a Sequence In Exercises 7-22,...Ch. 8.1 - Writing the Terms of a Sequence In Exercises 7-22,...Ch. 8.1 - Prob. 16ECh. 8.1 - Writing the Terms of a Sequence In Exercises 7-22,...Ch. 8.1 - Prob. 18ECh. 8.1 - Writing the Terms of a Sequence In Exercises 7-22,...Ch. 8.1 - Prob. 20ECh. 8.1 - Writing the Terms of a Sequence In Exercises 7-22,...Ch. 8.1 - Prob. 22ECh. 8.1 - Finding a Term of a Sequence In Exercises 23-26,...Ch. 8.1 - Finding a Term of a Sequence In Exercises 23-26,...Ch. 8.1 - Finding a Term of a Sequence In Exercises 23-26,...Ch. 8.1 - Finding a Term of a Sequence In Exercises 23-26,...Ch. 8.1 - Prob. 27ECh. 8.1 - Prob. 28ECh. 8.1 - Prob. 29ECh. 8.1 - Graphing the Terms of a Sequence In Exercises...Ch. 8.1 - Prob. 31ECh. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - Prob. 35ECh. 8.1 - Prob. 36ECh. 8.1 - Finding the n th Term of a Sequence In Exercises...Ch. 8.1 - Finding the n th Term of a Sequence In Exercises...Ch. 8.1 - Finding the n th Term of a Sequence In Exercises...Ch. 8.1 - Finding the n th Term of a Sequence In Exercises...Ch. 8.1 - Prob. 41ECh. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Prob. 46ECh. 8.1 - Prob. 47ECh. 8.1 - Prob. 48ECh. 8.1 - Finding the n th Term of a Sequence In Exercises...Ch. 8.1 - Prob. 50ECh. 8.1 - Writing the Terms of a Recursive Sequence In...Ch. 8.1 - Writing the Terms of a Recursive Sequence In...Ch. 8.1 - Writing the Terms of a Recursive Sequence In...Ch. 8.1 - Prob. 54ECh. 8.1 - Prob. 55ECh. 8.1 - Prob. 56ECh. 8.1 - Prob. 57ECh. 8.1 - Fibonacci Sequence In Exercises 57 and 58, use the...Ch. 8.1 - Writing the Terms of a Sequence Involving...Ch. 8.1 - Prob. 60ECh. 8.1 - Writing the Terms of a Sequence Involving...Ch. 8.1 - Prob. 62ECh. 8.1 - Simplifying a Factorial Expression In Exercises...Ch. 8.1 - Prob. 64ECh. 8.1 - Simplifying a Factorial Expression In Exercises...Ch. 8.1 - Prob. 66ECh. 8.1 - In Exercises 67-74, find the sum. i=043i2Ch. 8.1 - Prob. 68ECh. 8.1 - Prob. 69ECh. 8.1 - In Exercises 67-74, find the sum. i=152i1Ch. 8.1 - Prob. 71ECh. 8.1 - Prob. 72ECh. 8.1 - Prob. 73ECh. 8.1 - Prob. 74ECh. 8.1 - Finding a Sum In Exercises 75-78, use a graphing...Ch. 8.1 - Finding a Sum In Exercises 75-78, use a graphing...Ch. 8.1 - Finding a Sum In Exercises 75-78, use a graphing...Ch. 8.1 - Prob. 78ECh. 8.1 - Prob. 79ECh. 8.1 - Prob. 80ECh. 8.1 - Prob. 81ECh. 8.1 - Prob. 82ECh. 8.1 - Prob. 83ECh. 8.1 - Prob. 84ECh. 8.1 - Prob. 85ECh. 8.1 - Prob. 86ECh. 8.1 - Prob. 87ECh. 8.1 - Prob. 88ECh. 8.1 - Prob. 89ECh. 8.1 - Prob. 90ECh. 8.1 - Prob. 91ECh. 8.1 - Prob. 92ECh. 8.1 - Prob. 93ECh. 8.1 - Prob. 94ECh. 8.1 - Prob. 95ECh. 8.1 - Prob. 96ECh. 8.1 - Prob. 97ECh. 8.1 - Prob. 98ECh. 8.1 - Prob. 99ECh. 8.1 - Prob. 100ECh. 8.1 - Prob. 101ECh. 8.1 - Prob. 102ECh. 8.1 - Prob. 103ECh. 8.1 - Prob. 104ECh. 8.1 - Error Analysis In Exercises 105 and 106, describe...Ch. 8.1 - Prob. 106ECh. 8.1 - Cube A 333 cube is made up of 27 unit cubes (a...Ch. 8.2 - Write the first four terms of the arithmetic...Ch. 8.2 - Find a formula for the nth term of the arithmetic...Ch. 8.2 - The 8th term of an arithmetic sequence is 25, and...Ch. 8.2 - Find the 10th term of the arithmetic sequence that...Ch. 8.2 - Find the sum: 40 + 37 + 34 + 31 + 28 + 25 + 22.Ch. 8.2 - Find the sum of the integers (a) from 1 to 35 and...Ch. 8.2 - Find the 120th partial sum of the arithmetic...Ch. 8.2 - Find the 30th partial sum of the arithmetic...Ch. 8.2 - A company sells $160,000 worth of printing paper...Ch. 8.2 - Prob. 1ECh. 8.2 - Fill in the blanks The nth term of an arithmetic...Ch. 8.2 - Fill in the blanks When you know the nth term of...Ch. 8.2 - Prob. 4ECh. 8.2 - In Exercises 5-12, determine whether the sequence...Ch. 8.2 - Determining Whether a Sequence Is Arithmetic In...Ch. 8.2 - Determining Whether a Sequence Is Arithmetic In...Ch. 8.2 - Prob. 8ECh. 8.2 - Determining Whether a Sequence Is Arithmetic In...Ch. 8.2 - Prob. 10ECh. 8.2 - Determining Whether a Sequence Is Arithmetic In...Ch. 8.2 - Determining Whether a Sequence Is Arithmetic In...Ch. 8.2 - Writing