In Exercises 1-8, use inductive reasoning to predict the next three numbers or figures in the pattern. 1, 3, 8, 13, 18 , ....

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Answer 1

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Chapter 1, Problem 1RE

In Exercises 1-8, use inductive reasoning to predict the next three numbers or figures in the pattern.

1, 3, 8, 13, 18_{, ....}

Expert Solution & Answer

To determine

To predict: The next three numbers following the pattern.

Answer to Problem 1RE

The next three numbers for the pattern are $23,28,33$ .

Explanation of Solution

Given:

The pattern is $3,8,13,18,⋯$ .

Calculation:

From the given pattern, it is observed that numbers in the pattern are found by adding 5 to the previous.

$3+5=88+5=1313+5=18$

The last number is given as 18.

Thus, to continue the pattern, add 5 to number 18 and obtain that $18+5=23$ .

Use the same method and find the next two numbers.

Thus, add 5 to the obtained result 23 and discover the next number in the pattern as $23+5=28$ .

Similarly, add 5 to the obtained result 23 and discover the next number in the pattern as $28+5=33$ .

Hence, the next three numbers for the pattern are $23,28,33$ .

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Suppose you are gambling on a roulette wheel. Each time the wheel is spun, the result is one of the outcomes 0, 1, and so on through 36. Of these outcomes, 18 are red, 18 are black, and 1 is green. On each spin you bet $5 that a red outcome will occur and $1 that the green outcome will occur. If red occurs, you win a net $4. (You win $10 from red and nothing from green.) If green occurs, you win a net $24. (You win $30 from green and nothing from red.) If black occurs, you lose everything you bet for a loss of $6. a. Use simulation to generate 1,000 plays from this strategy. Each play should indicate the net amount won or lost. Then, based on these outcomes, calculate a 95% confidence interval for the total net amount won or lost from 1,000 plays of the game. (Round your answers to two decimal places and if your answer is negative value, enter "minus" sign.) I worked out the Upper Limit, but I can't seem to arrive at the correct answer for the Lower Limit. What is the Lower Limit?…

4. Consider Chebychev's equation (1 - x²)y" - xy + λy = 0 with boundary conditions y(-1) = 0 and y(1) = 0, where X is a constant. (a) Show that Chebychev's equation can be expressed in Sturm-Liouville form d · (py') + qy + Ary = 0, dx y(1) = 0, y(-1) = 0, where p(x) = (1 = x²) 1/2, q(x) = 0 and r(x) = (1 − x²)-1/2 (b) Show that the eigenfunctions of the Sturm-Liouville equation are extremals of the functional A[y], where A[y] = I[y] J[y]' and I[y] and [y] are defined by - I [y] = √, (my² — qy²) dx and J[y] = [[", ry² dx. Explain briefly how to use this to obtain estimates of the smallest eigenvalue >1. 1 (c) Let k > be a parameter. Explain why the functions y(x) = (1-x²) are suitable 4 trial functions for estimating the smallest eigenvalue. Show that the value of A[y] for these trial functions is 4k2 A[y] = = 4k - 1' and use this to estimate the smallest eigenvalue \1. Hint: L₁ x²(1 − ²)³¹ dr = 1 (1 - x²)³ dx (ẞ > 0). 2ẞ

2. If loga b + log, a = √√29, find all possible values of loga blog, a

Answer 2

Textbook Question

100%

Chapter 1, Problem 1RE

In Exercises 1-8, use inductive reasoning to predict the next three numbers or figures in the pattern.

1, 3, 8, 13, 18_{, ....}

Expert Solution & Answer

To determine

To predict: The next three numbers following the pattern.

Answer to Problem 1RE

The next three numbers for the pattern are $23,28,33$ .

Explanation of Solution

Given:

The pattern is $3,8,13,18,⋯$ .

Calculation:

From the given pattern, it is observed that numbers in the pattern are found by adding 5 to the previous.

$3+5=88+5=1313+5=18$

The last number is given as 18.

Thus, to continue the pattern, add 5 to number 18 and obtain that $18+5=23$ .

Use the same method and find the next two numbers.

Thus, add 5 to the obtained result 23 and discover the next number in the pattern as $23+5=28$ .

Similarly, add 5 to the obtained result 23 and discover the next number in the pattern as $28+5=33$ .

Hence, the next three numbers for the pattern are $23,28,33$ .

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Answer 3

Textbook Question

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Chapter 1, Problem 1RE

In Exercises 1-8, use inductive reasoning to predict the next three numbers or figures in the pattern.

