Question
1 of 271 of 27 Items
Question 1
Consider this problem.
If a box can hold 28 1/8
kilograms, how many 1 7/8
kilogram books will it hold?
Will you multiply or divide to solve this problem?
(1 point)
Responses
Multiply
Multiply
Divide
Divide
Question 2
Consider this problem.
If a box can hold 28 1/8
kilograms, how many 1 7/8
kilogram books will it hold?
(1 point)
Responses
15 books
15 books
35 books
35 books
48 books
48 books
52 books
52 books
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Answers
Answer
2 of 272 of 27 Items
Question 1
Consider the problem.
Joanne has 1314
yd of fabric to make 4.5 costumes. How many yards of fabric will Joanne use for each costume?
Which operation will you use?
(1 point)
Responses
Addition
Addition
Subtraction
Subtraction
Multiplication
Multiplication
Division
Division
Question 2
Joanne has 1314
yd of fabric to make 4.5 costumes. How many yards of fabric will Joanne use for each costume?(1 point)
Responses
21718
2 and 17 over 18
1853
18 over 53
1734
17 and 3 fourths
834
8 and 3 fourths
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Answer
3 of 273 of 27 Items
Question
Consider the following list of items from KMF's Doughnuts.
Thomas ordered 2 orders of doughnut holes, a cinnamon roll, and 3 doughnuts. The sales tax was $0.72.
(1 point)
Thomas owed $
.
He paid with a $20 bill. Thomas should receive $
in change.
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Answer
4 of 274 of 27 Items
Question
Candice and 4 friends went to a carnival. The entrance ticket costs $12 per person. They bought 2 orders of fried Oreos at $4.50 each and then each person bought their own beverage at $4.75 each.(1 point)
For each amount, remember to include the dollars and cents. For example, if the amount is 5 dollars, you will enter 5.00.
How much money was spent on the entrance tickets? $
What was the total amount spent on the fried Oreos? $
What was the total amount spent on the beverages? $
How much money did they spend in all? $
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Answer
5 of 275 of 27 Items
Question
Evan ate three-eighths of a hoagie for dinner. On the next day, he ate two-thirds of what was left for lunch. How much of the entire hoagie did Evan eat for lunch? Which process will you use to solve this problem?(1 point)
Responses
38÷23=916
3 eighths divided by 2 thirds is equal to 9 over 16
38+23=2524=1124
3 eighths plus 2 thirds is equal to 25 over 24 is equal to 1 and 1 over 24
38×23=6÷624÷6=14
3 eighths times 2 thirds is equal to the fraction with numerator 6 divided by 6 and denominator 24 divided by 6 is equal to 1 fourth
58×23=10÷224÷2=512
5 eighths times 2 thirds is equal to the fraction with numerator 10 divided by 2 and denominator 24 divided by 2 is equal to 5 over 12
58÷23=1516
5 eighths divided by 2 thirds is equal to 15 over 16
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Answer
8 of 278 of 27 Items
Question
Select all expressions that are equivalent to this algebraic expression.
(2x−1)−3.25(x+3)
(1 point)
Responses
2x−1−3.25x−9.75
2 x minus 1 minus 3 point 2 5 x minus 9 point 7 5
2x−3.25x−1−9.75
2 x minus 3 point 2 5 x minus 1 minus 9 point 7 5
−1.25x−1−9.75
negative 1 point 2 5 x minus 1 minus 9 point 7 5
−1.25x−10.75
negative 1 point 2 5 x minus 10 point 7 5
2x−1−3.25x+9.75
2 x minus 1 minus 3 point 2 5 x plus 9 point 7 5
1.25x+10.75
1 point 2 5 x plus 10 point 7 5
−1.25x−4
negative 1 point 2 5 x minus 4
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Answered by
GPT-4o mini
To solve the problem of how many 1 7/8 kilogram books can fit in a box that holds 28 1/8 kilograms, you will **divide** the total weight the box can hold by the weight of each book.
1. **Identify the weights:**
- Total weight the box can hold: 28 1/8 kg
- Weight of each book: 1 7/8 kg
2. **Convert the mixed numbers to improper fractions:**
- 28 1/8 can be converted to an improper fraction:
\[
28 \times 8 + 1 = 224 + 1 = 225 \Rightarrow \frac{225}{8}
\]
- 1 7/8 can be converted to an improper fraction:
\[
1 \times 8 + 7 = 8 + 7 = 15 \Rightarrow \frac{15}{8}
\]
3. **Perform the division:**
\[
\frac{225/8}{15/8} = \frac{225}{8} \times \frac{8}{15} = \frac{225}{15} = 15
\]
So, the box can hold **15 books**.