the Terms of a Sequence In Exercises...Ch. 8.2 - Prob. 14ECh. 8.2 - Writing the Terms of a Sequence In Exercises...Ch. 8.2 - Prob. 16ECh. 8.2 - Writing the Terms of a Sequence In Exercises...Ch. 8.2 - Prob. 18ECh. 8.2 - Writing the Terms of a Sequence In Exercises...Ch. 8.2 - Prob. 20ECh. 8.2 - Finding the nth Term In Exercises 21-30, find a...Ch. 8.2 - Prob. 22ECh. 8.2 - Finding the nth Term In Exercises 21-30, find a...Ch. 8.2 - Prob. 24ECh. 8.2 - Finding the nth Term In Exercises 21-30, find a...Ch. 8.2 - Prob. 26ECh. 8.2 - Finding the nth Term In Exercises 21-30, find a...Ch. 8.2 - Prob. 28ECh. 8.2 - Finding the nth Term In Exercises 21-30, find a...Ch. 8.2 - Prob. 30ECh. 8.2 - Writing the Terms of an Arithmetic Sequence In...Ch. 8.2 - Prob. 32ECh. 8.2 - Writing the Terms of an Arithmetic Sequence In...Ch. 8.2 - Prob. 34ECh. 8.2 - Writing the Terms of an Arithmetic SequenceIn...Ch. 8.2 - Writing the Terms of an Arithmetic Sequence In...Ch. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Prob. 39ECh. 8.2 - Prob. 40ECh. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Prob. 44ECh. 8.2 - Sum of a Finite Arithmetic Sequence In Exercises...Ch. 8.2 - Prob. 46ECh. 8.2 - Prob. 47ECh. 8.2 - Sum of a Finite Arithmetic Sequence In Exercises...Ch. 8.2 - Prob. 49ECh. 8.2 - Prob. 50ECh. 8.2 - Partial Sum of an Arithmetic Sequence In Exercises...Ch. 8.2 - Prob. 52ECh. 8.2 - Partial Sum of an Arithmetic Sequence In Exercises...Ch. 8.2 - Prob. 54ECh. 8.2 - Finding a Sum In Exercises 55-60, find the partial...Ch. 8.2 - Prob. 56ECh. 8.2 - Finding a Sum In Exercises 55-60, find the partial...Ch. 8.2 - Prob. 58ECh. 8.2 - Finding a Sum In Exercises 55-60, find the partial...Ch. 8.2 - Prob. 60ECh. 8.2 - Prob. 61ECh. 8.2 - Prob. 62ECh. 8.2 - Matching an Arithmetic Sequence with Its Graph In...Ch. 8.2 - Prob. 64ECh. 8.2 - Prob. 65ECh. 8.2 - Prob. 66ECh. 8.2 - Prob. 67ECh. 8.2 - Prob. 68ECh. 8.2 - Prob. 69ECh. 8.2 - Prob. 70ECh. 8.2 - Seating Capacity Determine the seating capacity of...Ch. 8.2 - A triangular brick wall is made by cutting some...Ch. 8.2 - Falling Object An object with negligible air...Ch. 8.2 - Prize Money A county fair is holding a baked goods...Ch. 8.2 - Total Sales An entrepreneur sells $15,000 worth of...Ch. 8.2 - Borrowing Money You borrow $5000 from your parents...Ch. 8.2 - Business The table shows the net numbers of new...Ch. 8.2 - Prob. 78ECh. 8.2 - Prob. 79ECh. 8.2 - Prob. 80ECh. 8.2 - Prob. 81ECh. 8.2 - Prob. 82ECh. 8.2 - Prob. 83ECh. 8.2 - Prob. 84ECh. 8.2 - Prob. 85ECh. 8.2 - Prob. 86ECh. 8.2 - Prob. 87ECh. 8.3 - Write the first four terms of the geometric...Ch. 8.3 - Prob. 2ECPCh. 8.3 - Find the 12th term of the geometric sequence whose...Ch. 8.3 - Find a formula for the nth term of the geometric...Ch. 8.3 - The second term of a geometric sequence is 6, and...Ch. 8.3 - Find the sum . i=11020.25i1Ch. 8.3 - Find each sum. a. n=050.5n b. 5+1+0.2+0.04+...Ch. 8.3 - An investor deposits $70 on the first day of each...Ch. 8.3 - Prob. 1ECh. 8.3 - Prob. 2ECh. 8.3 - Fill in the blanks. The sum of a finite geometric...Ch. 8.3 - Prob. 4ECh. 8.3 - Prob. 5ECh. 8.3 - In Exercises 5-12, determine whether the sequence...Ch. 8.3 - In Exercises 5-12, determine whether the sequence...Ch. 8.3 - In Exercises 5-12, determine whether the sequence...Ch. 8.3 - Prob. 9ECh. 8.3 - In Exercises 5-12, determine whether the sequence...Ch. 8.3 - Prob. 11ECh. 8.3 - In Exercises 5-12, determine whether the sequence...Ch. 8.3 - Prob. 13ECh. 8.3 - In Exercises 13-22, write the first five terms of...Ch. 8.3 - Prob. 15ECh. 8.3 - In Exercises 13-22, write the first five terms of...Ch. 8.3 - Prob. 17ECh. 8.3 - In Exercises 13-22, write the first five terms of...Ch. 8.3 - Prob. 19ECh. 8.3 - Prob. 20ECh. 8.3 - Prob. 21ECh. 8.3 - Prob. 22ECh. 8.3 - In Exercises 23-32, write an expression for the...Ch. 8.3 - In Exercises 23-32, write an expression for the...Ch. 8.3 - Prob. 25ECh. 8.3 - In Exercises 23-32, write an expression for the...Ch. 8.3 - Prob. 27ECh. 8.3 - In Exercises 23-32, write an expression