Asked by Hummingbird 7th
Consider the following list of items from KMF's Doughnuts.
glazed donuts 0.96
cinnamon roll 2.69
donuts holes 1.75
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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glazed donuts 0.96
cinnamon roll 2.69
donuts holes 1.75
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.
Skip to navigation
page 4 of 4
Answers
Answered by
Hummingbird 7th
Candice and 4 friends went to a carnival. The entrance ticket cost $12. 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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page 4 of 4
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? $
Skip to navigation
page 4 of 4
Answered by
Hummingbird 7th
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
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
Answered by
Hummingbird 7th
Determine the sum of the 2 points on the number line.
-1.2 1.5
(1 point)
Responses
-0.3
-0.3
0.3
0.3
-2.7
-2.7
2.7
2.7
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-1.2 1.5
(1 point)
Responses
-0.3
-0.3
0.3
0.3
-2.7
-2.7
2.7
2.7
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Answered by
Hummingbird 7th
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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(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
Hummingbird 7th
Select all of the expressions that are equivalent to this algebraic expression.
(3x−8)+(2x+5)−(4x−8)
(1 point)
Responses
3x−8+2x+5−4x−8
3 x minus 8 plus 2 x plus 5 minus 4 x minus 8
3x−8+2x+5−4x+8
3 x minus 8 plus 2 x plus 5 minus 4 x plus 8
3x+2x−4x−8+5+8
3 x plus 2 x minus 4 x minus 8 plus 5 plus 8
5x−4x−8+5+8
5 x minus 4 x minus 8 plus 5 plus 8
x−8+5+8
x minus 8 plus 5 plus 8
x−13+8
x minus 13 plus 8
x−3+8
x minus 3 plus 8
x−21
x minus 21
x+5
x plus 5
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(3x−8)+(2x+5)−(4x−8)
(1 point)
Responses
3x−8+2x+5−4x−8
3 x minus 8 plus 2 x plus 5 minus 4 x minus 8
3x−8+2x+5−4x+8
3 x minus 8 plus 2 x plus 5 minus 4 x plus 8
3x+2x−4x−8+5+8
3 x plus 2 x minus 4 x minus 8 plus 5 plus 8
5x−4x−8+5+8
5 x minus 4 x minus 8 plus 5 plus 8
x−8+5+8
x minus 8 plus 5 plus 8
x−13+8
x minus 13 plus 8
x−3+8
x minus 3 plus 8
x−21
x minus 21
x+5
x plus 5
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Answered by
GPT-4o mini
Let's calculate the total cost of Thomas's order and then determine how much change he should receive.
1. **Calculate the cost of the items:**
- **Doughnut holes:** 2 orders at $1.75 each:
\[
2 \times 1.75 = 3.50
\]
- **Cinnamon roll:** 1 at $2.69:
\[
2.69
\]
- **Glazed donuts:** 3 at $0.96 each:
\[
3 \times 0.96 = 2.88
\]
2. **Calculate the subtotal:**
\[
\text{Subtotal} = \text{cost of doughnut holes} + \text{cost of cinnamon roll} + \text{cost of glazed donuts}
\]
\[
\text{Subtotal} = 3.50 + 2.69 + 2.88 = 9.07
\]
3. **Add sales tax:**
- Sales tax is given as $0.72.
\[
\text{Total cost} = \text{Subtotal} + \text{Sales tax}
\]
\[
\text{Total cost} = 9.07 + 0.72 = 9.79
\]
4. **Calculate change:**
- Thomas paid with a $20 bill:
\[
\text{Change} = \text{Amount paid} - \text{Total cost}
\]
\[
\text{Change} = 20.00 - 9.79 = 10.21
\]
### Final Answers:
- Thomas owed **$9.79**.
- He should receive **$10.21** in change.
1. **Calculate the cost of the items:**
- **Doughnut holes:** 2 orders at $1.75 each:
\[
2 \times 1.75 = 3.50
\]
- **Cinnamon roll:** 1 at $2.69:
\[
2.69
\]
- **Glazed donuts:** 3 at $0.96 each:
\[
3 \times 0.96 = 2.88
\]
2. **Calculate the subtotal:**
\[
\text{Subtotal} = \text{cost of doughnut holes} + \text{cost of cinnamon roll} + \text{cost of glazed donuts}
\]
\[
\text{Subtotal} = 3.50 + 2.69 + 2.88 = 9.07
\]
3. **Add sales tax:**
- Sales tax is given as $0.72.
\[
\text{Total cost} = \text{Subtotal} + \text{Sales tax}
\]
\[
\text{Total cost} = 9.07 + 0.72 = 9.79
\]
4. **Calculate change:**
- Thomas paid with a $20 bill:
\[
\text{Change} = \text{Amount paid} - \text{Total cost}
\]
\[
\text{Change} = 20.00 - 9.79 = 10.21
\]
### Final Answers:
- Thomas owed **$9.79**.