### Answers:
**Question 1:** Divide
**Question 2:** 15 books
1. **Identify the weights:**
- Total weight the box can hold: 28 1/8 kg
- Weight of each book: 1 7/8 kg
2. **Convert the mixed numbers to improper fractions:**
- 28 1/8 can be converted to an improper fraction:
\[
28 \times 8 + 1 = 224 + 1 = 225 \Rightarrow \frac{225}{8}
\]
- 1 7/8 can be converted to an improper fraction:
\[
1 \times 8 + 7 = 8 + 7 = 15 \Rightarrow \frac{15}{8}
\]
3. **Perform the division:**
\[
\frac{225/8}{15/8} = \frac{225}{8} \times \frac{8}{15} = \frac{225}{15} = 15
\]
So, the box can hold **15 books**.
### Answers:
**Question 1:** Divide
**Question 2:** 15 books
Answered by
GPT-4o mini
To determine how many yards of fabric Joanne will use for each costume, you need to divide the total amount of fabric she has by the number of costumes she is making.
1. **Identify the numbers:**
- Total yards of fabric: 1314 yards
- Number of costumes: 4.5
2. **Operation:** To find out how many yards of fabric are used for each costume, you will **divide**.
### Answers:
**Question 1:** Division
Now, let's calculate how many yards of fabric Joanne will use for each costume:
3. **Perform the division:**
\[
\text{Yards per costume} = \frac{1314 \text{ yd}}{4.5}
\]
To make calculations easier, convert 4.5 to a fraction:
\[
4.5 = \frac{9}{2}
\]
So,
\[
\frac{1314}{4.5} = 1314 \div \frac{9}{2} = 1314 \times \frac{2}{9} = \frac{2628}{9} = 292 \text{ (approximately)}
\]
Now, let's check what this is in improper and mixed numbers:
\[
\frac{2628}{9} = 292 \text{ yards per costume}
\]
Checking the options again:
- **Answer options:**
- 217\(\frac{18}{25}\)
- 185\(\frac{3}{53}\)
- 173\(\frac{4}{3}\)
- 834\(\frac{3}{4}\)
None of the options seem correct based on the calculation. The correct calculation we arrived at indicates an approximate usage of **292 yards per costume**.
So, the closest approach we can take upon reviewing the operation and confirming it would still yield:
### Overall Answers Summary:
- **Question 1:** Division
- **Question 2:** Since the calculation of **292** yards does not match the provided options, possibly review the numbers to ensure clarity.
1. **Identify the numbers:**
- Total yards of fabric: 1314 yards
- Number of costumes: 4.5
2. **Operation:** To find out how many yards of fabric are used for each costume, you will **divide**.
### Answers:
**Question 1:** Division
Now, let's calculate how many yards of fabric Joanne will use for each costume:
3. **Perform the division:**
\[
\text{Yards per costume} = \frac{1314 \text{ yd}}{4.5}
\]
To make calculations easier, convert 4.5 to a fraction:
\[
4.5 = \frac{9}{2}
\]
So,
\[
\frac{1314}{4.5} = 1314 \div \frac{9}{2} = 1314 \times \frac{2}{9} = \frac{2628}{9} = 292 \text{ (approximately)}
\]
Now, let's check what this is in improper and mixed numbers:
\[
\frac{2628}{9} = 292 \text{ yards per costume}
\]
Checking the options again:
- **Answer options:**
- 217\(\frac{18}{25}\)
- 185\(\frac{3}{53}\)
- 173\(\frac{4}{3}\)
- 834\(\frac{3}{4}\)
None of the options seem correct based on the calculation. The correct calculation we arrived at indicates an approximate usage of **292 yards per costume**.
So, the closest approach we can take upon reviewing the operation and confirming it would still yield:
### Overall Answers Summary:
- **Question 1:** Division
- **Question 2:** Since the calculation of **292** yards does not match the provided options, possibly review the numbers to ensure clarity.
Answered by
GPT-4o mini
To calculate how much Thomas owed in total and how much change he should receive, we need some additional information about the prices of the doughnut holes, cinnamon roll, and doughnuts. However, let’s assume we can assign hypothetical prices to do the calculation.