for the...Ch. 8.3 - Prob. 29ECh. 8.3 - Prob. 30ECh. 8.3 - In Exercises 23-32, write an expression for the...Ch. 8.3 - In Exercises 23-32, write an expression for the...Ch. 8.3 - Prob. 33ECh. 8.3 - Writing the nth Term of a Geometric Sequence In...Ch. 8.3 - Prob. 35ECh. 8.3 - Prob. 36ECh. 8.3 - Prob. 37ECh. 8.3 - Writing the nth Term of a Geometric Sequence In...Ch. 8.3 - Prob. 39ECh. 8.3 - Finding a Term of a Geometric Sequence In...Ch. 8.3 - Prob. 41ECh. 8.3 - Finding a Term of a Geometric Sequence In...Ch. 8.3 - Prob. 43ECh. 8.3 - Finding a Term of a Geometric Sequence In...Ch. 8.3 - Prob. 45ECh. 8.3 - Prob. 46ECh. 8.3 - Matching a Geometric Sequence with Its Graph In...Ch. 8.3 - Matching a Geometric Sequence with Its Graph In...Ch. 8.3 - Prob. 49ECh. 8.3 - Matching a Geometric Sequence with Its Graph In...Ch. 8.3 - Prob. 51ECh. 8.3 - Prob. 52ECh. 8.3 - Prob. 53ECh. 8.3 - Prob. 54ECh. 8.3 - Sum of a Finite Geometric Sequence In Exercises...Ch. 8.3 - Sum of a Finite Geometric Sequence In Exercises...Ch. 8.3 - Prob. 57ECh. 8.3 - Sum of a Finite Geometric Sequence In Exercises...Ch. 8.3 - Prob. 59ECh. 8.3 - Prob. 60ECh. 8.3 - Prob. 61ECh. 8.3 - Prob. 62ECh. 8.3 - Prob. 63ECh. 8.3 - Prob. 64ECh. 8.3 - Using Summation Notation In Exercises 65-68, use...Ch. 8.3 - Prob. 66ECh. 8.3 - Using Summation Notation In Exercises 65-68, use...Ch. 8.3 - Using Summation Notation In Exercises 65-68, use...Ch. 8.3 - Prob. 69ECh. 8.3 - In Exercises 69-78, find the sum of the infinite...Ch. 8.3 - Prob. 71ECh. 8.3 - In Exercises 69-78, find the sum of the infinite...Ch. 8.3 - Prob. 73ECh. 8.3 - Prob. 74ECh. 8.3 - Prob. 75ECh. 8.3 - Prob. 76ECh. 8.3 - Prob. 77ECh. 8.3 - Prob. 78ECh. 8.3 - Prob. 79ECh. 8.3 - Prob. 80ECh. 8.3 - Prob. 81ECh. 8.3 - Prob. 82ECh. 8.3 - Depreciation A tool and die company buys a machine...Ch. 8.3 - Prob. 84ECh. 8.3 - An investor deposits P dollars on the first day of...Ch. 8.3 - Prob. 86ECh. 8.3 - Multiplier Effect In Exercises 87 and 88, use the...Ch. 8.3 - Prob. 88ECh. 8.3 - Geometry The sides of a square are 27 inches in...Ch. 8.3 - Distance A ball is dropped from a height of 6 feet...Ch. 8.3 - Salary An investment firm has a job opening with a...Ch. 8.3 - Prob. 92ECh. 8.3 - Prob. 93ECh. 8.3 - Prob. 94ECh. 8.3 - Prob. 95ECh. 8.3 - Prob. 96ECh. 8.4 - Find the statement Pk+1 for each given statement...Ch. 8.4 - Prob. 2ECPCh. 8.4 - Prob. 3ECPCh. 8.4 - Prob. 4ECPCh. 8.4 - Prob. 5ECPCh. 8.4 - Prob. 6ECPCh. 8.4 - Prob. 7ECPCh. 8.4 - Prob. 8ECPCh. 8.4 - Prob. 1ECh. 8.4 - Prob. 2ECh. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - In Exercises 5-10, find the statement pk+1 for the...Ch. 8.4 - Prob. 8ECh. 8.4 - Prob. 9ECh. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Prob. 12ECh. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - Prob. 15ECh. 8.4 - Prob. 16ECh. 8.4 - Prob. 17ECh. 8.4 - Prob. 18ECh. 8.4 - Using Mathematical Induction In Exercises 11-24,...Ch. 8.4 - Prob. 20ECh. 8.4 - Prob. 21ECh. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - Prob. 25ECh. 8.4 - Prob. 26ECh. 8.4 - Prob. 27ECh. 8.4 - Prob. 28ECh. 8.4 - Prob. 29ECh. 8.4 - Prob. 30ECh. 8.4 - Prob. 31ECh. 8.4 - Prob. 32ECh. 8.4 - Prob. 33ECh. 8.4 - Prob. 34ECh. 8.4 - Prob. 35ECh. 8.4 - Prob. 36ECh. 8.4 - Prob. 37ECh. 8.4 - Prob. 38ECh. 8.4 - Prob. 39ECh. 8.4 - Prob. 40ECh. 8.4 - Prob. 41ECh. 8.4 - Prob. 42ECh. 8.4 - Prob. 43ECh. 8.4 - Prob. 44ECh. 8.4 - Prob. 45ECh. 8.4 - Prob. 46ECh. 8.4 - Prob. 47ECh. 8.4 - Prob. 48ECh. 8.4 - Prob. 49ECh. 8.4 - Prob. 50ECh. 8.4 - Prob. 51ECh. 8.4 - Prob. 52ECh. 8.4 - Prob. 53ECh. 8.4 - Prob. 54ECh. 8.4 - Prob. 55ECh. 8.4 - Prob. 56ECh. 8.4 - Finding a Linear or Quadratic Model In Exercises...Ch. 8.4 - Prob. 58ECh. 8.4 - Prob. 59ECh. 8.4 - Prob. 60ECh. 8.4 - Linear Model, Quadratic Model, or Neither? In...Ch. 8.4 - Prob. 62ECh. 8.4 - Prob. 63ECh. 8.4 - Prob. 64ECh. 8.4 - Prob. 65ECh. 8.4 - Prob. 66ECh. 8.4 - Prob. 67ECh. 8.4 - Prob. 68ECh. 8.4 - Prob. 69ECh. 8.4 - Prob. 70ECh. 8.4 - Prob. 71ECh. 8.4 - Prob. 72ECh. 8.4 - Prob. 73ECh. 8.4 - Prob. 74ECh. 8.4 - Prob. 75ECh. 8.4 - Prob. 76ECh. 8.4 - Prob. 77ECh. 8.4 - Prob. 78ECh. 8.5 - Find each binomial coefficient....Ch. 8.5 - Prob. 2ECPCh. 