Question
Jasmine asked her classmates to name all the types of birds they found on a field trip to a local aviary.
1/8
reported finding a blue jay.
6/7
reported finding a finch.
1/3
reported finding a blackbird.
11/24
reported finding an owl.
Based on the results, determine which statements are true and which statements are false.
Over half the students found a finch.
More students found a blackbird than a finch.
More students found a blue jay than an owl.
More students found a finch than a blackbird.
More students found a blackbird than an owl.
1/8
reported finding a blue jay.
6/7
reported finding a finch.
1/3
reported finding a blackbird.
11/24
reported finding an owl.
Based on the results, determine which statements are true and which statements are false.
Over half the students found a finch.
More students found a blackbird than a finch.
More students found a blue jay than an owl.
More students found a finch than a blackbird.
More students found a blackbird than an owl.
Answers
GPT-4o mini
To determine the truth of the statements based on the proportions given, let's first convert each reported fraction into decimals or percentages for better comparison.
Let \( N \) be the total number of students.
1. Blue Jay: \( \frac{1}{8}N = 0.125N \)
2. Finch: \( \frac{6}{7}N \approx 0.857N \)
3. Blackbird: \( \frac{1}{3}N \approx 0.333N \)
4. Owl: \( \frac{11}{24}N \approx 0.458N \)
Now let's analyze each statement:
1. **Over half the students found a finch.**
- We know \( \frac{6}{7}N \approx 0.857N \) which is greater than half of \( N \) (which is \( 0.5N \)).
- **True**
2. **More students found a blackbird than a finch.**
- The number of students who found a blackbird is \( \frac{1}{3}N \approx 0.333N \) and for a finch, it's \( \frac{6}{7}N \approx 0.857N \).
- Since \( 0.333N < 0.857N \),
- **False**
3. **More students found a blue jay than an owl.**
- The number of students who found a blue jay is \( \frac{1}{8}N = 0.125N \) and for an owl, it's \( \frac{11}{24}N \approx 0.458N \).
- Since \( 0.125N < 0.458N \),
- **False**
4. **More students found a finch than a blackbird.**
- As calculated earlier, \( \frac{6}{7}N \approx 0.857N \) (finch) is greater than \( \frac{1}{3}N \approx 0.333N \) (blackbird).
- **True**
5. **More students found a blackbird than an owl.**
- The number of students who found a blackbird is \( \frac{1}{3}N \approx 0.333N \) compared to the number who found an owl \( \frac{11}{24}N \approx 0.458N \).
- Since \( 0.333N < 0.458N \),
- **False**
### Summary of the Statements
- **Over half the students found a finch:** **True**
- **More students found a blackbird than a finch:** **False**
- **More students found a blue jay than an owl:** **False**
- **More students found a finch than a blackbird:** **True**
- **More students found a blackbird than an owl:** **False**
Let \( N \) be the total number of students.
1. Blue Jay: \( \frac{1}{8}N = 0.125N \)
2. Finch: \( \frac{6}{7}N \approx 0.857N \)
3. Blackbird: \( \frac{1}{3}N \approx 0.333N \)
4. Owl: \( \frac{11}{24}N \approx 0.458N \)
Now let's analyze each statement:
1. **Over half the students found a finch.**
- We know \( \frac{6}{7}N \approx 0.857N \) which is greater than half of \( N \) (which is \( 0.5N \)).
- **True**
2. **More students found a blackbird than a finch.**
- The number of students who found a blackbird is \( \frac{1}{3}N \approx 0.333N \) and for a finch, it's \( \frac{6}{7}N \approx 0.857N \).
- Since \( 0.333N < 0.857N \),
- **False**
3. **More students found a blue jay than an owl.**
- The number of students who found a blue jay is \( \frac{1}{8}N = 0.125N \) and for an owl, it's \( \frac{11}{24}N \approx 0.458N \).
- Since \( 0.125N < 0.458N \),
- **False**
4. **More students found a finch than a blackbird.**
- As calculated earlier, \( \frac{6}{7}N \approx 0.857N \) (finch) is greater than \( \frac{1}{3}N \approx 0.333N \) (blackbird).
- **True**
5. **More students found a blackbird than an owl.**
- The number of students who found a blackbird is \( \frac{1}{3}N \approx 0.333N \) compared to the number who found an owl \( \frac{11}{24}N \approx 0.458N \).
- Since \( 0.333N < 0.458N \),
- **False**
### Summary of the Statements
- **Over half the students found a finch:** **True**
- **More students found a blackbird than a finch:** **False**
- **More students found a blue jay than an owl:** **False**
- **More students found a finch than a blackbird:** **True**
- **More students found a blackbird than an owl:** **False**