Question 1

Use inductive reasoning to make a conjecture about a rule that relates the original number to the final
Answer. Try to prove your conjecture using deductive reasoning.
Select a number.
Add 90.
Multiply by 6.
Subtract 540.
Divide by 6.
Subtract the original number.
A)The answer is always the original number.
B)The answer is always 450.
C)The answer is always -450.
D)The answer is always 0.

Accepted Answer

Let's use a specific number, say 10, to test our rule.
- Add 90: 10 + 90 = 100
- Multiply by 6: 100 * 6 = 600
- Subtract 540: 600 - 540 = 60
- Divide by 6: 60 / 6 = 10
- Subtract the original number: 10 - 10 = 0
As we can see, we end up with the original number (10) as the final answer. This works for any number we choose, so we can use deductive reasoning to prove that the answer is always 0. 
Let x be the original number. Then:
- Add 90: x + 90
- Multiply by 6: 6(x + 90)
- Subtract 540: 6(x + 90) - 540
- Divide by 6: (6(x + 90) - 540) / 6
- Subtract the original number: (6(x + 90) - 540) / 6 - x
Simplifying this expression, we get:
(6x + 540 - 540) / 6 - x
6x/6 - x
x - x
0
Therefore, the answer is always 0. When the steps are carried out, we get (x + 90) * 6 - 540 - x = 6x + 540 - 540 - x = 5x.
Therefore, the final answer is always 5 times the original number x. It means, it is always some multiple of x, and the only multiple of x that is guaranteed to be in every case is 0. Hence, the answer is always 0. Therefore, the best choice is D.

Question 2

Use inductive reasoning to conjecture the rule that relates the number you selected to the final answer.
Try to prove your conjecture using deductive reasoning.
Select a number:
Multiply by 7:
Subtract 56 from the
Divide by 7:
Subtract the original number:

Accepted Answer

Final answer is always -8.

Question 3

Determine whether the type of reasoning used is inductive or deductive reasoning.
If a computer tech says it will cost $225 to fix my computer, it will actually cost $300. Since
A computer tech told me it would cost $225 to fix my computer, I can expect it to cost me $300.
A)deductive reasoning
B)inductive reasoning

Accepted Answer

This is an example of deductive reasoning because it starts with a specific statement ("a computer tech says it will cost $225 to fix my computer") and logically determines a conclusion based on that statement ("it will actually cost $300"). This is deductive reasoning because the conclusion (it will cost $300) is drawn from the premise that the computer tech said it would cost $225 and the premise that the tech's estimate is unreliable.

Question 4

An item that originally cost $279.99 is on sale for 20% off. Estimate the sale price of the item.

Accepted Answer

The answer of An item that originally cost $279.99 is...

Question 5

Use inductive reasoning to find a pattern for the answers. Then use the pattern to guess the result of
The final calculation, and perform the operation to see if your answer is correct. 
A)555,555,510
B)444,444,444
C)666,666,666
D)555,555,555

Accepted Answer

By looking at the pattern of the given numbers in the calculation, we can notice that the first number (11) is added to the following number, then this result is multiplied by 111,111,111 and then the first number is added again. Therefore, the answer can be calculated as: 
(11+235)*111,111,111+11 = 2,611,111,166 
So, the closest answer to this is D: 555,555,555. Observing the pattern of the numbers in the calculation, we see that each number is multiplied by 5 and then subtracted by 1. So, starting from 9, if we apply this pattern, we get 44, 219, 1094, 5469 and finally 27,344,219. If we subtract 1 from this, we get 27,344,218 which when divided by 5 gives us 5,468,843.6 which rounds up to 5,468,844. Multiplying this by 5 and subtracting 1 gives us 27,344,219 which is the same as the answer in the calculation. Therefore, the correct choice is D)555,555,555

Question 6

Round to the nearest ten.
202

Accepted Answer

The answer of Round to the nearest ten.
202...

Question 7

Read the following scenario and determine whether the type of reasoning used by Leanne is
inductive or deductive. Explain how you decided.
Leanne was concerned that if she continued to be late for work, she would lose her job.

Accepted Answer

The answer of Read the following scenario and determine whether...

Question 8

Determine whether the type of reasoning used is inductive or deductive reasoning.
Victor has already lost 3 cameras. He didn't spend a lot of money on his newest camera because he
Knows he'll eventually lose that one too.
A)inductive reasoning
B)deductive reasoning

Accepted Answer

This is an example of inductive reasoning as it uses specific observations (Victor losing 3 cameras) to make a generalization (he knows he'll eventually lose his newest camera). This is an example of inductive reasoning because the conclusion is based on a pattern observed from specific instances (Victor losing his cameras) and then applied to a generalization (he will eventually lose his newest camera).

Question 9

Use inductive reasoning to find a pattern for the answers. Then use the pattern to guess the result of
The final calculation, and perform the operation to see if your answer is correct. 
A)111
B) 
C) 
D)120

Accepted Answer

The answer of Use inductive reasoning to find a pattern...

Question 10

Write a counter example to show that the statement is false.
When any number is multiplied by 5 and the digits of the answer are added, the sum will be divisible by
5.
A)111 × 5 = 555; 5 + 5 + 5 = 15, which is not divisible by 5.
B)11 × 5 = 55; 5 + 5 = 10, which is divisible by 5.
C)2 × 5 = 10; 1 + 0 = 1, which is not divisible by 5.
D)10 × 5 = 50; 5 + 0 = 5, which is divisible by 5.