8.5 - Prob. 3ECPCh. 8.5 - Prob. 4ECPCh. 8.5 - Prob. 5ECPCh. 8.5 - Prob. 6ECPCh. 8.5 - Prob. 7ECPCh. 8.5 - Prob. 1ECh. 8.5 - Prob. 2ECh. 8.5 - Prob. 3ECh. 8.5 - Prob. 4ECh. 8.5 - Finding a Binomial Coefficient In Exercises 5-12,...Ch. 8.5 - Prob. 6ECh. 8.5 - Finding a Binomial Coefficient In Exercises 5-12,...Ch. 8.5 - Prob. 8ECh. 8.5 - Finding a Binomial Coefficient In Exercises 5-12,...Ch. 8.5 - Prob. 10ECh. 8.5 - Finding a Binomial Coefficient In Exercises 5-12,...Ch. 8.5 - Prob. 12ECh. 8.5 - Using Pascal’s Triangle In Exercises 13-16,...Ch. 8.5 - Prob. 14ECh. 8.5 - Using Pascal’s Triangle In Exercises 13-16,...Ch. 8.5 - Prob. 16ECh. 8.5 - Expanding a Binomial In Exercises 17-24, use the...Ch. 8.5 - Prob. 18ECh. 8.5 - Expanding a Binomial In Exercises 17-24, use the...Ch. 8.5 - Prob. 20ECh. 8.5 - Expanding a Binomial In Exercises 17-24, use the...Ch. 8.5 - Prob. 22ECh. 8.5 - Expanding a Binomial In Exercises 17-24, use the...Ch. 8.5 - Prob. 24ECh. 8.5 - Expanding an Expression In Exercises 25-38, expand...Ch. 8.5 - Prob. 26ECh. 8.5 - Expanding an Expression In Exercises 25-38, expand...Ch. 8.5 - Prob. 28ECh. 8.5 - Expanding an Expression In Exercises 25-38, expand...Ch. 8.5 - Expanding an Expression In Exercises 25-38, expand...Ch. 8.5 - Expanding an Expression In Exercises 25-38, expand...Ch. 8.5 - Expanding an Expression In Exercises 25-38, expand...Ch. 8.5 - Expanding an Expression In Exercises 25-38, expand...Ch. 8.5 - Prob. 34ECh. 8.5 - Prob. 35ECh. 8.5 - Prob. 36ECh. 8.5 - Prob. 37ECh. 8.5 - Prob. 38ECh. 8.5 - Prob. 39ECh. 8.5 - Prob. 40ECh. 8.5 - Prob. 41ECh. 8.5 - Prob. 42ECh. 8.5 - Prob. 43ECh. 8.5 - Prob. 44ECh. 8.5 - Finding a Term In Exercises 39-46, find the...Ch. 8.5 - Prob. 46ECh. 8.5 - Prob. 47ECh. 8.5 - Prob. 48ECh. 8.5 - Finding a Coefficient In Exercises 47-54, find the...Ch. 8.5 - Prob. 50ECh. 8.5 - Finding a Coefficient In Exercises 47-54, find the...Ch. 8.5 - Prob. 52ECh. 8.5 - Prob. 53ECh. 8.5 - Prob. 54ECh. 8.5 - Expanding an Expression In Exercises 55-60, use...Ch. 8.5 - Prob. 56ECh. 8.5 - Prob. 57ECh. 8.5 - Prob. 58ECh. 8.5 - Prob. 59ECh. 8.5 - Prob. 60ECh. 8.5 - Simplifying a Difference Quotient In Exercises...Ch. 8.5 - Prob. 62ECh. 8.5 - Prob. 63ECh. 8.5 - Prob. 64ECh. 8.5 - Prob. 65ECh. 8.5 - Prob. 66ECh. 8.5 - Prob. 67ECh. 8.5 - Prob. 68ECh. 8.5 - Expanding a Complex Number In Exercises 67-72, use...Ch. 8.5 - Prob. 70ECh. 8.5 - Prob. 71ECh. 8.5 - Prob. 72ECh. 8.5 - Prob. 73ECh. 8.5 - Prob. 74ECh. 8.5 - Approximation In Exercises 73-76, use the Binomial...Ch. 8.5 - Prob. 76ECh. 8.5 - Prob. 77ECh. 8.5 - Prob. 78ECh. 8.5 - Probability In Exercises 77-80, consider n...Ch. 8.5 - Prob. 80ECh. 8.5 - Prob. 81ECh. 8.5 - Prob. 82ECh. 8.5 - Finding a Pattern Describe the pattern formed by...Ch. 8.5 - Prob. 84ECh. 8.5 - Prob. 85ECh. 8.5 - Prob. 86ECh. 8.5 - Prob. 87ECh. 8.5 - Prob. 88ECh. 8.5 - Prob. 89ECh. 8.5 - Prob. 90ECh. 8.5 - Prob. 91ECh. 8.5 - Prob. 92ECh. 8.5 - Prob. 93ECh. 8.5 - Prob. 94ECh. 8.5 - Prob. 95ECh. 8.5 - In Exercises 93-96, prove the property for all...Ch. 8.5 - Binomial Coefficients and Pascal’s Triangle...Ch. 8.6 - In Example 1, how many different ways can you...Ch. 8.6 - In Example 2, how many different ways can you...Ch. 8.6 - A combination lock will open when you select the...Ch. 8.6 - A product’s catalog number is made up of one...Ch. 8.6 - How many permutations of the letters W, X, Y, and...Ch. 8.6 - A coin club has five members. In how many...Ch. 8.6 - In how many distinguishable ways can the letters...Ch. 8.6 - In how many different ways can two letters be...Ch. 8.6 - In three-card poker, a hand consists of three...Ch. 8.6 - In Example 10, the team must consist of six boys...Ch. 8.6 - Fill in the blanks. The states that when there...Ch. 8.6 - Prob. 2ECh. 8.6 - Prob. 3ECh. 8.6 - Prob. 4ECh. 8.6 - Prob. 5ECh. 8.6 - Prob. 6ECh. 8.6 - Random Selection In Exercises 7-14, determine the...Ch. 8.6 - Prob. 