Question
Six members of the math club are forming two teams for a contest.
The teams will be determined by having each student draw a number
from a box.
PART C
PART B
PART A
The table shows the results of the draw. The students who drew rational
numbers will form the team called the Tigers. The students who drew
irrational numbers will form the team called the Lions.
List the members of each team.
The student on each team who drew the greatest number will be the captain
of that team. Who will be the captain of the Tigers? Show your work.
Who will be the captain of the Lions? Show your work.
Student
Number Drawn
Lydia
√___38
Marcy
6.3¯4
Caleb
√___36
Ryan
6.343443444…
Anya
6.¯34
Chan
√___34
The teams will be determined by having each student draw a number
from a box.
PART C
PART B
PART A
The table shows the results of the draw. The students who drew rational
numbers will form the team called the Tigers. The students who drew
irrational numbers will form the team called the Lions.
List the members of each team.
The student on each team who drew the greatest number will be the captain
of that team. Who will be the captain of the Tigers? Show your work.
Who will be the captain of the Lions? Show your work.
Student
Number Drawn
Lydia
√___38
Marcy
6.3¯4
Caleb
√___36
Ryan
6.343443444…
Anya
6.¯34
Chan
√___34
Answers
GPT-4o mini
To determine the members of the two teams and their captains, we first need to evaluate each student's number drawn and classify it as either rational or irrational.
### Definitions:
- **Rational numbers** are numbers that can be expressed as a fraction or a ratio of two integers. This includes terminating decimals and repeating decimals.
- **Irrational numbers** cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions.
### Student Draws:
1. **Lydia**: \( \sqrt{38} \) - This is irrational.
2. **Marcy**: \( 6.3\overline{4} \) - This is a repeating decimal, so it is rational.
3. **Caleb**: \( \sqrt{36} \) - This simplifies to \( 6 \), which is rational.
4. **Ryan**: \( 6.343443444...\) - This decimal does not repeat and does not terminate, so it is irrational.
5. **Anya**: \( 6.\overline{34} \) - This is a repeating decimal, so it is rational.
6. **Chan**: \( \sqrt{34} \) - This is irrational.
### Classifying the Teams:
Based on the classifications:
- **Tigers (Rational Numbers)**:
- Marcy (6.3̅4)
- Caleb (6)
- Anya (6.̅34)
- **Lions (Irrational Numbers)**:
- Lydia (√38)
- Ryan (6.343443444...)
- Chan (√34)
### Finding the Captains:
To determine the captain of each team, we need to compare the numbers drawn by the members of each team.
- **Team Tigers**:
- Marcy: \( 6.3\overline{4} \) (approximately 6.344)
- Caleb: \( 6 \)
- Anya: \( 6.\overline{34} \) (approximately 6.343)
The greatest number is Marcy's \( 6.3̅4 \) (or approximately 6.344). Thus, the captain of the Tigers is **Marcy**.
- **Team Lions**:
- Lydia: \( \sqrt{38} \approx 6.164 \)
- Ryan: \( 6.343443444...\) (actually a bit more than 6.343)
- Chan: \( \sqrt{34} \approx 5.831 \)
Comparing these, we find that Ryan's \( 6.343443444...\) is the greatest. Thus, the captain of the Lions is **Ryan**.
### Summary:
- **Members of the Tigers**: Marcy, Caleb, Anya
- **Captain of the Tigers**: Marcy (greatest number \( 6.3\overline{4} \))
- **Members of the Lions**: Lydia, Ryan, Chan
- **Captain of the Lions**: Ryan (greatest number \( 6.343443444... \))
### Definitions:
- **Rational numbers** are numbers that can be expressed as a fraction or a ratio of two integers. This includes terminating decimals and repeating decimals.
- **Irrational numbers** cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions.
### Student Draws:
1. **Lydia**: \( \sqrt{38} \) - This is irrational.
2. **Marcy**: \( 6.3\overline{4} \) - This is a repeating decimal, so it is rational.
3. **Caleb**: \( \sqrt{36} \) - This simplifies to \( 6 \), which is rational.
4. **Ryan**: \( 6.343443444...\) - This decimal does not repeat and does not terminate, so it is irrational.
5. **Anya**: \( 6.\overline{34} \) - This is a repeating decimal, so it is rational.
6. **Chan**: \( \sqrt{34} \) - This is irrational.
### Classifying the Teams:
Based on the classifications:
- **Tigers (Rational Numbers)**:
- Marcy (6.3̅4)
- Caleb (6)
- Anya (6.̅34)
- **Lions (Irrational Numbers)**:
- Lydia (√38)
- Ryan (6.343443444...)
- Chan (√34)
### Finding the Captains:
To determine the captain of each team, we need to compare the numbers drawn by the members of each team.
- **Team Tigers**:
- Marcy: \( 6.3\overline{4} \) (approximately 6.344)
- Caleb: \( 6 \)
- Anya: \( 6.\overline{34} \) (approximately 6.343)
The greatest number is Marcy's \( 6.3̅4 \) (or approximately 6.344). Thus, the captain of the Tigers is **Marcy**.
- **Team Lions**:
- Lydia: \( \sqrt{38} \approx 6.164 \)
- Ryan: \( 6.343443444...\) (actually a bit more than 6.343)
- Chan: \( \sqrt{34} \approx 5.831 \)
Comparing these, we find that Ryan's \( 6.343443444...\) is the greatest. Thus, the captain of the Lions is **Ryan**.
### Summary:
- **Members of the Tigers**: Marcy, Caleb, Anya
- **Captain of the Tigers**: Marcy (greatest number \( 6.3\overline{4} \))
- **Members of the Lions**: Lydia, Ryan, Chan
- **Captain of the Lions**: Ryan (greatest number \( 6.343443444... \))