1, 3, 8, 13, 18_{, ....}

Expert Solution & Answer

To determine

To predict: The next three numbers following the pattern.

Answer to Problem 1RE

The next three numbers for the pattern are $23,28,33$ .

Explanation of Solution

Given:

The pattern is $3,8,13,18,⋯$ .

Calculation:

From the given pattern, it is observed that numbers in the pattern are found by adding 5 to the previous.

$3+5=88+5=1313+5=18$

The last number is given as 18.

Thus, to continue the pattern, add 5 to number 18 and obtain that $18+5=23$ .

Use the same method and find the next two numbers.

Thus, add 5 to the obtained result 23 and discover the next number in the pattern as $23+5=28$ .

Similarly, add 5 to the obtained result 23 and discover the next number in the pattern as $28+5=33$ .

Hence, the next three numbers for the pattern are $23,28,33$ .

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Answer 4

Textbook Question

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Chapter 1, Problem 1RE

In Exercises 1-8, use inductive reasoning to predict the next three numbers or figures in the pattern.

1, 3, 8, 13, 18_{, ....}

Expert Solution & Answer

To determine

To predict: The next three numbers following the pattern.

Answer to Problem 1RE

The next three numbers for the pattern are $23,28,33$ .

Explanation of Solution

Given:

The pattern is $3,8,13,18,⋯$ .

Calculation:

From the given pattern, it is observed that numbers in the pattern are found by adding 5 to the previous.

$3+5=88+5=1313+5=18$

The last number is given as 18.

Thus, to continue the pattern, add 5 to number 18 and obtain that $18+5=23$ .

Use the same method and find the next two numbers.

Thus, add 5 to the obtained result 23 and discover the next number in the pattern as $23+5=28$ .

Similarly, add 5 to the obtained result 23 and discover the next number in the pattern as $28+5=33$ .

Hence, the next three numbers for the pattern are $23,28,33$ .

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Answer 5

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Answer 6

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Answer 7

Expert Solution & Answer

To determine

To predict: The next three numbers following the pattern.

Answer to Problem 1RE

The next three numbers for the pattern are $23,28,33$ .

Explanation of Solution

Given:

The pattern is $3,8,13,18,⋯$ .

Calculation:

From the given pattern, it is observed that numbers in the pattern are found by adding 5 to the previous.

$3+5=88+5=1313+5=18$

The last number is given as 18.

Thus, to continue the pattern, add 5 to number 18 and obtain that $18+5=23$ .

Use the same method and find the next two numbers.

Thus, add 5 to the obtained result 23 and discover the next number in the pattern as $23+5=28$ .

Similarly, add 5 to the obtained result 23 and discover the next number in the pattern as $28+5=33$ .

Hence, the next three numbers for the pattern are $23,28,33$ .

Answer 8

Expert Solution & Answer

To determine

To predict: The next three numbers following the pattern.

Answer to Problem 1RE

The next three numbers for the pattern are $23,28,33$ .

Explanation of Solution

Given:

The pattern is $3,8,13,18,⋯$ .

Calculation:

From the given pattern, it is observed that numbers in the pattern are found by adding 5 to the previous.

$3+5=88+5=1313+5=18$

The last number is given as 18.

Thus, to continue the pattern, add 5 to number 18 and obtain that $18+5=23$ .

Use the same method and find the next two numbers.

Thus, add 5 to the obtained result 23 and discover the next number in the pattern as $23+5=28$ .

Similarly, add 5 to the obtained result 23 and discover the next number in the pattern as $28+5=33$ .

Hence, the next three numbers for the pattern are $23,28,33$ .

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

To predict: The next three numbers following the pattern.

Answer 12

Answer to Problem 1RE

The next three numbers for the pattern are $23,28,33$ .

Answer 13

Explanation of Solution

Given:

The pattern is $3,8,13,18,⋯$ .

Calculation:

From the given pattern, it is observed that numbers in the pattern are found by adding 5 to the previous.

$3+5=88+5=1313+5=18$

The last number is given as 18.

Thus, to continue the pattern, add 5 to number 18 and obtain that $18+5=23$ .

Use the same method and find the next two numbers.

Thus, add 5 to the obtained result 23 and discover the next number in the pattern as $23+5=28$ .

Similarly, add 5 to the obtained result 23 and discover the next number in the pattern as $28+5=33$ .

Hence, the next three numbers for the pattern are $23,28,33$ .

Answer 14

In Exercises 1-8, use inductive reasoning to predict the next three numbers or figures in the pattern. 1, 3, 8, 13, 18 , ....

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