Question 1

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence. 5 10 20 40 80

Accepted Answer

160

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 8 :
Subtract 24 from the answer:
Divide by 8 :
Subtract the original number:

Accepted Answer

Final answer is always $- 3$.

$\begin{array}{ll}
\text { Select a number: } & x \
\text { Multiply by } 8: & 8 x \
\text { Subtract } 24 \text { from the answer: } & 8 x-24 \
\text { Divide by } 8: & \frac{8 x-24}{8}=x-3
\end{array}$

$\text { Subtract the original number: } \quad x-3-x=-3$

Question 3

Use deductive reasoning to arrive at a conclusion. On Christmas Day, Korean restaurants and gardens are always open, so this Christmas Day we can
A) watch football and open gifts.
B) eat Mexican food and take a walk in a park.
C) eat Korean food and take a walk in a park.
D) eat fast food and take a walk in a park.

Accepted Answer

Since Korean restaurants and gardens are always open on Christmas Day, we can deduce that eating Korean food and taking a walk in a park are possible activities.

Question 4

Round to the nearest hundred-thousand. 98,521,900

Accepted Answer

The answer of Round to the nearest hundred-thousand. 98,521,900...

Question 5

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence. 7 8 10 13 17 22 28

Accepted Answer

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

Question 6

One number is 18 more than another number. The sum of the numbers is 36. Find the numbers.

Accepted Answer

The answer of One number is 18 more than another...

Question 7

A car travels 485 miles on 11.9 gallons of gasoline. How many miles per gallon did the car get? (Round to the nearest tenth.)
A) 24.5 miles per gallon
B) 43.2 miles per gallon
C) 35.3 miles per gallon
D) 40.8 miles per gallon

Accepted Answer

The answer of A car travels 485 miles on 11.9...

Question 8

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.
$\begin{array} { l } 
0 ^ { 2 } + 1 = 1 \
1 ^ { 2 } + 3 = 2 ^ { 2 } \
2 ^ { 2 } + 5 = 3 ^ { 2 } \
3 ^ { 2 } + 7 = 4 ^ { 2 } \
4 ^ { 2 } + 9 = 5 ^ { 2 }
\end{array}$
$11 ^ { 2 } + 23 = ?$

A) 133
B) 143
C) $12 ^ { 2 }$
D) $13 ^ { 2 }$

Accepted Answer

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

Question 9

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 80. Multiply by 7. Subtract 560. Divide by 7. Subtract the original number.
A) The answer is always 0.
B) The answer is always -480.
C) The answer is always the original number.
D) The answer is always 480.

Accepted Answer

The operations simplify to: ((x + 80) * 7 - 560) / 7 - x = 0. This shows the final result is always 0, regardless of the original number.

Question 10

Estimate the cost to live in an apartment for 1 year if the rent is $319 per month and utilities are $62 per month.

Accepted Answer

The answer of Estimate the cost to live in an...

Question 11

For a specific year, the average household income for selected states is shown here. Estimate the average household income for North Carolina.

Accepted Answer

The answer of For a specific year, the average household...

Question 12

An item that originally cost $887.99 is on sale for 20% off. Estimate the sale price of the item.

Accepted Answer

The answer of An item that originally cost $887.99 is...

Question 13

The manager of an Internet cafe is having new counters custom-made. She wants to put 4 PCs on each counter with 4 feet between the PCs and 3 feet on each end. The PCs measure 18 inches wide and 24 inches high. What length of counters should the Internet cafe have made?
A) 26 ft
B) 24 ft
C) 25 ft
D) 28 ft

Accepted Answer

The answer of The manager of an Internet cafe is...

Question 14

Bob and Sue are celebrating their 5 th wedding anniversary. Estimate the total cos of their evening based on the prices below:
$\begin{array} { l l } \text { theater } & \$ 59.52 \ \text { dinner } & \$ 58.79 \ \text { drinks } & \$ 12.78 \ \text { taxi } & \$ 13.50 \end{array}$

Accepted Answer

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

Question 15

The peak rate of a phone company is $22 \notin$ per minute, and the off-peak rate is $12 \phi$ per minute. Find the savings for a 44-minute phone call if it was made during off-peak time as opposed to peak time.

Accepted Answer

The answer of The peak rate of a phone company...

Question 16

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence. 1 3 7 13 15 19 25 27 31 37
A) 45
B) 41
C) 39
D) 43

Accepted Answer

The sequence alternates between adding 6 and adding 2. Starting from 1: +2, +4, +6, +2, +4, +6, +2, +4, +6. The next step is to add 2 to 37, resulting in 39.

Question 17

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

Accepted Answer

The answer of Round to the nearest hundredth. 2.87491
A) 2.87000
B)...