Let's assume the following hypothetical prices for the items:
- **Doughnut Holes:** $2.00 per order
- **Cinnamon Roll:** $3.00
- **Doughnuts:** $1.50 each
### Step 1: Calculate the total cost of items before tax.
1. **Calculate cost of doughnut holes:**
\[
2 \, \text{orders of doughnut holes} = 2 \times 2.00 = 4.00
\]
2. **Cost of cinnamon roll:**
\[
1 \, \text{cinnamon roll} = 3.00
\]
3. **Calculate cost of doughnuts:**
\[
3 \, \text{doughnuts} = 3 \times 1.50 = 4.50
\]
4. **Calculate total cost of items (before tax):**
\[
\text{Total cost} = 4.00 + 3.00 + 4.50 = 11.50
\]
### Step 2: Add sales tax to total.
5. **Add sales tax to the total:**
\[
\text{Total with tax} = 11.50 + 0.72 = 12.22
\]
### Step 3: Determine how much change Thomas should receive.
6. **Amount paid by Thomas:**
\[
\text{Paid with} = 20.00
\]
7. **Calculate change:**
\[
\text{Change} = 20.00 - 12.22 = 7.78
\]
### Final Answers:
- **Thomas owed:** $12.22
- **Change:** $7.78
If you have specific prices for the items, please provide those, and I can calculate it accurately based on the given prices!
Let's assume the following hypothetical prices for the items:
- **Doughnut Holes:** $2.00 per order
- **Cinnamon Roll:** $3.00
- **Doughnuts:** $1.50 each
### Step 1: Calculate the total cost of items before tax.
1. **Calculate cost of doughnut holes:**
\[
2 \, \text{orders of doughnut holes} = 2 \times 2.00 = 4.00
\]
2. **Cost of cinnamon roll:**
\[
1 \, \text{cinnamon roll} = 3.00
\]
3. **Calculate cost of doughnuts:**
\[
3 \, \text{doughnuts} = 3 \times 1.50 = 4.50
\]
4. **Calculate total cost of items (before tax):**
\[
\text{Total cost} = 4.00 + 3.00 + 4.50 = 11.50
\]
### Step 2: Add sales tax to total.
5. **Add sales tax to the total:**
\[
\text{Total with tax} = 11.50 + 0.72 = 12.22
\]
### Step 3: Determine how much change Thomas should receive.
6. **Amount paid by Thomas:**
\[
\text{Paid with} = 20.00
\]
7. **Calculate change:**
\[
\text{Change} = 20.00 - 12.22 = 7.78
\]
### Final Answers:
- **Thomas owed:** $12.22
- **Change:** $7.78
If you have specific prices for the items, please provide those, and I can calculate it accurately based on the given prices!
Answered by
GPT-4o mini
Let's break this down step by step to find out how much money Candice and her 4 friends spent at the carnival.
### 1. Entrance Ticket Cost:
- **Number of people:** Candice + 4 friends = 5 people
- **Cost per ticket:** $12
**Total spent on entrance tickets:**
\[
\text{Total Entrance Cost} = 5 \times 12 = 60.00
\]
### 2. Total Amount Spent on Fried Oreos:
- **Number of orders:** 2 orders
- **Cost per order:** $4.50
**Total spent on fried Oreos:**
\[
\text{Total Fried Oreos Cost} = 2 \times 4.50 = 9.00
\]
### 3. Total Amount Spent on Beverages:
- **Number of people:** 5
- **Cost per beverage:** $4.75
**Total spent on beverages:**
\[
\text{Total Beverages Cost} = 5 \times 4.75 = 23.75
\]
### 4. Total Money Spent in All:
**Total money spent:**
\[
\text{Total Spending} = \text{Entrance Cost} + \text{Fried Oreos Cost} + \text{Beverages Cost}
\]
\[
\text{Total Spending} = 60.00 + 9.00 + 23.75 = 92.75
\]
### Summary of the Answers:
1. **How much money was spent on the entrance tickets?** $60.00
2. **What was the total amount spent on the fried Oreos?** $9.00
3. **What was the total amount spent on the beverages?** $23.75
4. **How much money did they spend in all?** $92.75
These calculations should help you fill in the required amounts accurately!
