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Christine(C) and Ty(T) save quarters in a jar together The jar had $28 in it, then Christine put in C quarters and Ty put in T...Asked by nope
Christine(C) and Ty(T) save quarters in a jar together. The jar had $28 in it, then Christine put in C quarters and Ty put in T quarters. Which expression can be used to represent the amount of money in the bank now?(1 point)
Responses
CT + 28
CT + 28
0.50(C + T) + 28
0.50(C + T) + 28
0.25C + 0.25T + 28
0.25C + 0.25T + 28
0.25FJ + 28
Responses
CT + 28
CT + 28
0.50(C + T) + 28
0.50(C + T) + 28
0.25C + 0.25T + 28
0.25C + 0.25T + 28
0.25FJ + 28
Answers
Answered by
nope
A ribbon 6 1/8
feet in length is shortened by having 2 1/12
feet cut off one end. What is the length of the shortened ribbon?(1 point)
Responses
4 1/24
feet
4 and 1 over 24 feet
4 5/24
feet
4 and 5 over 24 feet
4 9/24
feet
4 and 9 over 24 feet
3 5/24
feet
feet in length is shortened by having 2 1/12
feet cut off one end. What is the length of the shortened ribbon?(1 point)
Responses
4 1/24
feet
4 and 1 over 24 feet
4 5/24
feet
4 and 5 over 24 feet
4 9/24
feet
4 and 9 over 24 feet
3 5/24
feet
Answered by
nope
Simplify the expression.
0.625+3/4
(1 point)
Responses
11/8
11 eighths
3/2
3 halves
11/9
11 ninths
8/11
0.625+3/4
(1 point)
Responses
11/8
11 eighths
3/2
3 halves
11/9
11 ninths
8/11
Answered by
nope
Divide.
−4/17÷−3/4
(1 point)
Responses
−3/17
negative 3 over 17
3/17
3 over 17
−16/51
negative 16 over 51
16/51
−4/17÷−3/4
(1 point)
Responses
−3/17
negative 3 over 17
3/17
3 over 17
−16/51
negative 16 over 51
16/51
Answered by
nope
At Georgia Connections Academy, 2/5
of the students are in a club. Of the students in a club, 1/4
participate in eSports club. What fraction of the students at GACA participate in eSports?(1 point)
Responses
1/10
1 tenth
1/5
1 fifth
2/9
2 ninths
2/3
of the students are in a club. Of the students in a club, 1/4
participate in eSports club. What fraction of the students at GACA participate in eSports?(1 point)
Responses
1/10
1 tenth
1/5
1 fifth
2/9
2 ninths
2/3
Answered by
nope
Mr. Brokaw's class has 60 students, 1/4
of the students needed help for an upcoming test. If Mr. Brokaw equally divides the students that need help into 5 small groups, how many students are in each group?(1 point)
Responses
15
15
12
12
3
3
5
of the students needed help for an upcoming test. If Mr. Brokaw equally divides the students that need help into 5 small groups, how many students are in each group?(1 point)
Responses
15
15
12
12
3
3
5
Answered by
GPT-4o mini
To represent the amount of money in the bank after Christine and Ty both add their quarters, we first need to understand that each quarter is worth $0.25.
1. **Christine adds C quarters**: This is equivalent to adding \(0.25C\) dollars.
2. **Ty adds T quarters**: This is equivalent to adding \(0.25T\) dollars.
3. **The initial amount in the jar**: This is $28.
Therefore, the total amount of money in the bank after both of them have added their quarters can be expressed as:
\[
0.25C + 0.25T + 28
\]
So the correct response is:
**0.25C + 0.25T + 28**
1. **Christine adds C quarters**: This is equivalent to adding \(0.25C\) dollars.
2. **Ty adds T quarters**: This is equivalent to adding \(0.25T\) dollars.
3. **The initial amount in the jar**: This is $28.
Therefore, the total amount of money in the bank after both of them have added their quarters can be expressed as:
\[
0.25C + 0.25T + 28
\]
So the correct response is:
**0.25C + 0.25T + 28**
Answered by
GPT-4o mini
To find the length of the shortened ribbon, we start with the original length of the ribbon and subtract the amount cut off.
1. **Original length of the ribbon**: \(6 \frac{1}{8}\) feet
2. **Length cut off**: \(2 \frac{1}{12}\) feet
### Step 1: Convert Mixed Numbers to Improper Fractions
- **Convert \(6 \frac{1}{8}\)**:
\[
6 \frac{1}{8} = \frac{6 \times 8 + 1}{8} = \frac{48 + 1}{8} = \frac{49}{8}
\]
- **Convert \(2 \frac{1}{12}\)**:
\[
2 \frac{1}{12} = \frac{2 \times 12 + 1}{12} = \frac{24 + 1}{12} = \frac{25}{12}
\]
### Step 2: Find a Common Denominator
We need to subtract these two fractions, so we should find a common denominator. The least common multiple of 8 and 12 is 24.
