Answer :
Let's analyze each statement in the context of the provided data on paramecium contractile vacuole contractions:
### Given Data:
- Very high concentration: 2 contractions per minute
- High concentration: 8 contractions per minute
- Medium concentration: 15 contractions per minute
- Low concentration: 22 contractions per minute
- Very low concentration: 30 contractions per minute
### Statements to Evaluate:
1. The graph has five bars of equal height.
- To evaluate this statement, we look at the given contractions per minute for each concentration.
- The values are [tex]\(2, 8, 15, 22, 30\)[/tex]. Clearly, these are different values.
- Therefore, the statement that the bars are of equal height is false.
2. The bars range from tallest for very high concentration to shortest for very low concentration.
- This statement suggests that the tallest bar represents the very high concentration, and the shortest represents the very low concentration.
- The given data shows that the very high concentration has 2 contractions per minute, while the very low concentration has 30 contractions per minute.
- Therefore, the tallest bar should represent 30 contractions per minute (very low concentration), and the shortest bar should represent 2 contractions per minute (very high concentration). The statement implies the opposite.
- Hence, this statement is false.
3. The bar for very low concentration is twice the height of the bar for medium concentration.
- For this statement to be true, the contractions for very low concentration should be twice that of the medium concentration.
- The contractions per minute for very low concentration are 30, and for medium concentration, they are 15.
- [tex]\( 30 \text{ (very low) } = 2 \times 15 \text{ (medium) } \)[/tex]
- This statement is true since 30 is indeed twice 15.
4. The bar for very high concentration is five times the height of the bar for very low concentration.
- For this statement to be true, the contractions for very high concentration should be five times that of the very low concentration.
- The contractions per minute for very high concentration are 2, and for very low concentration, they are 30.
- [tex]\( 2 \text{ (very high) } \)[/tex] is not [tex]\( 5 \times 30 \text{ (very low) }\)[/tex]
- This statement is false because 2 is not equal to 150.
### Summary of Evaluations:
- The first statement is false.
- The second statement is false.
- The third statement is true.
- The fourth statement is false.
Thus, the correct answers describing the bar graph are:
- The graph has five bars of equal height: [tex]\(0\)[/tex] (False)
- The bars range from tallest for very high concentration to shortest for very low concentration: [tex]\(0\)[/tex] (False)
- The bar for very low concentration is twice the height of the bar for medium concentration: [tex]\(1\)[/tex] (True)
- The bar for very high concentration is five times the height of the bar for very low concentration: [tex]\(0\)[/tex] (False)
The numerical result representing the truth value of each statement is [tex]\( (0, 0, 1, 0) \)[/tex].
### Given Data:
- Very high concentration: 2 contractions per minute
- High concentration: 8 contractions per minute
- Medium concentration: 15 contractions per minute
- Low concentration: 22 contractions per minute
- Very low concentration: 30 contractions per minute
### Statements to Evaluate:
1. The graph has five bars of equal height.
- To evaluate this statement, we look at the given contractions per minute for each concentration.
- The values are [tex]\(2, 8, 15, 22, 30\)[/tex]. Clearly, these are different values.
- Therefore, the statement that the bars are of equal height is false.
2. The bars range from tallest for very high concentration to shortest for very low concentration.
- This statement suggests that the tallest bar represents the very high concentration, and the shortest represents the very low concentration.
- The given data shows that the very high concentration has 2 contractions per minute, while the very low concentration has 30 contractions per minute.
- Therefore, the tallest bar should represent 30 contractions per minute (very low concentration), and the shortest bar should represent 2 contractions per minute (very high concentration). The statement implies the opposite.
- Hence, this statement is false.
3. The bar for very low concentration is twice the height of the bar for medium concentration.
- For this statement to be true, the contractions for very low concentration should be twice that of the medium concentration.
- The contractions per minute for very low concentration are 30, and for medium concentration, they are 15.
- [tex]\( 30 \text{ (very low) } = 2 \times 15 \text{ (medium) } \)[/tex]
- This statement is true since 30 is indeed twice 15.
4. The bar for very high concentration is five times the height of the bar for very low concentration.
- For this statement to be true, the contractions for very high concentration should be five times that of the very low concentration.
- The contractions per minute for very high concentration are 2, and for very low concentration, they are 30.
- [tex]\( 2 \text{ (very high) } \)[/tex] is not [tex]\( 5 \times 30 \text{ (very low) }\)[/tex]
- This statement is false because 2 is not equal to 150.
### Summary of Evaluations:
- The first statement is false.
- The second statement is false.
- The third statement is true.
- The fourth statement is false.
Thus, the correct answers describing the bar graph are:
- The graph has five bars of equal height: [tex]\(0\)[/tex] (False)
- The bars range from tallest for very high concentration to shortest for very low concentration: [tex]\(0\)[/tex] (False)
- The bar for very low concentration is twice the height of the bar for medium concentration: [tex]\(1\)[/tex] (True)
- The bar for very high concentration is five times the height of the bar for very low concentration: [tex]\(0\)[/tex] (False)
The numerical result representing the truth value of each statement is [tex]\( (0, 0, 1, 0) \)[/tex].