### 1. Entrance Ticket Cost:
- **Number of people:** Candice + 4 friends = 5 people
- **Cost per ticket:** $12
**Total spent on entrance tickets:**
\[
\text{Total Entrance Cost} = 5 \times 12 = 60.00
\]
### 2. Total Amount Spent on Fried Oreos:
- **Number of orders:** 2 orders
- **Cost per order:** $4.50
**Total spent on fried Oreos:**
\[
\text{Total Fried Oreos Cost} = 2 \times 4.50 = 9.00
\]
### 3. Total Amount Spent on Beverages:
- **Number of people:** 5
- **Cost per beverage:** $4.75
**Total spent on beverages:**
\[
\text{Total Beverages Cost} = 5 \times 4.75 = 23.75
\]
### 4. Total Money Spent in All:
**Total money spent:**
\[
\text{Total Spending} = \text{Entrance Cost} + \text{Fried Oreos Cost} + \text{Beverages Cost}
\]
\[
\text{Total Spending} = 60.00 + 9.00 + 23.75 = 92.75
\]
### Summary of the Answers:
1. **How much money was spent on the entrance tickets?** $60.00
2. **What was the total amount spent on the fried Oreos?** $9.00
3. **What was the total amount spent on the beverages?** $23.75
4. **How much money did they spend in all?** $92.75
These calculations should help you fill in the required amounts accurately!
Answered by
GPT-4o mini
To solve this problem, we need to figure out how much of the hoagie Evan had left after eating three-eighths of it and then determine how much he ate when he consumed two-thirds of what was left for lunch.
### Step 1: Determine what is left after dinner
Evan ate three-eighths of the hoagie, which is denoted as:
\[
\text{Amount eaten for dinner} = \frac{3}{8}
\]
Thus, the amount left after dinner is:
\[
\text{Amount left} = 1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8}
\]
### Step 2: Determine what he ate for lunch
Evan then ate two-thirds of what was left, which can be calculated as:
\[
\text{Amount eaten for lunch} = \frac{2}{3} \times \frac{5}{8}
\]
To perform this multiplication, multiply the numerators and the denominators:
\[
\text{Amount eaten for lunch} = \frac{2 \times 5}{3 \times 8} = \frac{10}{24}
\]
### Step 3: Simplify the fraction
Now, simplify \( \frac{10}{24} \):
\[
\frac{10}{24} = \frac{5}{12}
\]
Thus, Evan ate \( \frac{5}{12} \) of the entire hoagie for lunch.
### Process Used
The process used to solve this problem is:
- Multiplication of fractions to find how much of the remaining hoagie Evan consumed.
### Final Answers
So, when looking at the responses you provided, we can conclude:
1. **How much of the entire hoagie did Evan eat for lunch?** \( \frac{5}{12} \)
2. **Which process will you use to solve this problem?** The specific answer choice should reflect that he multiplied three-eighths of the remaining hoagie left:
The closest correct operation is:
- **58 × 23 = 10 ÷ 22 = 5/12**, meaning you multiply \( \frac{5}{8} \) by \( \frac{2}{3} \).
If that choice is not listed, just take note of the multiplication of the remaining hoagie portion and the fraction eaten for lunch.
### Step 1: Determine what is left after dinner
Evan ate three-eighths of the hoagie, which is denoted as:
\[
\text{Amount eaten for dinner} = \frac{3}{8}
\]
Thus, the amount left after dinner is:
\[
\text{Amount left} = 1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8}
\]
### Step 2: Determine what he ate for lunch
Evan then ate two-thirds of what was left, which can be calculated as:
\[
\text{Amount eaten for lunch} = \frac{2}{3} \times \frac{5}{8}
\]
To perform this multiplication, multiply the numerators and the denominators:
\[
\text{Amount eaten for lunch} = \frac{2 \times 5}{3 \times 8} = \frac{10}{24}
\]
### Step 3: Simplify the fraction
Now, simplify \( \frac{10}{24} \):
\[
\frac{10}{24} = \frac{5}{12}
\]
Thus, Evan ate \( \frac{5}{12} \) of the entire hoagie for lunch.
### Process Used
The process used to solve this problem is:
- Multiplication of fractions to find how much of the remaining hoagie Evan consumed.
### Final Answers
So, when looking at the responses you provided, we can conclude:
1. **How much of the entire hoagie did Evan eat for lunch?** \( \frac{5}{12} \)
2. **Which process will you use to solve this problem?** The specific answer choice should reflect that he multiplied three-eighths of the remaining hoagie left:
The closest correct operation is:
- **58 × 23 = 10 ÷ 22 = 5/12**, meaning you multiply \( \frac{5}{8} \) by \( \frac{2}{3} \).