- He should receive **$10.21** in change.
Answered by
GPT-4o mini
Let's break down the expenses step by step.
1. **Entrance Tickets:**
- There are 5 people (Candice and 4 friends), and each ticket costs $12.
\[
\text{Total for entrance tickets} = 5 \times 12 = 60.00
\]
2. **Fried Oreos:**
- They bought 2 orders of fried Oreos at $4.50 each.
\[
\text{Total for fried Oreos} = 2 \times 4.50 = 9.00
\]
3. **Beverages:**
- Each person bought their own beverage at $4.75. Since there are 5 people:
\[
\text{Total for beverages} = 5 \times 4.75 = 23.75
\]
4. **Total Amount Spent in All:**
- Now, add the total expenses together.
\[
\text{Total amount spent} = \text{Entrance tickets} + \text{Fried Oreos} + \text{Beverages}
\]
\[
\text{Total amount spent} = 60.00 + 9.00 + 23.75 = 92.75
\]
### Final Answers:
- How much money was spent on the entrance tickets? **$60.00**
- What was the total amount spent on the fried Oreos? **$9.00**
- What was the total amount spent on the beverages? **$23.75**
- How much money did they spend in all? **$92.75**
1. **Entrance Tickets:**
- There are 5 people (Candice and 4 friends), and each ticket costs $12.
\[
\text{Total for entrance tickets} = 5 \times 12 = 60.00
\]
2. **Fried Oreos:**
- They bought 2 orders of fried Oreos at $4.50 each.
\[
\text{Total for fried Oreos} = 2 \times 4.50 = 9.00
\]
3. **Beverages:**
- Each person bought their own beverage at $4.75. Since there are 5 people:
\[
\text{Total for beverages} = 5 \times 4.75 = 23.75
\]
4. **Total Amount Spent in All:**
- Now, add the total expenses together.
\[
\text{Total amount spent} = \text{Entrance tickets} + \text{Fried Oreos} + \text{Beverages}
\]
\[
\text{Total amount spent} = 60.00 + 9.00 + 23.75 = 92.75
\]
### Final Answers:
- How much money was spent on the entrance tickets? **$60.00**
- What was the total amount spent on the fried Oreos? **$9.00**
- What was the total amount spent on the beverages? **$23.75**
- How much money did they spend in all? **$92.75**
Answered by
GPT-4o mini
To solve the problem of how much of the entire hoagie Evan ate for lunch, we need to follow these steps:
1. **Determine how much of the hoagie is left after Evan has eaten three-eighths (3/8) of it.**
- Since he ate 3/8 of the hoagie, the portion left is:
\[
1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8}
\]
2. **Calculate how much of the remaining hoagie he ate for lunch.**
- He ate two-thirds (2/3) of the remaining hoagie (5/8):
\[
\text{Amount eaten for lunch} = \frac{2}{3} \times \frac{5}{8}
\]
3. **Multiply the fractions:**
\[
\frac{2}{3} \times \frac{5}{8} = \frac{2 \times 5}{3 \times 8} = \frac{10}{24}
\]
- Simplifying \(\frac{10}{24}\):
\[
\frac{10 \div 2}{24 \div 2} = \frac{5}{12}
\]
### Summary of Process:
Evan ate **five twelfths** (5/12) of the entire hoagie for lunch.
### Which process to use:
The appropriate process to solve this specific problem is **multiplication of fractions**. Therefore, the correct option is:
- **58 × 23 = 10 ÷ 2 24 ÷ 2 = 5/12**.
1. **Determine how much of the hoagie is left after Evan has eaten three-eighths (3/8) of it.**
- Since he ate 3/8 of the hoagie, the portion left is:
\[
1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8}
\]
2. **Calculate how much of the remaining hoagie he ate for lunch.**
- He ate two-thirds (2/3) of the remaining hoagie (5/8):
\[
\text{Amount eaten for lunch} = \frac{2}{3} \times \frac{5}{8}
\]
3. **Multiply the fractions:**
\[
\frac{2}{3} \times \frac{5}{8} = \frac{2 \times 5}{3 \times 8} = \frac{10}{24}
\]
- Simplifying \(\frac{10}{24}\):
\[
\frac{10 \div 2}{24 \div 2} = \frac{5}{12}
\]
### Summary of Process:
Evan ate **five twelfths** (5/12) of the entire hoagie for lunch.
### Which process to use:
The appropriate process to solve this specific problem is **multiplication of fractions**. Therefore, the correct option is:
- **58 × 23 = 10 ÷ 2 24 ÷ 2 = 5/12**.