8ECh. 8.6 - Random Selection In Exercises 7-14, determine the...Ch. 8.6 - Prob. 10ECh. 8.6 - Random Selection In Exercises 7-14, determine the...Ch. 8.6 - Prob. 12ECh. 8.6 - Random Selection In Exercises 7-14, determine the...Ch. 8.6 - Prob. 14ECh. 8.6 - Prob. 15ECh. 8.6 - Job Applicants A small college needs two...Ch. 8.6 - Prob. 17ECh. 8.6 - Physiology In a physiology class, a student must...Ch. 8.6 - True-False Exam In how many ways can you answer a...Ch. 8.6 - True-False Exam In how many ways can you answer a...Ch. 8.6 - License Plate Numbers In the state of...Ch. 8.6 - License Plate Numbers In a certain state, each...Ch. 8.6 - Three-Digit Numbers How many three-digit numbers...Ch. 8.6 - Prob. 24ECh. 8.6 - Prob. 25ECh. 8.6 - Prob. 26ECh. 8.6 - Prob. 27ECh. 8.6 - Single File In how many orders can four girls and...Ch. 8.6 - Prob. 29ECh. 8.6 - Prob. 30ECh. 8.6 - Evaluating Pnr In Exercises 31-34, evaluate Pnr....Ch. 8.6 - Prob. 32ECh. 8.6 - Evaluating Pnr In Exercises 31-34, evaluate Pnr....Ch. 8.6 - Prob. 34ECh. 8.6 - Evaluating Pnr In Exercises 35-38, use a graphing...Ch. 8.6 - Prob. 36ECh. 8.6 - Prob. 37ECh. 8.6 - Prob. 38ECh. 8.6 - Kidney Donors A patient with end-stage kidney...Ch. 8.6 - Choosing Officers From a pool of 12 candidates,...Ch. 8.6 - Batting Order A baseball coach is creating a...Ch. 8.6 - Prob. 42ECh. 8.6 - Prob. 43ECh. 8.6 - Prob. 44ECh. 8.6 - Prob. 45ECh. 8.6 - Prob. 46ECh. 8.6 - Prob. 47ECh. 8.6 - Prob. 48ECh. 8.6 - Evaluating Cnr In Exercises 49-52, evaluate Cnr...Ch. 8.6 - Prob. 50ECh. 8.6 - Evaluating Cnr In Exercises 49-52, evaluate Cnr...Ch. 8.6 - Prob. 52ECh. 8.6 - Evaluating Cnr In Exercises 53-56, use a graphing...Ch. 8.6 - Prob. 54ECh. 8.6 - Prob. 55ECh. 8.6 - Prob. 56ECh. 8.6 - Prob. 57ECh. 8.6 - Forming an Experimental Group To conduct an...Ch. 8.6 - Jury Selection In how many different ways can a...Ch. 8.6 - Committee Members A U.S. Senate Committee has 14...Ch. 8.6 - Prob. 61ECh. 8.6 - Prob. 62ECh. 8.6 - Defective Units A shipment of 25 television sets...Ch. 8.6 - Prob. 64ECh. 8.6 - Prob. 65ECh. 8.6 - Job Applicants An employer interviews 12 people...Ch. 8.6 - Forming a Committee A local college is forming a...Ch. 8.6 - Prob. 68ECh. 8.6 - Geometry In Exercises 69-72, find the number of...Ch. 8.6 - Prob. 70ECh. 8.6 - Prob. 71ECh. 8.6 - Prob. 72ECh. 8.6 - Geometry Three points that are not collinear...Ch. 8.6 - Lottery Powerball is a lottery game that is...Ch. 8.6 - Solving an Equation In Exercises 75-82, solve for...Ch. 8.6 - Solving an Equation In Exercises 75-82, solve for...Ch. 8.6 - Prob. 77ECh. 8.6 - Prob. 78ECh. 8.6 - Prob. 79ECh. 8.6 - Prob. 80ECh. 8.6 - Prob. 81ECh. 8.6 - Prob. 82ECh. 8.6 - True or False? In Exercises 83 and 84, determine...Ch. 8.6 - Prob. 84ECh. 8.6 - Prob. 85ECh. 8.6 - Prob. 86ECh. 8.6 - Prob. 87ECh. 8.6 - Prob. 88ECh. 8.6 - Prob. 89ECh. 8.6 - Prob. 90ECh. 8.6 - Prob. 91ECh. 8.7 - Find the sample space for the experiment. You toss...Ch. 8.7 - a. You toss three coins. What is the probability...Ch. 8.7 - You toss two six-sided dice. What is the...Ch. 8.7 - Show that the probability of drawing a club at...Ch. 8.7 - In Example 5, what is the probability that an...Ch. 8.7 - In Pennsylvania’s Cash 5 game, a player chooses...Ch. 8.7 - You draw one card at random from a standard deck...Ch. 8.7 - In Example 8, what is the probability that an...Ch. 8.7 - A random number generator selects two integers...Ch. 8.7 - In Example 10, researchers selected five people at...Ch. 8.7 - A manufacturer has determined that a machine...Ch. 8.7 - Prob. 1ECh. 8.7 - Prob. 2ECh. 8.7 - Prob. 3ECh. 8.7 - Prob. 4ECh. 8.7 - Prob. 5ECh. 8.7 - Prob. 6ECh. 8.7 - Prob. 7ECh. 8.7 - Match the probability formula with the correct...Ch. 8.7 - Finding a Sample Space In Exercises 9-14, find the...Ch. 8.7 - Prob. 10ECh. 8.7 - Finding a Sample Space In Exercises 9-14, find the...Ch. 8.7 - Prob. 12ECh. 8.7 - Prob. 13ECh. 8.7 - Prob. 14ECh. 8.7 - Tossing a Coin In Exercises 15-20, find the...Ch. 8.7 - Prob. 16ECh. 8.7 - Prob. 17ECh. 8.7 - Prob. 18ECh. 8.7 - Prob. 