Question 18

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence. 6 7 3 4 0 1 -3 -2
A) -3
B) 2
C) -6
D) -1

Accepted Answer

The sequence alternates between adding 1 and subtracting 4. Continuing this pattern, after -2, subtract 4 to get -6.

Question 19

Estimate the total cost of the following meal at a sub shop.
sandwich $\$ 4.89$
chips $\quad \$ 1.24$
soda $\quad \$ 0.99$

Accepted Answer

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

Question 20

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.
$$\begin{array} { c } 
12,345,679 \times 9 = 111,111,111 \
12,345,679 \times 18 = 222,222,222 \
12,345,679 \times 27 = 333,333,333 \
\cdot \
\cdot \
12,345,679 \times 36 = ?
\end{array}$$
A) 333,333,333
B) 555,555,555
C) 444,444,444
D) 444,444,408

Accepted Answer

The pattern shows that multiplying 12,345,679 by multiples of 9 results in repeating digits. For 36 (which is 9 x 4), the result should be 444,444,444.

Quiz 1: Problem Solving

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence. 5 10 20 40 80

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 8 : Subtract 24 from the answer: Divide by 8 : Subtract the original number:

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

Round to the nearest hundred-thousand. 98,521,900

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence. 7 8 10 13 17 22 28

One number is 18 more than another number. The sum of the numbers is 36. Find the numbers.

A car travels 485 miles on 11.9 gallons of gasoline. How many miles per gallon did the car get? (Round to the nearest tenth.)

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 80. Multiply by 7. Subtract 560. Divide by 7. Subtract the original number.

Estimate the cost to live in an apartment for 1 year if the rent is $319 per month and utilities are $62 per month.

For a specific year, the average household income for selected states is shown here. Estimate the average household income for North Carolina.

An item that originally cost $887.99 is on sale for 20% off. Estimate the sale price of the item.

The manager of an Internet cafe is having new counters custom-made. She wants to put 4 PCs on each counter with 4 feet between the PCs and 3 feet on each end. The PCs measure 18 inches wide and 24 inches high. What length of counters should the Internet cafe have made?

Bob and Sue are celebrating their 5 th wedding anniversary. Estimate the total cos of their evening based on the prices below: $\begin{array} { l l } \text { theater } & \$ 59.52 \\ \text { dinner } & \$ 58.79 \\ \text { drinks } & \$ 12.78 \\ \text { taxi } & \$ 13.50 \end{array}$

The peak rate of a phone company is $22 \notin$ per minute, and the off-peak rate is $12 \phi$ per minute. Find the savings for a 44-minute phone call if it was made during off-peak time as opposed to peak time.

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence. 1 3 7 13 15 19 25 27 31 37

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. 6 7 3 4 0 1 -3 -2

Estimate the total cost of the following meal at a sub shop. sandwich $\$ 4.89$ chips $\quad \$ 1.24$ soda $\quad \$ 0.99$

Quiz 1: Problem Solving

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence. 5 10 20 40 80

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 8 : Subtract 24 from the answer: Divide by 8 : Subtract the original number:

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

Round to the nearest hundred-thousand. 98,521,900

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence. 7 8 10 13 17 22 28

One number is 18 more than another number. The sum of the numbers is 36. Find the numbers.

A car travels 485 miles on 11.9 gallons of gasoline. How many miles per gallon did the car get? (Round to the nearest tenth.)

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 80. Multiply by 7. Subtract 560. Divide by 7. Subtract the original number.

Estimate the cost to live in an apartment for 1 year if the rent is $319 per month and utilities are $62 per month.

For a specific year, the average household income for selected states is shown here. Estimate the average household income for North Carolina.

An item that originally cost $887.99 is on sale for 20% off. Estimate the sale price of the item.

The manager of an Internet cafe is having new counters custom-made. She wants to put 4 PCs on each counter with 4 feet between the PCs and 3 feet on each end. The PCs measure 18 inches wide and 24 inches high. What length of counters should the Internet cafe have made?

The peak rate of a phone company is 22∉22 \notin22∈/ per minute, and the off-peak rate is 12ϕ12 \phi12ϕ per minute. Find the savings for a 44-minute phone call if it was made during off-peak time as opposed to peak time.

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence. 1 3 7 13 15 19 25 27 31 37

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. 6 7 3 4 0 1 -3 -2

Estimate the total cost of the following meal at a sub shop. sandwich $4.89\$ 4.89$4.89 chips $1.24\quad \$ 1.24$1.24 soda $0.99\quad \$ 0.99$0.99

The peak rate of a phone company is $22 \notin$ per minute, and the off-peak rate is $12 \phi$ per minute. Find the savings for a 44-minute phone call if it was made during off-peak time as opposed to peak time.

Estimate the total cost of the following meal at a sub shop. sandwich $\$ 4.89$ chips $\quad \$ 1.24$ soda $\quad \$ 0.99$