- Convert \(\frac{49}{8}\) to a denominator of 24:
\[
\frac{49}{8} = \frac{49 \times 3}{8 \times 3} = \frac{147}{24}
\]
- Convert \(\frac{25}{12}\) to a denominator of 24:
\[
\frac{25}{12} = \frac{25 \times 2}{12 \times 2} = \frac{50}{24}
\]
### Step 3: Subtract the Fractions
Now we subtract \(\frac{50}{24}\) from \(\frac{147}{24}\):
\[
\frac{147}{24} - \frac{50}{24} = \frac{147 - 50}{24} = \frac{97}{24}
\]
### Step 4: Convert Back to Mixed Number
Now, we convert \(\frac{97}{24}\) back to a mixed number:
- \(97\) divided by \(24\) is \(4\) (since \(24 \times 4 = 96\)), with a remainder of \(1\).
\[
\frac{97}{24} = 4 \frac{1}{24}
\]
Thus, the length of the shortened ribbon is:
**4 1/24 feet**
1. **Original length of the ribbon**: \(6 \frac{1}{8}\) feet
2. **Length cut off**: \(2 \frac{1}{12}\) feet
### Step 1: Convert Mixed Numbers to Improper Fractions
- **Convert \(6 \frac{1}{8}\)**:
\[
6 \frac{1}{8} = \frac{6 \times 8 + 1}{8} = \frac{48 + 1}{8} = \frac{49}{8}
\]
- **Convert \(2 \frac{1}{12}\)**:
\[
2 \frac{1}{12} = \frac{2 \times 12 + 1}{12} = \frac{24 + 1}{12} = \frac{25}{12}
\]
### Step 2: Find a Common Denominator
We need to subtract these two fractions, so we should find a common denominator. The least common multiple of 8 and 12 is 24.
- Convert \(\frac{49}{8}\) to a denominator of 24:
\[
\frac{49}{8} = \frac{49 \times 3}{8 \times 3} = \frac{147}{24}
\]
- Convert \(\frac{25}{12}\) to a denominator of 24:
\[
\frac{25}{12} = \frac{25 \times 2}{12 \times 2} = \frac{50}{24}
\]
### Step 3: Subtract the Fractions
Now we subtract \(\frac{50}{24}\) from \(\frac{147}{24}\):
\[
\frac{147}{24} - \frac{50}{24} = \frac{147 - 50}{24} = \frac{97}{24}
\]
### Step 4: Convert Back to Mixed Number
Now, we convert \(\frac{97}{24}\) back to a mixed number:
- \(97\) divided by \(24\) is \(4\) (since \(24 \times 4 = 96\)), with a remainder of \(1\).
\[
\frac{97}{24} = 4 \frac{1}{24}
\]
Thus, the length of the shortened ribbon is:
**4 1/24 feet**
Answered by
GPT-4o mini
To simplify the expression \(0.625 + \frac{3}{4}\), we first convert \(0.625\) to a fraction.
### Step 1: Convert \(0.625\) to a Fraction
\(0.625\) can be expressed as:
\[
0.625 = \frac{625}{1000}
\]
Next, we can simplify \(\frac{625}{1000}\) by dividing the numerator and denominator by their greatest common divisor, which is \(125\):
\[
\frac{625 \div 125}{1000 \div 125} = \frac{5}{8}
\]
So, \(0.625\) is equal to \(\frac{5}{8}\).
### Step 2: Add \(\frac{5}{8}\) and \(\frac{3}{4}\)
We need a common denominator to add these two fractions. The denominator of \(\frac{3}{4}\) can be converted to eighths:
\[
\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}
\]
### Step 3: Add the Two Fractions
Now we can add:
\[
\frac{5}{8} + \frac{6}{8} = \frac{5 + 6}{8} = \frac{11}{8}
\]
### Conclusion
The simplified expression \(0.625 + \frac{3}{4}\) is:
**11/8** (or "11 eighths")
### Step 1: Convert \(0.625\) to a Fraction
\(0.625\) can be expressed as:
\[
0.625 = \frac{625}{1000}
\]
Next, we can simplify \(\frac{625}{1000}\) by dividing the numerator and denominator by their greatest common divisor, which is \(125\):
\[
\frac{625 \div 125}{1000 \div 125} = \frac{5}{8}
\]
So, \(0.625\) is equal to \(\frac{5}{8}\).
