Lottery game application Program plan: Import necessary package. Create a class “Lottery”, Define the method “main ()”, Declare and initialize the necessary variables. Generate the three random numbers. Combine three random numbers into a single three digit number. Get the first digit entered into the first dialog box. Assign the integer value returned form the method “parseInt()”. Get the second digit entered into the second dialog box. Assign the integer value returned form the method “parseInt()”. Get the third digit entered into the third dialog box. Assign the integer value returned form the method “parseInt()”. Check whether the first, second and third digit is equal to the first, second and third random number generated respectively, If it is true, set the match count to “4”. Otherwise, check whether the first digit is equal to the first random number generated, If it is true, increment the match count by “1”. Set the first random value to “99”. Otherwise, check whether the first digit is equal to the second random number generated, If it is true, increment the match count by “1”. Set the first random value to “99”. Otherwise, check whether the first digit is equal to the third random number generated, If it is true, increment the match count by “1”. Set the first random value to “99”. Check whether the second digit is equal to the first random number generated, If it is true, increment the match count by “1”. Set the first random value to “99”. Otherwise, check whether the second digit is equal to the second random number generated, If it is true, increment the match count by “1”. Set the first random value to “99”. Otherwise, check whether the second digit is equal to the third random number generated, If it is true, increment the match count by “1”. Set the first random value to “99”. Check whether the third digit is equal to the first random number generated, If it is true, increment the match count by “1”. Set the first random value to “99”. Otherwise, check whether the third digit is equal to the second random number generated, If it is true, increment the match count by “1”. Set the first random value to “99”. Otherwise, check whether the third digit is equal to the third random number generated, If it is true, increment the match count by “1”. Set the first random value to “99”. Check whether the match count is “4”, If it is true,set the highest winning. Otherwise, check whether the match count is “3”, Set the second best winning. Otherwise, check whether the match count is “2”, If it is true, set the third best winning. Otherwise, check whether the match count is “1”, If it is true, set the low winning. Otherwise, set the winning to “0”. Display the output message in dialog box.

Question

(1 point) 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*…

Answer 1

Question

Chapter 5, Problem 2GZ

Program Plan Intro

Lottery game application

Program plan:

Import necessary package.

Create a class “Lottery”,

Define the method “main ()”,

Declare and initialize the necessary variables.

Generate the three random numbers.

Combine three random numbers into a single three digit number.

Get the first digit entered into the first dialog box.

Assign the integer value returned form the method “parseInt()”.

Get the second digit entered into the second dialog box.

Assign the integer value returned form the method “parseInt()”.

Get the third digit entered into the third dialog box.

Assign the integer value returned form the method “parseInt()”.

Check whether the first, second and third digit is equal to the first, second and third random number generated respectively,

If it is true, set the match count to “4”.

Otherwise, check whether the first digit is equal to the first random number generated,

If it is true, increment the match count by “1”.

Set the first random value to “99”.

Otherwise, check whether the first digit is equal to the second random number generated,

If it is true, increment the match count by “1”.

Set the first random value to “99”.

Otherwise, check whether the first digit is equal to the third random number generated,

If it is true, increment the match count by “1”.

Set the first random value to “99”.

Check whether the second digit is equal to the first random number generated,

If it is true, increment the match count by “1”.

Set the first random value to “99”.

Otherwise, check whether the second digit is equal to the second random number generated,

If it is true, increment the match count by “1”.

Set the first random value to “99”.

Otherwise, check whether the second digit is equal to the third random number generated,

If it is true, increment the match count by “1”.

Set the first random value to “99”.

Check whether the third digit is equal to the first random number generated,

If it is true, increment the match count by “1”.

Set the first random value to “99”.

Otherwise, check whether the third digit is equal to the second random number generated,

If it is true, increment the match count by “1”.

Set the first random value to “99”.

Otherwise, check whether the third digit is equal to the third random number generated,

If it is true, increment the match count by “1”.

Set the first random value to “99”.

Check whether the match count is “4”,

If it is true,set the highest winning.

Otherwise, check whether the match count is “3”,

Set the second best winning.

Otherwise, check whether the match count is “2”,

If it is true, set the third best winning.

Otherwise, check whether the match count is “1”,

If it is true, set the low winning.

Otherwise, set the winning to “0”.

Display the output message in dialog box.

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(1 point) 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*…

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