Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
11th Edition
ISBN: 9780134670942
Author: Y. Daniel Liang
Publisher: PEARSON
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Chapter 7, Problem 7.28PE
(Math: combinations) Write a
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By dragging statements from the left column to the right column below, give a proof by induction of the following statement:
an
=
= 9" - 1 is a solution to the recurrence relation an = 9an-18 with ao
=
: 0.
The correct proof will use 8 of the statements below.
Statements to choose from:
Note that a₁ =
9a0 + 8.
Now assume that P(n) is true for all n ≥ 0.
Your Proof: Put chosen statements in order in this
column and press the Submit Answers button.
Let P(n) be the predicate, "a = 9″ – 1".
απ = 90 − 1 =
Note that
Let P(n) be the predicate, "an
9" - 1 is a
solution to the recurrence relation an = 9an-1 +8
with ao = 0."
-
Now assume that P(k + 1) is true.
Thus P(k) is true for all k.
Thus P(k+1) is true.
Then ak+1
=
9ak +8, so P(k + 1) is true.
= 1 − 1 = 0, as required.
Then = 9k — 1.
ak
Now assume that P(k) is true for an arbitrary
integer k ≥ 1.
By the recurrence relation, we have
ak+1 =
ak+1 =
= 9ak + 8 = 9(9k − 1) + 8
This simplifies to
9k+19+8 = 9k+1 − 1
Then 9k+1 − 1 = 9(9*…
Given the following request to an AI chatbot, which response is more accurate? (You should use Google to verify that the factual claims in each response are accurate.)
Prompt
Is this true? The first recorded use of the phrase "when pigs fly" in print is in a 1616 play by Ben Jonson called "The Devil is an Ass," in which a character says, "When pigs fly, good-night!!"
Response
Response A
Response B
Yes, that's true! The phrase "when pigs fly" indeed appears in Ben Jonson's 1616 play The Devil is an Ass and was said during the second act in a conversation between Fitzdottrel and Pug. The phrase was first used to express skepticism or disbelief, suggesting that something is as unlikely to happen as the fanciful idea of pigs flying. This usage is often cited as one of the earliest instances of the phrase in print.
The claim that the phrase "when pigs fly" was first recorded in Ben Jonson's 1616 play "The Devil is an Ass" is not accurate. There is no evidence from the…
This is for my Computer Organization & Assembly Language Class
Chapter 7 Solutions
Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
Ch. 7.2 - Prob. 7.2.1CPCh. 7.2 - Prob. 7.2.2CPCh. 7.2 - What is the output of the following code? int x =...Ch. 7.2 - Indicate true or false for the following...Ch. 7.2 - Which of the following statements are valid? a....Ch. 7.2 - Prob. 7.2.6CPCh. 7.2 - What is the array index type? What is the lowest...Ch. 7.2 - Write statements to do the following: a. Create an...Ch. 7.2 - What happens when your program attempts to access...Ch. 7.2 - Identify and fix the errors in the following code:...
Ch. 7.2 - What is the output of the following code? 1....Ch. 7.4 - Will the program pick four random cards if you...Ch. 7.5 - Use the arraycopy method to copy the following...Ch. 7.5 - Prob. 7.5.2CPCh. 7.7 - Suppose the following code is written to reverse...Ch. 7.8 - Prob. 7.8.1CPCh. 7.8 - Prob. 7.8.2CPCh. 7.9 - Prob. 7.9.1CPCh. 7.9 - Prob. 7.9.2CPCh. 7.10 - If high is a very large integer such as the...Ch. 7.10 - Prob. 7.10.2CPCh. 7.10 - Prob. 7.10.3CPCh. 7.11 - Prob. 7.11.1CPCh. 7.11 - How do you modify the selectionSort method in...Ch. 7.12 - What types of array can be sorted using the...Ch. 7.12 - To apply java.util.Arrays.binarySearch (array,...Ch. 7.12 - Show the output of the following code: int[] list1...Ch. 7.13 - This book declares the main method as public...Ch. 7.13 - Show the output of the following program when...Ch. 7 - (Assign grades) Write a program that reads student...Ch. 7 - (Reverse the numbers entered) Write a program that...Ch. 7 - (Count occurrence of numbers) Write a program that...Ch. 7 - (Analyze scores) Write a program that reads an...Ch. 7 - (Print distinct numbers) Write a program that...Ch. 7 - (Revise Listing 5.1 5, PrimeNumber.java) Listing...Ch. 7 - (Count single digits) Write a program that...Ch. 7 - (Average an array) Write two overloaded methods...Ch. 7 - (Find the smallest element) Write a method that...Ch. 7 - Prob. 7.10PECh. 7 - (Statistics: compute deviation) Programming...Ch. 7 - (Reverse an array) The reverse method in Section...Ch. 7 - Prob. 7.13PECh. 7 - Prob. 7.14PECh. 7 - 7 .15 (Eliminate duplicates) Write a method that...Ch. 7 - (Execution time) Write a program that randomly...Ch. 7 - Prob. 7.17PECh. 7 - (Bubble sort) Write a sort method that uses the...Ch. 7 - (Sorted?) Write the following method that returns...Ch. 7 - (Revise selection sort) In Listing 7 .8, you used...Ch. 7 - (Sum integers) Write a program that passes an...Ch. 7 - (Find the number of uppercase letters in a string)...Ch. 7 - (Game: locker puzzle) A school bas 100 lockers and...Ch. 7 - (Simulation: coupon collectors problem) Coupon...Ch. 7 - (Algebra: solve quadratic equations) Write a...Ch. 7 - (Strictly identical arrays) The arrays 1ist1 and...Ch. 7 - (Identical arrays) The arrays 1ist1 and 1ist2 are...Ch. 7 - (Math: combinations) Write a program that prompts...Ch. 7 - (Game: pick four cards) Write a program that picks...Ch. 7 - (Pattern recognition: consecutive four equal...Ch. 7 - (Merge two sorted Lists) Write the following...Ch. 7 - (Partition of a list) Write the following method...Ch. 7 - Prob. 7.33PECh. 7 - (Sort characters in a string) Write a method that...Ch. 7 - (Game: hangman) Write a hangman game that randomly...Ch. 7 - (Game: Eight Queens) The classic Eight Queens...Ch. 7 - Prob. 7.37PE
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