19ECh. 8.7 - Prob. 20ECh. 8.7 - Prob. 21ECh. 8.7 - Prob. 22ECh. 8.7 - Drawing a Card In Exercises 21-24, find the...Ch. 8.7 - Prob. 24ECh. 8.7 - Tossing a Die In Exercises 25-30, find the...Ch. 8.7 - Prob. 26ECh. 8.7 - Prob. 27ECh. 8.7 - Prob. 28ECh. 8.7 - Tossing a Die In Exercises 25-30, find the...Ch. 8.7 - Prob. 30ECh. 8.7 - Prob. 31ECh. 8.7 - Prob. 32ECh. 8.7 - Prob. 33ECh. 8.7 - Prob. 34ECh. 8.7 - Unemployment In 2015, there were approximately 8.3...Ch. 8.7 - Political Poll An independent polling organization...Ch. 8.7 - Education In a high school graduating class of 128...Ch. 8.7 - Prob. 38ECh. 8.7 - Prob. 39ECh. 8.7 - Prob. 40ECh. 8.7 - Prob. 41ECh. 8.7 - Payroll Error A payroll clerk addresses five...Ch. 8.7 - Prob. 43ECh. 8.7 - Card Game The deck for a card game contains 108...Ch. 8.7 - Prob. 45ECh. 8.7 - Prob. 46ECh. 8.7 - Shipment A shipment of 12 microwave ovens contains...Ch. 8.7 - PIN Code ATM personal identification number (PIN)...Ch. 8.7 - Random Number Generator A random number generator...Ch. 8.7 - Flexible Work Hours In a recent survey, people...Ch. 8.7 - Probability of a Complement In Exercises 51-54,...Ch. 8.7 - Prob. 52ECh. 8.7 - Prob. 53ECh. 8.7 - Prob. 54ECh. 8.7 - Prob. 55ECh. 8.7 - Prob. 56ECh. 8.7 - Prob. 57ECh. 8.7 - Prob. 58ECh. 8.7 - Backup System A space vehicle has an independent...Ch. 8.7 - Backup Vehicle A fire department keeps two rescue...Ch. 8.7 - Roulette American roulette is a game in which a...Ch. 8.7 - Prob. 62ECh. 8.7 - Geometry You and a friend agree to meet at your...Ch. 8.7 - Prob. 64ECh. 8.7 - Prob. 65ECh. 8.7 - Prob. 66ECh. 8.7 - Prob. 67ECh. 8.7 - HOW DO YOU SEE IT? The circle graphs show the...Ch. 8 - Exercises 1-4, write the first five terms of the...Ch. 8 - Exercises 1-4, write the first five terms of the...Ch. 8 - Exercises 1-4, write the first five terms of the...Ch. 8 - Exercises 1-4, write the first five terms of the...Ch. 8 - Prob. 5RECh. 8 - Finding the nth Term of a Sequence In Exercises...Ch. 8 - Prob. 7RECh. 8 - Finding the nth Term of a Sequence In Exercises...Ch. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Prob. 17RECh. 8 - Finding the Sum of an Infinite Series In Exercises...Ch. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Prob. 23RECh. 8 - Prob. 24RECh. 8 - Prob. 25RECh. 8 - Prob. 26RECh. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Prob. 30RECh. 8 - Prob. 31RECh. 8 - Sum of a Finite Arithmetic Sequence Find the sum...Ch. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RECh. 8 - Prob. 36RECh. 8 - Job Offer The starting salary for a job is $43,800...Ch. 8 - Baling Hay In the first two trips baling hay...Ch. 8 - Determining Whether a Sequence Is Geometric In...Ch. 8 - Prob. 40RECh. 8 - Determining Whether a Sequence Is Geometric In...Ch. 8 - Prob. 42RECh. 8 - Prob. 43RECh. 8 - Prob. 44RECh. 8 - Prob. 45RECh. 8 - Prob. 46RECh. 8 - Prob. 47RECh. 8 - Prob. 48RECh. 8 - Prob. 49RECh. 8 - Prob. 50RECh. 8 - Sum of a Finite Geometric Sequence In Exercises...Ch. 8 - Prob. 52RECh. 8 - Prob. 53RECh. 8 - Prob. 54RECh. 8 - Prob. 55RECh. 8 - Prob. 56RECh. 8 - Prob. 57RECh. 8 - Prob. 58RECh. 8 - Prob. 59RECh. 8 - Prob. 60RECh. 8 - Prob. 61RECh. 8 - Prob. 62RECh. 8 - Depreciation A paper manufacturer buys a machine...Ch. 8 - Prob. 64RECh. 8 - Prob. 65RECh. 8 - Prob. 66RECh. 8 - Prob. 67RECh. 8 - Prob. 68RECh. 8 - Finding a Formula for a Finite Sum In Exercises...Ch. 8 - Finding a Formula for a Finite Sum In Exercises...Ch. 8 - Prob. 71RECh. 8 - Prob. 72RECh. 8 - Prob. 73RECh. 8 - Prob. 74RECh. 8 - Prob. 75RECh. 8 - Prob. 76RECh. 8 - Prob. 77RECh. 8 - Prob. 78RECh. 8 - Prob. 79RECh. 8 - Prob. 80RECh. 8 - Prob. 81RECh. 8 - Prob. 82RECh. 8 - Prob. 83RECh. 8 - Prob. 84RECh. 8 - Prob. 85RECh. 8 - Random Selection In Exercises 85 and 86, determine...Ch. 8 - Prob. 87RECh. 8 - Prob. 88RECh. 8 - Prob. 89RECh. 8 - Prob. 90RECh. 8 - Jury Selection In how many different ways can a...Ch. 8 - Menu Choices A local sandwich shop offers five...Ch. 8 - Prob. 93RECh. 8 - Bookshelf Order A child returns a five-volume set...Ch. 