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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Textbook Question
Chapter 10, Problem 10.19PE
(Mersenne prime)A prime number is called a Mersenne prime if it can be written in the form 2p – 1 for some positive integer p. Write a
(Hint: You have to use BigInteger to store the number because it is too big to be stored in long. Your program may take several hours to run.)
| p | 2^p – 1 |
| 2 | 3 |
| 3 | 7 |
| 5 | 31 |
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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 10 Solutions
Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
Ch. 10.2 - Prob. 10.2.1CPCh. 10.3 - Is the BMI class defined in Listing 10.4...Ch. 10.4 - Prob. 10.4.1CPCh. 10.4 - Prob. 10.4.2CPCh. 10.4 - Prob. 10.4.3CPCh. 10.4 - Prob. 10.4.4CPCh. 10.7 - Prob. 10.7.1CPCh. 10.7 - Prob. 10.7.2CPCh. 10.7 - How do you convert an integer into a string? How...Ch. 10.7 - Show the output of the following code: public...
Ch. 10.7 - Prob. 10.7.5CPCh. 10.8 - What are autoboxing and autounboxing? Are the...Ch. 10.8 - Show the output of the following code. public...Ch. 10.9 - What is the output of the following code? public...Ch. 10.10 - Suppose s1, s2, s3, and s4 are four strings, given...Ch. 10.10 - To create the string Welcome to Java, you may use...Ch. 10.10 - What is the output of the following code? String...Ch. 10.10 - Let s1 be Welcome and s2 be welcome Write the...Ch. 10.10 - Prob. 10.10.5CPCh. 10.10 - Prob. 10.10.6CPCh. 10.10 - Prob. 10.10.7CPCh. 10.10 - Prob. 10.10.8CPCh. 10.10 - What is wrong in the following program? 1public...Ch. 10.10 - Show the output of the following code: public...Ch. 10.10 - Show the output of the following code: public...Ch. 10.11 - Prob. 10.11.1CPCh. 10.11 - Prob. 10.11.2CPCh. 10.11 - Prob. 10.11.3CPCh. 10.11 - Prob. 10.11.4CPCh. 10.11 - Prob. 10.11.5CPCh. 10.11 - Suppose s1 and s2 are given as fot tows:...Ch. 10.11 - Show the output of the following program: public...Ch. 10 - (The Time class) Design a class named Time. The...Ch. 10 - (The BMI class) Add the following new constructor...Ch. 10 - (The MyInteger class) Design a class named...Ch. 10 - Prob. 10.4PECh. 10 - (Display the prime factors) Write a program that...Ch. 10 - (Display the prime numbers) Write a program that...Ch. 10 - Prob. 10.7PECh. 10 - Prob. 10.8PECh. 10 - (The Course class) Revise the Course class as...Ch. 10 - Prob. 10.10PECh. 10 - Prob. 10.11PECh. 10 - (Geometry: the Triangle2D class) Define the...Ch. 10 - (Geometry: the MyRectangle 2D class) Define the...Ch. 10 - (The MyDate class) Design a class named MyDate....Ch. 10 - (Geometry: the bounding rectangle) A bounding...Ch. 10 - (Divisible by 2 or 3) Find the first 10 numbers...Ch. 10 - (Square numbers) Find the first 10 square numbers...Ch. 10 - (Mersenne prime)A prime number is called a...Ch. 10 - (Approximate e) Programming Exercise 5.26...Ch. 10 - (Divisible by 5 or 6) Find the first 10 numbers...Ch. 10 - (Implement the String class) The String class is...Ch. 10 - (Implement the String class) The String class is...Ch. 10 - (Implement the Character class) The Character...Ch. 10 - (New string split method) The split method in the...Ch. 10 - (Implement the StringBuilder class) The...Ch. 10 - (Implement the StringBuilder class) The...
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