Jasmine asked her classmates to name all the types of trees they found while on a field trip at a local park.

Question

1/7 reported finding a birch tree.
9/7 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. •

Answer 1

To analyze the statements, we first need to consider the fractions of students that reported finding each type of tree.

1. Birch tree: $\frac{1}{7}$
2. Pine tree: $\frac{9}{7}$ (This fraction is greater than 1, which is impossible in this context; it suggests that at least 9 students reported finding a pine tree while implying more than total students, which makes no sense.)
3. Maple tree: $\frac{1}{4}$
4. Oak tree: $\frac{11}{23}$

Since there's an issue with the pine tree fraction, we would need to assume that it is at least 1 (representing a whole student). Therefore, we should interpret these fractions within the context of a common denominator and students.

Let’s use a total number of students, for example, let’s take 28 as a base number of total students (the least common multiple of the denominators 7 and 4 would be 28).

• For the birch tree: $$\frac{1}{7}\times 28=4\text{ students}$$
• For the pine tree: $$\frac{9}{7}\text{ instead could mean at least 9 students.}$$
• For the maple tree: $$\frac{1}{4}\times 28=7\text{ students}$$
• For the oak tree: $$\frac{11}{23}\text{ means approximately }11\times (\frac{28}{23})\approx 13\text{ students}$$

Therefore:

• Birch: 4 students
• Pine: 9 or more students (could assume 9)
• Maple: 7 students
• Oak: Approximately 13 students

Using that context, we can analyze the statements:

1. Over half the students found a pine tree.
   False. Assuming at least 9 students (assuming the minimum of 9 based on purely the fractions), that would be $9<14$ (half of 28 is 14), which is not over half.

2. More students found a maple tree than a pine tree.
   False. If 9 students reported a pine tree, 7 reported a maple tree. Therefore, more students found a pine tree (9) than a maple (7).

3. More students found a birch tree than an oak tree.
   False. 4 students found birch, while about 13 students found oak.

4. More students found a pine tree than a birch tree.
   True. With at least 9 reporting pine and 4 reporting birch, more students did indeed find pine trees than birch trees.

Final results for the statements:

1. False
2. False
3. False
4. True

Answer 2

Sorry there are 5 questions

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 a oak tree.

Answer 3

Let's clarify the previous analysis and include all five statements now. To do this accurately, let's determine the number of students associated with each tree type based on the fractions provided. For ease of analysis, we can look at an assumed total number of students that is compatible with the denominators given (i.e., 28).

Total students: 28

1. Birch tree: $$\frac{1}{7}\times 28=4\text{ students}$$

2. Pine tree: $$\frac{9}{7}\text{ (assumes this means more than the total)},\text{ likely indicating at least 9.}$$

   But let's clarify with the assumption that this indicates any number beyond the total is strictly infeasible and thus cannot be computed as valid in this context. Let's assume it was poorly stated, and we take a value of 9.

3. Maple tree: $$\frac{1}{4}\times 28=7\text{ students}$$

4. Oak tree: $$\frac{11}{23}\times 28=\approx 13\text{ students}$$

Now the count of students finding each tree:

• Birch: 4 students
• Pine: 9 students
• Maple: 7 students
• Oak: approximately 13 students

Now we can evaluate the statements:

1. Over half the students found a pine tree.
   False. Given the assumption of 28 total students, half would be 14. Since 9 is not greater than 14, this statement is false.

2. More students found a maple tree than a pine tree.
   False. Since 7 (maple) is less than 9 (pine), this statement is false.

3. More students found a birch tree than an oak tree.
   False. 4 (birch) is less than 13 (oak), so this statement is false.

4. More students found a pine tree than a birch tree.
   True. 9 (pine) is indeed greater than 4 (birch), so this statement is true.

5. More students found a maple tree than an oak tree.
   False. 7 (maple) is less than 13 (oak), making this statement false.

Summary of statements:

1. Over half the students found a pine tree. False
2. More students found a maple tree than a pine tree. False
3. More students found a birch tree than an oak tree. False
4. More students found a pine tree than a birch tree. True
5. More students found a maple tree than an oak tree. False

Let me know if you need any further clarifications!