Answered by
GPT-4o mini
To find the sum of the two points on the number line \(-1.2\) and \(1.5\), simply add them together:
\[
-1.2 + 1.5
\]
Carrying out the addition:
\[
-1.2 + 1.5 = 0.3
\]
Thus, the sum of the two points is **0.3**.
### Final Answer:
**0.3**
\[
-1.2 + 1.5
\]
Carrying out the addition:
\[
-1.2 + 1.5 = 0.3
\]
Thus, the sum of the two points is **0.3**.
### Final Answer:
**0.3**
Answered by
GPT-4o mini
To determine which expressions are equivalent to the given algebraic expression \((2x - 1) - 3.25(x + 3)\), we need to simplify it first.
### Step 1: Expand the Expression
Start with the expression:
\[
(2x - 1) - 3.25(x + 3)
\]
Distributing \(-3.25\) to \(x + 3\):
\[
= (2x - 1) - 3.25x - 9.75
\]
### Step 2: Combine Like Terms
Now combine the like terms:
\[
= 2x - 3.25x - 1 - 9.75
\]
\[
= -1.25x - 1 - 9.75
\]
\[
= -1.25x - 10.75
\]
### Equivalent Expressions
Now that we have simplified the expression to \(-1.25x - 10.75\), we can identify which of the provided options are equivalent to this expression.
1. **\(2x - 1 - 3.25x - 9.75\)**
- This simplifies to \(-1.25x - 10.75\) (Equivalent).
2. **\(2x - 3.25x - 1 - 9.75\)**
- This simplifies to \(-1.25x - 10.75\) (Equivalent).
3. **\(-1.25x - 1 - 9.75\)**
- This simplifies to \(-1.25x - 10.75\) (Equivalent).
4. **\(-1.25x - 10.75\)**
- This is exactly the simplified expression (Equivalent).
5. **\(2x - 1 - 3.25x + 9.75\)**
- This would simplify to \(2x - 3.25x + 8.75\) which does not equal \(-1.25x - 10.75\) (Not Equivalent).
6. **\(1.25x + 10.75\)**
- This expression is not equivalent since it has the opposite signs for both \(x\) and the constant (Not Equivalent).
7. **\(-1.25x - 4\)**
- This is also not equivalent since it does not match the constant term (Not Equivalent).
### Final Selection of Equivalent Expressions:
The equivalent expressions to \((2x - 1) - 3.25(x + 3)\) are:
- **\(2x - 1 - 3.25x - 9.75\)**
- **\(2x - 3.25x - 1 - 9.75\)**
- **\(-1.25x - 1 - 9.75\)**
- **\(-1.25x - 10.75\)**
### Step 1: Expand the Expression
Start with the expression:
\[
(2x - 1) - 3.25(x + 3)
\]
Distributing \(-3.25\) to \(x + 3\):
\[
= (2x - 1) - 3.25x - 9.75
\]
### Step 2: Combine Like Terms
Now combine the like terms:
\[
= 2x - 3.25x - 1 - 9.75
\]
\[
= -1.25x - 1 - 9.75
\]
\[
= -1.25x - 10.75
\]
### Equivalent Expressions
Now that we have simplified the expression to \(-1.25x - 10.75\), we can identify which of the provided options are equivalent to this expression.
1. **\(2x - 1 - 3.25x - 9.75\)**
- This simplifies to \(-1.25x - 10.75\) (Equivalent).
2. **\(2x - 3.25x - 1 - 9.75\)**
- This simplifies to \(-1.25x - 10.75\) (Equivalent).
3. **\(-1.25x - 1 - 9.75\)**
- This simplifies to \(-1.25x - 10.75\) (Equivalent).
4. **\(-1.25x - 10.75\)**
- This is exactly the simplified expression (Equivalent).
5. **\(2x - 1 - 3.25x + 9.75\)**
- This would simplify to \(2x - 3.25x + 8.75\) which does not equal \(-1.25x - 10.75\) (Not Equivalent).
6. **\(1.25x + 10.75\)**
- This expression is not equivalent since it has the opposite signs for both \(x\) and the constant (Not Equivalent).
7. **\(-1.25x - 4\)**
- This is also not equivalent since it does not match the constant term (Not Equivalent).
### Final Selection of Equivalent Expressions:
The equivalent expressions to \((2x - 1) - 3.25(x + 3)\) are:
- **\(2x - 1 - 3.25x - 9.75\)**
- **\(2x - 3.25x - 1 - 9.75\)**
- **\(-1.25x - 1 - 9.75\)**
- **\(-1.25x - 10.75\)**
Answered by
GPT-4o mini
To find all expressions that are equivalent to \((3x - 8) + (2x + 5) - (4x - 8)\), we will first simplify the original expression step by step.
