Question
Jasmine asked her classmates to name all the types of trees they found while on a field trip at a local park.
1/7 reported finding a birch tree.
7/9 reported finding a pine tree.
1/4 reported finding a maple tree.
11/23 reported finding an oak tree.
Based on the results, determine which statements are true and which statements are false.
(5 points)
True
False
Over half the students found a pine tree.
More students found a maple tree than a pine tree.
More students found a birch tree than an oak tree.
More students found a pine tree than a birch tree.
More students found a maple tree than an oak tree.
1/7 reported finding a birch tree.
7/9 reported finding a pine tree.
1/4 reported finding a maple tree.
11/23 reported finding an oak tree.
Based on the results, determine which statements are true and which statements are false.
(5 points)
True
False
Over half the students found a pine tree.
More students found a maple tree than a pine tree.
More students found a birch tree than an oak tree.
More students found a pine tree than a birch tree.
More students found a maple tree than an oak tree.
Answers
GPT-4o mini
To determine the truth values of the statements, we will need to compare the fractions of students that reported finding each type of tree. Let's assume there are a total of 1,000 students for ease of calculation. Here’s how many students would correspond to each fraction:
1. **Birch tree: \( \frac{1}{7} \)**
- \( \frac{1}{7} \times 1000 = \approx 142.86 \) ⇒ about 143 students.
2. **Pine tree: \( \frac{7}{9} \)**
- \( \frac{7}{9} \times 1000 \approx 777.78 \) ⇒ about 778 students.
3. **Maple tree: \( \frac{1}{4} \)**
- \( \frac{1}{4} \times 1000 = 250 \) ⇒ 250 students.
4. **Oak tree: \( \frac{11}{23} \)**
- \( \frac{11}{23} \times 1000 \approx 478.26 \) ⇒ about 478 students.
Now, let's analyze the statements one by one.
1. **Over half the students found a pine tree.**
- 778 students found a pine tree. Since \( \frac{778}{1000} = 0.778 \), which is greater than 0.5, **True**.
2. **More students found a maple tree than a pine tree.**
- 250 students found a maple tree, which is less than 778 students who found a pine tree. **False**.
3. **More students found a birch tree than an oak tree.**
- 143 students found a birch tree, while about 478 students found an oak tree. **False**.
4. **More students found a pine tree than a birch tree.**
- 778 students found a pine tree, and 143 students found a birch tree. **True**.
5. **More students found a maple tree than an oak tree.**
- 250 students found a maple tree, while about 478 students found an oak tree. **False**.
### Summary:
- **True**: Over half the students found a pine tree.
- **False**: More students found a maple tree than a pine tree.
- **False**: More students found a birch tree than an oak tree.
- **True**: More students found a pine tree than a birch tree.
- **False**: More students found a maple tree than an oak tree.
1. **Birch tree: \( \frac{1}{7} \)**
- \( \frac{1}{7} \times 1000 = \approx 142.86 \) ⇒ about 143 students.
2. **Pine tree: \( \frac{7}{9} \)**
- \( \frac{7}{9} \times 1000 \approx 777.78 \) ⇒ about 778 students.
3. **Maple tree: \( \frac{1}{4} \)**
- \( \frac{1}{4} \times 1000 = 250 \) ⇒ 250 students.
4. **Oak tree: \( \frac{11}{23} \)**
- \( \frac{11}{23} \times 1000 \approx 478.26 \) ⇒ about 478 students.
Now, let's analyze the statements one by one.
1. **Over half the students found a pine tree.**
- 778 students found a pine tree. Since \( \frac{778}{1000} = 0.778 \), which is greater than 0.5, **True**.
2. **More students found a maple tree than a pine tree.**
- 250 students found a maple tree, which is less than 778 students who found a pine tree. **False**.
3. **More students found a birch tree than an oak tree.**
- 143 students found a birch tree, while about 478 students found an oak tree. **False**.
4. **More students found a pine tree than a birch tree.**
- 778 students found a pine tree, and 143 students found a birch tree. **True**.
5. **More students found a maple tree than an oak tree.**
- 250 students found a maple tree, while about 478 students found an oak tree. **False**.
### Summary:
- **True**: Over half the students found a pine tree.
- **False**: More students found a maple tree than a pine tree.
- **False**: More students found a birch tree than an oak tree.
- **True**: More students found a pine tree than a birch tree.
- **False**: More students found a maple tree than an oak tree.