8 - Prob. 95RECh. 8 - Opinion Poll In a survey, a sample of college...Ch. 8 - Prob. 97RECh. 8 - Prob. 98RECh. 8 - Prob. 99RECh. 8 - Prob. 100RECh. 8 - Prob. 101RECh. 8 - Prob. 102RECh. 8 - Prob. 103RECh. 8 - Prob. 104RECh. 8 - Prob. 105RECh. 8 - Prob. 106RECh. 8 - Prob. 107RECh. 8 - Prob. 108RECh. 8 - Prob. 1TCh. 8 - Write an expression for the apparent nth term (an)...Ch. 8 - Write the next three terms of the series. Then...Ch. 8 - The 5th term of an arithmetic sequence is 45, and...Ch. 8 - The second term of a geometric sequence is 14, and...Ch. 8 - In Exercises 6-9, find the sum. i=1502i2+5Ch. 8 - Prob. 7TCh. 8 - Prob. 8TCh. 8 - In Exercises 6-9, find the sum. n=113nCh. 8 - Use mathematical induction to prove the formula...Ch. 8 - Use the Binomial Theorem to write the expansion of...Ch. 8 - Expand 3(x2)5+4(x2)3 by using Pascal’s Triangle to...Ch. 8 - Prob. 13TCh. 8 - In Exercises 14 and 15, evaluate each expression....Ch. 8 - In Exercises 14 and 15, evaluate each expression....Ch. 8 - Prob. 16TCh. 8 - Eight people are going for a ride in a boat that...Ch. 8 - You attend a karaoke night and hope to hear your...Ch. 8 - You and three of your friends are at a party....Ch. 8 - Prob. 20TCh. 8 - Prob. 1CTCh. 8 - Prob. 2CTCh. 8 - Prob. 3CTCh. 8 - Prob. 4CTCh. 8 - A custom-blend bird seed is made by mixing two...Ch. 8 - Prob. 6CTCh. 8 - Prob. 7CTCh. 8 - Prob. 8CTCh. 8 - In Exercises 8 and 9, sketch the graph of the...Ch. 8 - Sketch the region corresponding to the system of...Ch. 8 - Prob. 11CTCh. 8 - Prob. 12CTCh. 8 - Prob. 13CTCh. 8 - Prob. 14CTCh. 8 - Prob. 15CTCh. 8 - Prob. 16CTCh. 8 - Prob. 17CTCh. 8 - Prob. 18CTCh. 8 - Prob. 19CTCh. 8 - Prob. 20CTCh. 8 - Prob. 21CTCh. 8 - Prob. 22CTCh. 8 - Prob. 23CTCh. 8 - Prob. 24CTCh. 8 - Prob. 25CTCh. 8 - Write the first five terms of the sequence...Ch. 8 - Prob. 27CTCh. 8 - Find the 16th partial sum of the arithmetic...Ch. 8 - Prob. 29CTCh. 8 - Prob. 30CTCh. 8 - Prob. 31CTCh. 8 - Prob. 32CTCh. 8 - Prob. 33CTCh. 8 - In Exercises 34-37, evaluate the expression. P143Ch. 8 - Use the Binomial Theorem to write the expansion of...Ch. 8 - Prob. 36CTCh. 8 - Prob. 37CTCh. 8 - Prob. 38CTCh. 8 - Prob. 39CTCh. 8 - There are 10 applicants for three sales positions...Ch. 8 - On a game show, a contestant is given the digits...Ch. 8 - Prob. 1PSCh. 8 - Prob. 2PSCh. 8 - Greek Mythology Can the Greek hero Achilles,...Ch. 8 - Prob. 4PSCh. 8 - Prob. 5PSCh. 8 - Sequences of Powers the following sequence of...Ch. 8 - Prob. 7PSCh. 8 - Prob. 8PSCh. 8 - Pentagonal Numbers The numbers 1, 5, 12, 22, 35,...Ch. 8 - Prob. 10PSCh. 8 - Prob. 11PSCh. 8 - Prob. 12PSCh. 8 - Prob. 13PSCh. 8 - Prob. 14PSCh. 8 - Prob. 15PSCh. 8 - Prob. 16PS
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- Assume a bivariate patch p(u, v) over the unit square [0, 1]² that is given as a tensor product patch where u-sections (u fixed to some constant û; v varying across [0, 1]) are quadratic polynomials Pu:û(v) = p(û, v) while v-sections are lines pv:ô (u) = p(u, v). The boundary lines pv:o(u) and pv:1 (u) are specified by their end points p(0,0) 0.8 and p(1,0) 0.2 as well as p(0, 1) 0.3 and p(1, 1) = 0.8. The boundary quadratics pu:o(v) and pu:1 (v) interpolate p(0,0.5) = 0.1 and p(1, 0.5) = 0.9 in addition to the above given four corner-values. = = = Use Pu:û(v) = (1, v, v² ) Mq (Pu:û(0), Pu:û (0.5), Pu:û(1)) with Ma = 1 0 0 -3 4-1 2 4 2 (Pv:ô as well as pu: (u) = (1, u) M₁ (pv:v (0), P: (1)) with M₁ = = (19) 0 to formulate p(u, v) using the "geometric input" G with G = = (P(0,0%) p(0,0) p(0,0.5) p(0,1) ) = ( 0.39 0.8 0.1 0.3 0.2 0.9 0.8 p(1,0) p(1, 0.5) p(1, 1) See the figure below for (left) a selection of iso-lines of p(u, v) and (right) a 3D rendering of p(u, v) as a height surface…arrow_forwardO Functions Composition of two functions: Domain and... Two functions ƒ and g are defined in the figure below. 76 2 8 5 7 8 19 8 9 Domain of f Range of f Domain of g Range of g 3/5 Anthony Find the domain and range of the composition g.f. Write your answers in set notation. (a) Domain of gof: ☐ (b) Range of gof: ☐ Х Explanation Check 0,0,... Español لكا ©2025 McGraw Hill LLC. All Rights Reserved Torms of lico Privacy Contor Accessibility.arrow_forwardTwo functions ƒ and g are defined in the figure below. g 6 6 7 8 8 8 9 Domain of f Range of f Domain of g Range of g Find the domain and range of the composition g.f. Write your answers in set notation. (a) Domain of gof: (b) Range of gof: ☐ ☑ 0,0,...arrow_forward
