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Sagot :
To address this question, let's examine Jared's recorded results along with the predictions made. Here is the table of Jared's results:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Glass} & \begin{array}{c} \text{0} \\ \text{minutes} \end{array} & \begin{array}{c} \text{15} \\ \text{minutes} \end{array} & \begin{array}{c} \text{30} \\ \text{minutes} \end{array} & \begin{array}{c} \text{45} \\ \text{minutes} \end{array} & \begin{array}{c} \text{60} \\ \text{minutes} \end{array} \\ \hline \text{A} & 0\ \text{cm} & 0\ \text{cm} & 0\ \text{cm} & 0\ \text{cm} & 0\ \text{cm} \\ \hline \text{B} & 0\ \text{cm} & 2\ \text{cm} & 4\ \text{cm} & 5\ \text{cm} & 6\ \text{cm} \\ \hline \text{C} & 0\ \text{cm} & 0\ \text{cm} & 0\ \text{cm} & 0\ \text{cm} & 0\ \text{cm} \\ \hline \text{D} & 0\ \text{cm} & 0\ \text{cm} & 0.5\ \text{cm} & 1\ \text{cm} & 1\ \text{cm} \\ \hline \text{E} & 0\ \text{cm} & 2\ \text{cm} & 4\ \text{cm} & 5\ \text{cm} & 6\ \text{cm} \\ \hline \end{array} \][/tex]
Let’s compare this data with the predictions for each glass:
1. Glass A:
- Prediction: No change.
- Result: 0 cm at all time intervals.
- Match: The prediction matches the result exactly. No change was observed.
2. Glass B:
- Prediction: Gradual increase.
- Result: 0 cm, 2 cm, 4 cm, 5 cm, 6 cm.
- Match: The prediction matches the result. There is a gradual increase observed over time.
3. Glass C:
- Prediction: No change.
- Result: 0 cm at all time intervals.
- Match: The prediction matches the result exactly. No change was observed.
4. Glass D:
- Prediction: Slight increase.
- Result: 0 cm, 0 cm, 0.5 cm, 1 cm, 1 cm.
- Match: The prediction matches the result. There is a slight increase from 0 cm to 1 cm over time.
5. Glass E:
- Prediction: Gradual increase.
- Result: 0 cm, 2 cm, 4 cm, 5 cm, 6 cm.
- Match: The prediction matches the result. There is a gradual increase observed over time.
Summarizing these findings:
- Glass A: Prediction: No change. Result: No change. Match: True
- Glass B: Prediction: Gradual increase. Result: Gradual increase. Match: True
- Glass C: Prediction: No change. Result: No change. Match: True
- Glass D: Prediction: Slight increase. Result: Slight increase. Match: True
- Glass E: Prediction: Gradual increase. Result: Gradual increase. Match: True
Therefore, we can conclude that Jared's results matched the predictions for all glasses as follows:
```
{'A': True, 'B': True, 'C': True, 'D': True, 'E': True}
```
Each glass showed behavior in line with the initial predictions, with all predictions being accurate.
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Glass} & \begin{array}{c} \text{0} \\ \text{minutes} \end{array} & \begin{array}{c} \text{15} \\ \text{minutes} \end{array} & \begin{array}{c} \text{30} \\ \text{minutes} \end{array} & \begin{array}{c} \text{45} \\ \text{minutes} \end{array} & \begin{array}{c} \text{60} \\ \text{minutes} \end{array} \\ \hline \text{A} & 0\ \text{cm} & 0\ \text{cm} & 0\ \text{cm} & 0\ \text{cm} & 0\ \text{cm} \\ \hline \text{B} & 0\ \text{cm} & 2\ \text{cm} & 4\ \text{cm} & 5\ \text{cm} & 6\ \text{cm} \\ \hline \text{C} & 0\ \text{cm} & 0\ \text{cm} & 0\ \text{cm} & 0\ \text{cm} & 0\ \text{cm} \\ \hline \text{D} & 0\ \text{cm} & 0\ \text{cm} & 0.5\ \text{cm} & 1\ \text{cm} & 1\ \text{cm} \\ \hline \text{E} & 0\ \text{cm} & 2\ \text{cm} & 4\ \text{cm} & 5\ \text{cm} & 6\ \text{cm} \\ \hline \end{array} \][/tex]
Let’s compare this data with the predictions for each glass:
1. Glass A:
- Prediction: No change.
- Result: 0 cm at all time intervals.
- Match: The prediction matches the result exactly. No change was observed.
2. Glass B:
- Prediction: Gradual increase.
- Result: 0 cm, 2 cm, 4 cm, 5 cm, 6 cm.
- Match: The prediction matches the result. There is a gradual increase observed over time.
3. Glass C:
- Prediction: No change.
- Result: 0 cm at all time intervals.
- Match: The prediction matches the result exactly. No change was observed.
4. Glass D:
- Prediction: Slight increase.
- Result: 0 cm, 0 cm, 0.5 cm, 1 cm, 1 cm.
- Match: The prediction matches the result. There is a slight increase from 0 cm to 1 cm over time.
5. Glass E:
- Prediction: Gradual increase.
- Result: 0 cm, 2 cm, 4 cm, 5 cm, 6 cm.
- Match: The prediction matches the result. There is a gradual increase observed over time.
Summarizing these findings:
- Glass A: Prediction: No change. Result: No change. Match: True
- Glass B: Prediction: Gradual increase. Result: Gradual increase. Match: True
- Glass C: Prediction: No change. Result: No change. Match: True
- Glass D: Prediction: Slight increase. Result: Slight increase. Match: True
- Glass E: Prediction: Gradual increase. Result: Gradual increase. Match: True
Therefore, we can conclude that Jared's results matched the predictions for all glasses as follows:
```
{'A': True, 'B': True, 'C': True, 'D': True, 'E': True}
```
Each glass showed behavior in line with the initial predictions, with all predictions being accurate.
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