### Step 2: Add \(\frac{5}{8}\) and \(\frac{3}{4}\)
We need a common denominator to add these two fractions. The denominator of \(\frac{3}{4}\) can be converted to eighths:
\[
\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}
\]
### Step 3: Add the Two Fractions
Now we can add:
\[
\frac{5}{8} + \frac{6}{8} = \frac{5 + 6}{8} = \frac{11}{8}
\]
### Conclusion
The simplified expression \(0.625 + \frac{3}{4}\) is:
**11/8** (or "11 eighths")
Answered by
GPT-4o mini
To divide the fractions \(-\frac{4}{17} \div -\frac{3}{4}\), we follow these steps:
### Step 1: Change Division to Multiplication
When dividing by a fraction, we multiply by its reciprocal. Therefore:
\[
-\frac{4}{17} \div -\frac{3}{4} = -\frac{4}{17} \times -\frac{4}{3}
\]
### Step 2: Multiply the Fractions
Now we multiply the numerators and the denominators:
\[
\frac{(-4) \times (-4)}{17 \times 3} = \frac{16}{51}
\]
### Conclusion
The result of the division \(-\frac{4}{17} \div -\frac{3}{4}\) is:
**16/51**
### Step 1: Change Division to Multiplication
When dividing by a fraction, we multiply by its reciprocal. Therefore:
\[
-\frac{4}{17} \div -\frac{3}{4} = -\frac{4}{17} \times -\frac{4}{3}
\]
### Step 2: Multiply the Fractions
Now we multiply the numerators and the denominators:
\[
\frac{(-4) \times (-4)}{17 \times 3} = \frac{16}{51}
\]
### Conclusion
The result of the division \(-\frac{4}{17} \div -\frac{3}{4}\) is:
**16/51**
Answered by
GPT-4o mini
To find the fraction of the students at Georgia Connections Academy (GACA) that participate in the eSports club, we can follow these steps:
### Step 1: Determine the Fraction of Students in the Club
Given that \( \frac{2}{5} \) of the students are in a club.
### Step 2: Determine the Fraction of Students in the eSports Club
Of the students in the club, \( \frac{1}{4} \) participate in the eSports club.
### Step 3: Calculate the Fraction of Students Participating in eSports
To find the fraction of all students that participate in eSports, we multiply the fraction of students in the club by the fraction of club members who are in the eSports club:
\[
\text{Fraction of students in eSports} = \left(\frac{2}{5}\right) \times \left(\frac{1}{4}\right) = \frac{2 \times 1}{5 \times 4} = \frac{2}{20}
\]
### Step 4: Simplify the Fraction
Now simplify \( \frac{2}{20} \):
\[
\frac{2}{20} = \frac{1}{10}
\]
### Conclusion
The fraction of the students at GACA who participate in eSports is:
**1/10** (or "1 tenth").
### Step 1: Determine the Fraction of Students in the Club
Given that \( \frac{2}{5} \) of the students are in a club.
### Step 2: Determine the Fraction of Students in the eSports Club
Of the students in the club, \( \frac{1}{4} \) participate in the eSports club.
### Step 3: Calculate the Fraction of Students Participating in eSports
To find the fraction of all students that participate in eSports, we multiply the fraction of students in the club by the fraction of club members who are in the eSports club:
\[
\text{Fraction of students in eSports} = \left(\frac{2}{5}\right) \times \left(\frac{1}{4}\right) = \frac{2 \times 1}{5 \times 4} = \frac{2}{20}
\]
### Step 4: Simplify the Fraction
Now simplify \( \frac{2}{20} \):
\[
\frac{2}{20} = \frac{1}{10}
\]
### Conclusion
The fraction of the students at GACA who participate in eSports is:
**1/10** (or "1 tenth").
Answered by
GPT-4o mini
To determine how many students are in each group, we will follow these steps:
### Step 1: Find the Number of Students Needing Help
Given that there are 60 students in Mr. Brokaw's class and \( \frac{1}{4} \) of them needed help:
\[
\text{Number of students needing help} = \frac{1}{4} \times 60 = 15
\]
### Step 2: Divide the Students Needing Help into Groups
Mr. Brokaw divides the 15 students who need help into 5 small groups:
\[
\text{Number of students in each group} = \frac{15}{5} = 3
\]
### Conclusion
The number of students in each group is:
**3**
### Step 1: Find the Number of Students Needing Help
Given that there are 60 students in Mr. Brokaw's class and \( \frac{1}{4} \) of them needed help:
\[
\text{Number of students needing help} = \frac{1}{4} \times 60 = 15
\]
### Step 2: Divide the Students Needing Help into Groups
Mr. Brokaw divides the 15 students who need help into 5 small groups:
\[
\text{Number of students in each group} = \frac{15}{5} = 3
\]
### Conclusion
The number of students in each group is:
**3**
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