Accepted Answer

The sum of the digits of 10 is 1, which is not divisible by 5, providing a counterexample to the statement.

Question 11

Read the following scenario and determine whether the type of reasoning used by Paul is inductive
or deductive. Explain how you decided.
Paul knew that his friend, Leanne, had been late the past 8 workdays, so he didn't save a seat for
her at morning meeting.

Accepted Answer

The answer of Read the following scenario and determine whether...

Question 12

Round to the nearest hundredth.
2.87491
A)2.87500
B)2.88000
C)2.87400
D)2.87000

Accepted Answer

The answer of Round to the nearest hundredth.
2.87491
A)2.87500
B)2.88000
C)2.87400
D)2.87000...

Question 13

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the
sequence.

Accepted Answer

The answer of Use inductive reasoning to find a pattern,...

Question 14

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the
Sequence. 
A)34
B)36
C)26
D)28

Accepted Answer

The answer of Use inductive reasoning to find a pattern,...

Question 15

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the
Sequence. 
A)39
B)45
C)41
D)43

Accepted Answer

The answer of Use inductive reasoning to find a pattern,...

Question 16

Estimate the total cost of the following meal at a sub shop.

Accepted Answer

The answer of Estimate the total cost of the following...

Question 17

Round 560,565,131 to the nearest ten-million.
A)560,000,000
B)560,570,000
C)561,000,000
D)600,000,000

Accepted Answer

The digit in the ten-millionth place is 5, which is halfway between 0 and 10. When rounding to the nearest ten-million, we round up to the nearest ten-million, which is 560,000,000.

Question 18

Use deductive reasoning to arrive at a conclusion.
On Christmas Day, Japanese restaurants and ski slopes are always open, so this Christmas Day we can
A)eat Japanese food and go skiing.
B)watch football and open gifts.
C)eat Mexican food and go skiing.
D)eat fast food and go skiing.

Accepted Answer

Deductive reasoning tells us that since Japanese restaurants and ski slopes are always open on Christmas Day, we can conclude that we can eat Japanese food and go skiing on this day. The other options are not supported by the given statement. The given premises state that Japanese restaurants and ski slopes are always open on Christmas Day, so it logically follows that the best choice would be to eat Japanese food and go skiing. The other options are not supported by the given information.

Question 19

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the
sequence.

Accepted Answer

The answer of Use inductive reasoning to find a pattern,...

Question 20

Bob and Sue are celebrating their 5th wedding anniversary. Estimate the total cost of their evening based on
the prices below:
theater $63.59
dinner $76.83
drinks $17.71
taxi $13.25

Accepted Answer

The answer of Bob and Sue are celebrating their 5th...

Quiz 1: Problem Solving

Use inductive reasoning to make a conjecture about a rule that relates the original number to the final Answer. Try to prove your conjecture using deductive reasoning. Select a number. Add 90. Multiply by 6. Subtract 540. Divide by 6. Subtract the original number.

Use inductive reasoning to conjecture the rule that relates the number you selected to the final answer. Try to prove your conjecture using deductive reasoning. Select a number: Multiply by 7: Subtract 56 from the Divide by 7: Subtract the original number:

Determine whether the type of reasoning used is inductive or deductive reasoning. If a computer tech says it will cost $225 to fix my computer, it will actually cost $300. Since A computer tech told me it would cost $225 to fix my computer, I can expect it to cost me $300.

An item that originally cost $279.99 is on sale for 20% off. Estimate the sale price of the item.

Use inductive reasoning to find a pattern for the answers. Then use the pattern to guess the result of The final calculation, and perform the operation to see if your answer is correct.

Round to the nearest ten. 202

Read the following scenario and determine whether the type of reasoning used by Leanne is inductive or deductive. Explain how you decided. Leanne was concerned that if she continued to be late for work, she would lose her job.

Determine whether the type of reasoning used is inductive or deductive reasoning. Victor has already lost 3 cameras. He didn't spend a lot of money on his newest camera because he Knows he'll eventually lose that one too.

Use inductive reasoning to find a pattern for the answers. Then use the pattern to guess the result of The final calculation, and perform the operation to see if your answer is correct.

Write a counter example to show that the statement is false. When any number is multiplied by 5 and the digits of the answer are added, the sum will be divisible by 5.

Read the following scenario and determine whether the type of reasoning used by Paul is inductive or deductive. Explain how you decided. Paul knew that his friend, Leanne, had been late the past 8 workdays, so he didn't save a seat for her at morning meeting.

Round to the nearest hundredth. 2.87491

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence.

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the Sequence.

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the Sequence.

Estimate the total cost of the following meal at a sub shop.

Round 560,565,131 to the nearest ten-million.

Use deductive reasoning to arrive at a conclusion. On Christmas Day, Japanese restaurants and ski slopes are always open, so this Christmas Day we can

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence.

Bob and Sue are celebrating their 5th wedding anniversary. Estimate the total cost of their evening based on the prices below: theater $63.59 dinner $76.83 drinks $17.71 taxi $13.25