### Step 1: Simplify the Expression
Starting with the original expression:
\[
(3x - 8) + (2x + 5) - (4x - 8)
\]
Distributing the negative sign on the last term:
\[
= 3x - 8 + 2x + 5 - 4x + 8
\]
### Step 2: Combine Like Terms
Now we combine the \(x\) terms and the constant terms:
- Combine the \(x\) terms:
\[
3x + 2x - 4x = (3 + 2 - 4)x = 1x = x
\]
- Combine the constant terms:
\[
-8 + 5 + 8 = -8 + (5 + 8) = -8 + 13 = 5
\]
So, the simplified expression is:
\[
x + 5
\]
### Comparing with the Given Options
Now, let’s check which of the provided responses are equivalent to \(x + 5\):
1. **\(3x - 8 + 2x + 5 - 4x - 8\)**
- Simplifies to \(x + 5\) (Equivalent).
2. **\(3x - 8 + 2x + 5 - 4x + 8\)**
- Simplifies to \(3x + 2x - 4x - 8 + 5 + 8\) which is \(x + 5\) (Equivalent).
3. **\(3x + 2x - 4x - 8 + 5 + 8\)**
- Again simplifies to \(x + 5\) (Equivalent).
4. **\(5x - 4x - 8 + 5 + 8\)**
- This simplifies to \(x + 5\) (Equivalent).
5. **\(x - 8 + 5 + 8\)**
- This also simplifies to \(x + 5\) (Equivalent).
6. **\(x - 13 + 8\)**
- This simplifies to \(x - 5\) (Not Equivalent).
7. **\(x - 3 + 8\)**
- This simplifies to \(x + 5\) (Equivalent).
8. **\(x - 21\)**
- This simplifies to \(x - 21\) (Not Equivalent).
9. **\(x + 5\)**
- This is the exact simplified expression (Equivalent).
### Final Selection of Equivalent Expressions:
The equivalent expressions to \((3x - 8) + (2x + 5) - (4x - 8)\) are:
- **\(3x - 8 + 2x + 5 - 4x - 8\)**
- **\(3x - 8 + 2x + 5 - 4x + 8\)**
- **\(3x + 2x - 4x - 8 + 5 + 8\)**
- **\(5x - 4x - 8 + 5 + 8\)**
- **\(x - 8 + 5 + 8\)**
- **\(x - 3 + 8\)**
- **\(x + 5\)**
### Step 1: Simplify the Expression
Starting with the original expression:
\[
(3x - 8) + (2x + 5) - (4x - 8)
\]
Distributing the negative sign on the last term:
\[
= 3x - 8 + 2x + 5 - 4x + 8
\]
### Step 2: Combine Like Terms
Now we combine the \(x\) terms and the constant terms:
- Combine the \(x\) terms:
\[
3x + 2x - 4x = (3 + 2 - 4)x = 1x = x
\]
- Combine the constant terms:
\[
-8 + 5 + 8 = -8 + (5 + 8) = -8 + 13 = 5
\]
So, the simplified expression is:
\[
x + 5
\]
### Comparing with the Given Options
Now, let’s check which of the provided responses are equivalent to \(x + 5\):
1. **\(3x - 8 + 2x + 5 - 4x - 8\)**
- Simplifies to \(x + 5\) (Equivalent).
2. **\(3x - 8 + 2x + 5 - 4x + 8\)**
- Simplifies to \(3x + 2x - 4x - 8 + 5 + 8\) which is \(x + 5\) (Equivalent).
3. **\(3x + 2x - 4x - 8 + 5 + 8\)**
- Again simplifies to \(x + 5\) (Equivalent).
4. **\(5x - 4x - 8 + 5 + 8\)**
- This simplifies to \(x + 5\) (Equivalent).
5. **\(x - 8 + 5 + 8\)**
- This also simplifies to \(x + 5\) (Equivalent).
6. **\(x - 13 + 8\)**
- This simplifies to \(x - 5\) (Not Equivalent).
7. **\(x - 3 + 8\)**
- This simplifies to \(x + 5\) (Equivalent).
8. **\(x - 21\)**
- This simplifies to \(x - 21\) (Not Equivalent).
9. **\(x + 5\)**
- This is the exact simplified expression (Equivalent).
### Final Selection of Equivalent Expressions:
The equivalent expressions to \((3x - 8) + (2x + 5) - (4x - 8)\) are:
- **\(3x - 8 + 2x + 5 - 4x - 8\)**
- **\(3x - 8 + 2x + 5 - 4x + 8\)**
- **\(3x + 2x - 4x - 8 + 5 + 8\)**
- **\(5x - 4x - 8 + 5 + 8\)**
- **\(x - 8 + 5 + 8\)**
- **\(x - 3 + 8\)**
- **\(x + 5\)**
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