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
Answers
GPT-4o mini
To determine the members of each team and their captains, we need to categorize the numbers drawn by each student as either rational or irrational.
**Rational Numbers:** A number that can be expressed as a fraction of two integers (e.g., 6.3, 6.34).
**Irrational Numbers:** A number that cannot be expressed as a simple fraction (e.g., the square root of a non-perfect square).
Let's analyze the numbers drawn by each student:
1. **Lydia:** \( \sqrt{38} \) (irrational)
2. **Marcy:** \( 6.3\overline{4} = 6.344444...\) (rational)
3. **Caleb:** \( \sqrt{36} = 6 \) (rational)
4. **Ryan:** \( 6.343443444...\) (rational)
5. **Anya:** \( 6.\overline{34} = 6.343434...\) (rational)
6. **Chan:** \( \sqrt{34} \) (irrational)
**Team Members:**
- **Tigers (Rational):**
- Marcy (6.3̄4)
- Caleb (6)
- Ryan (6.343443444…)
- Anya (6.̄34)
- **Lions (Irrational):**
- Lydia (√38)
- Chan (√34)
**Captains:**
Now, we need to identify the captains of each team by selecting the student with the greatest number on each team.
1. **Tigers:**
- Marcy: \(6.344444...\) (approx. 6.34)
- Caleb: \(6\)
- Ryan: \(6.343443444...\) (approx. 6.34)
- Anya: \(6.343434...\) (approx. 6.34)
- The greatest number is **Marcy** with \(6.3\overline{4} \approx 6.34\).
2. **Lions:**
- Lydia: \( \sqrt{38} \approx 6.164 \)
- Chan: \( \sqrt{34} \approx 5.831 \)
- The greatest number is **Lydia** with \( \sqrt{38} \approx 6.164 \).
**Final Summary:**
- **Tigers:** Marcy, Caleb, Ryan, Anya — Captain: Marcy.
- **Lions:** Lydia, Chan — Captain: Lydia.
**Rational Numbers:** A number that can be expressed as a fraction of two integers (e.g., 6.3, 6.34).
**Irrational Numbers:** A number that cannot be expressed as a simple fraction (e.g., the square root of a non-perfect square).
Let's analyze the numbers drawn by each student:
1. **Lydia:** \( \sqrt{38} \) (irrational)
2. **Marcy:** \( 6.3\overline{4} = 6.344444...\) (rational)
3. **Caleb:** \( \sqrt{36} = 6 \) (rational)
4. **Ryan:** \( 6.343443444...\) (rational)
5. **Anya:** \( 6.\overline{34} = 6.343434...\) (rational)
6. **Chan:** \( \sqrt{34} \) (irrational)
**Team Members:**
- **Tigers (Rational):**
- Marcy (6.3̄4)
- Caleb (6)
- Ryan (6.343443444…)
- Anya (6.̄34)
- **Lions (Irrational):**
- Lydia (√38)
- Chan (√34)
**Captains:**
Now, we need to identify the captains of each team by selecting the student with the greatest number on each team.
1. **Tigers:**
- Marcy: \(6.344444...\) (approx. 6.34)
- Caleb: \(6\)
- Ryan: \(6.343443444...\) (approx. 6.34)
- Anya: \(6.343434...\) (approx. 6.34)
- The greatest number is **Marcy** with \(6.3\overline{4} \approx 6.34\).
2. **Lions:**
- Lydia: \( \sqrt{38} \approx 6.164 \)
- Chan: \( \sqrt{34} \approx 5.831 \)
- The greatest number is **Lydia** with \( \sqrt{38} \approx 6.164 \).
**Final Summary:**
- **Tigers:** Marcy, Caleb, Ryan, Anya — Captain: Marcy.
- **Lions:** Lydia, Chan — Captain: Lydia.