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.
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.
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 of the statements, we first need to establish a common denominator for the fractions given for each type of tree. This will allow us to compare the reported findings directly.
The fractions given are:
- Birch tree: \( \frac{1}{7} \)
- Pine tree: \( \frac{7}{9} \)
- Maple tree: \( \frac{1}{4} \)
- Oak tree: \( \frac{11}{23} \)
The least common multiple (LCM) of the denominators (7, 9, 4, and 23) can be found to be 126:
- For Birch: \( \frac{1}{7} = \frac{18}{126} \)
- For Pine: \( \frac{7}{9} = \frac{98}{126} \)
- For Maple: \( \frac{1}{4} = \frac{31.5}{126} \) (which is not possible, so it makes more sense to convert it directly)
- For Oak: \( \frac{11}{23} = \frac{60}{126} \)
Now we can convert each fraction into a comparable number of students based on a hypothetical total (let's assume there are 126 students total). This yields:
- Birch tree: 18 students
- Pine tree: 98 students
- Maple tree: 31.5 shouldn't be used since we can't have half students. Let's round that given the context to 31 (there could be a slight misunderstanding in numbers).
- Oak tree: 60 students
Now, let's assess each statement:
1. **Over half the students found a pine tree.**
- True, because 98 out of 126 is more than half.
2. **More students found a maple tree than a pine tree.**
- False, because 31 is less than 98.
3. **More students found a birch tree than an oak tree.**
- False, because 18 is less than 60.
4. **More students found a pine tree than a birch tree.**
- True, because 98 is greater than 18.
5. **More students found a maple tree than an oak tree.**
- False, because 31 is less than 60.
In summary:
1. True
2. False
3. False
4. True
5. False
The fractions given are:
- Birch tree: \( \frac{1}{7} \)
- Pine tree: \( \frac{7}{9} \)
- Maple tree: \( \frac{1}{4} \)
- Oak tree: \( \frac{11}{23} \)
The least common multiple (LCM) of the denominators (7, 9, 4, and 23) can be found to be 126:
- For Birch: \( \frac{1}{7} = \frac{18}{126} \)
- For Pine: \( \frac{7}{9} = \frac{98}{126} \)
- For Maple: \( \frac{1}{4} = \frac{31.5}{126} \) (which is not possible, so it makes more sense to convert it directly)
- For Oak: \( \frac{11}{23} = \frac{60}{126} \)
Now we can convert each fraction into a comparable number of students based on a hypothetical total (let's assume there are 126 students total). This yields:
- Birch tree: 18 students
- Pine tree: 98 students
- Maple tree: 31.5 shouldn't be used since we can't have half students. Let's round that given the context to 31 (there could be a slight misunderstanding in numbers).
- Oak tree: 60 students
Now, let's assess each statement:
1. **Over half the students found a pine tree.**
- True, because 98 out of 126 is more than half.
2. **More students found a maple tree than a pine tree.**
- False, because 31 is less than 98.
3. **More students found a birch tree than an oak tree.**
- False, because 18 is less than 60.
4. **More students found a pine tree than a birch tree.**
- True, because 98 is greater than 18.
5. **More students found a maple tree than an oak tree.**
- False, because 31 is less than 60.
In summary:
1. True
2. False
3. False
4. True
5. False