If that choice is not listed, just take note of the multiplication of the remaining hoagie portion and the fraction eaten for lunch.
Answered by
GPT-4o mini
To determine which expressions are equivalent to the algebraic expression \( (2x - 1) - 3.25(x + 3) \), we will first simplify this expression step-by-step.
### Step 1: Distribute \( -3.25 \) into \( (x + 3) \)
\[
-3.25(x + 3) = -3.25x - 3.25 \times 3 = -3.25x - 9.75
\]
### Step 2: Substitute back into the expression
Now, we replace the distributed part back into the original expression:
\[
(2x - 1) - 3.25(x + 3) = 2x - 1 - 3.25x - 9.75
\]
### Step 3: Combine like terms
Now we combine the like terms:
- Combine \( 2x - 3.25x \):
\[
2x - 3.25x = -1.25x
\]
- Combine \( -1 - 9.75 \):
\[
-1 - 9.75 = -10.75
\]
Putting it all together gives:
\[
(2x - 1) - 3.25(x + 3) = -1.25x - 10.75
\]
### Summary of Equivalent Expressions
Now, let's look through the provided options to identify which expressions are equivalent to \(-1.25x - 10.75\):
1. **\( 2x - 1 - 3.25x - 9.75 \)**
This matches because it simplifies exactly to \( -1.25x - 10.75 \).
2. **\( 2x - 3.25x - 1 - 9.75 \)**
This also matches the same simplification, resulting in \( -1.25x - 10.75 \).
3. **\( -1.25x - 1 - 9.75 \)**
This can be simplified to \( -1.25x - 10.75 \).
4. **\( -1.25x - 10.75 \)**
This is exactly the result we found.
5. **\( 2x - 1 - 3.25x + 9.75 \)**
This does not match since \( 9.75 \) is incorrectly added rather than subtracted.
6. **\( 1.25x + 10.75 \)**
This does not match either; it’s incorrect in sign.
7. **\( -1.25x - 4 \)**
This does not match, since \( -4 \) is incorrect.
### Final Answer
The equivalent expressions are:
- **\( 2x - 1 - 3.25x - 9.75 \)**
- **\( 2x - 3.25x - 1 - 9.75 \)**
- **\( -1.25x - 1 - 9.75 \)**
- **\( -1.25x - 10.75 \)**
These expressions are all equivalent to the original expression \( (2x - 1) - 3.25(x + 3) \).
### Step 1: Distribute \( -3.25 \) into \( (x + 3) \)
\[
-3.25(x + 3) = -3.25x - 3.25 \times 3 = -3.25x - 9.75
\]
### Step 2: Substitute back into the expression
Now, we replace the distributed part back into the original expression:
\[
(2x - 1) - 3.25(x + 3) = 2x - 1 - 3.25x - 9.75
\]
### Step 3: Combine like terms
Now we combine the like terms:
- Combine \( 2x - 3.25x \):
\[
2x - 3.25x = -1.25x
\]
- Combine \( -1 - 9.75 \):
\[
-1 - 9.75 = -10.75
\]
Putting it all together gives:
\[
(2x - 1) - 3.25(x + 3) = -1.25x - 10.75
\]
### Summary of Equivalent Expressions
Now, let's look through the provided options to identify which expressions are equivalent to \(-1.25x - 10.75\):
1. **\( 2x - 1 - 3.25x - 9.75 \)**
This matches because it simplifies exactly to \( -1.25x - 10.75 \).
2. **\( 2x - 3.25x - 1 - 9.75 \)**
This also matches the same simplification, resulting in \( -1.25x - 10.75 \).
3. **\( -1.25x - 1 - 9.75 \)**
This can be simplified to \( -1.25x - 10.75 \).
4. **\( -1.25x - 10.75 \)**
This is exactly the result we found.
5. **\( 2x - 1 - 3.25x + 9.75 \)**
This does not match since \( 9.75 \) is incorrectly added rather than subtracted.
6. **\( 1.25x + 10.75 \)**
This does not match either; it’s incorrect in sign.
7. **\( -1.25x - 4 \)**
This does not match, since \( -4 \) is incorrect.
### Final Answer
The equivalent expressions are:
- **\( 2x - 1 - 3.25x - 9.75 \)**
- **\( 2x - 3.25x - 1 - 9.75 \)**
- **\( -1.25x - 1 - 9.75 \)**
- **\( -1.25x - 10.75 \)**
These expressions are all equivalent to the original expression \( (2x - 1) - 3.25(x + 3) \).