- Done Oli ○ Functions Composition of two functions: Domain and range Two functions 0 g 3 4 6 www-awy.aleks.com g and ƒ are defined in the figure below. 8 8 9 Domain of g Range of g Domain of f Range of f 0/5 Anthony Find the domain and range of the composition f.g. Write your answers in set notation. (a) Domain of fog: ☐ (b) Range of fog: ☐ Х Explanation Check 0,0,... Español © 2025 McGraw HillLLC. AIL Rights Reserved Terms of Use | Privacy Center Accessibilityarrow_forwardUse the graph of the function y = g(x) below to answer the questions. y' -5 -4 4- 3- 27 -2 -3+ -4 x 4 (a) Is g(-2) negative? Yes No (b) For which value(s) of x is g(x) > 0? Write your answer using interval notation. ☐ (c) For which value(s) of x is g(x) = 0? If there is more than one value, separate them with commas. 0,0... (0,0) (0,0) (0,0) (0,0) OVO 0arrow_forwardIt is given that E4E3E2E1A=⎡⎣⎢⎢⎢−1002−40488⎤⎦⎥⎥⎥. Here the matrices E4, E3, E2, and, E1 are: E1=⎡⎣⎢⎢⎢100010008⎤⎦⎥⎥⎥E2=⎡⎣⎢⎢⎢100010−501⎤⎦⎥⎥⎥E3=⎡⎣⎢⎢⎢1000−10001⎤⎦⎥⎥⎥E4=⎡⎣⎢⎢⎢001010100⎤⎦⎥⎥⎥arrow_forward
- It is given that E4E3E2E1A=⎡⎣⎢⎢⎢−1002−40488⎤⎦⎥⎥⎥. Here the matrices E4, E3, E2, and, E1 are: E1=⎡⎣⎢⎢⎢100010008⎤⎦⎥⎥⎥E2=⎡⎣⎢⎢⎢100010−501⎤⎦⎥⎥⎥E3=⎡⎣⎢⎢⎢1000−10001⎤⎦⎥⎥⎥E4=⎡⎣⎢⎢⎢001010100⎤⎦⎥⎥⎥ What is the determinant of A?arrow_forwardUse the graph of the function y = f(x) below to answer the questions. 4 3- 2+ 1 -5 -4 -3 -2 -1 3 -1+ -2+ -3+ -4- -5+ (a) Isf (3) negative? Yes No (b) For which value(s) of x is f(x) = 0? If there is more than one value, separate them with commas. (c) For which value(s) of x is f(x) ≤0? Write your answer using interval notation.arrow_forwardName: Date: Transformations of Quadratic Functions y=a(x-h)²+k Describe all transformations for each quadratic function. 1. 2. -2 2 -4 2 2arrow_forward
- 5:45 Done ⚫ myopenmath.com Oli Score on last try: 0 of 12 pts. See Details for more. > Next question You can retry this question. below 384 Draw a graph that models the connecting relationships in the floorplan below. The vertices represent the rooms and the edges represent doorways connecting the rooms. Vertex D represents the outdoors. D A B C Is it possible to find a path through the house that uses each doorway once? If so, enter the sequence of rooms(vertices) visited, for example ABCDA. If it is not possible, enter DNE. DCBACD Question Help: ☑Video 1 > Video 2 Submit Questionarrow_forwardUse the graph of the function y = f(x) below to answer the questions. У 5- 4- 3- 2+ 1- 4 -3 -2 -1 3 4 -N -2 -3- -4 -5- (a) Isf(1) positive? Yes No (b) For which value(s) of x is f(x) > 0? Write your answer using interval notation. (c) For which value(s) of x is f(x) = 0? If there is more than one value, separate them with commas. 0,0,... (0,0) (0,0) (0,0) (0,0) QUO 0arrow_forwardConsider the following Gauss elimination: What is the determinant of A ?arrow_forward
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Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Bayes' Theorem 1: Introduction and conditional probability; Author: Dr Nic's Maths and Stats;https://www.youtube.com/watch?v=lQVkXfJ-rpU;License: Standard YouTube License, CC-BY
What is Conditional Probability | Bayes Theorem | Conditional Probability Examples & Problems; Author: ACADGILD;https://www.youtube.com/watch?v=MxOny_1y2Q4;License: Standard YouTube License, CC-BY
Bayes' Theorem of Probability With Tree Diagrams & Venn Diagrams; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=OByl4RJxnKA;License: Standard YouTube License, CC-BY
Bayes' Theorem - The Simplest Case; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=XQoLVl31ZfQ;License: Standard Youtube License