In a certain learning experiment, each participant had three trials and was assigned, for each trial, a score of either -2, -1, 0, 1, or 2. The participants final score consisted of the sum of the first trial score, 2 times the second trial score, and 3 times the third trial score. If Anne received scores of 1 and -1 for her first two trials, not necessarily in that order, which of the following could NOT be her final score?a)-4b)-2c)1d)5e)6Correct answer is option 'E'. Can you explain this answer?

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In a certain learning experiment, each participant had three trials and was assigned, for each trial, a score of either -2, -1, 0, 1, or 2. The participant's final score consisted of the sum of the first trial score, 2 times the second trial score, and 3 times the third trial score. If Anne received scores of 1 and -1 for her first two trials, not necessarily in that order, which of the following could NOT be her final score?

a)
-4
b)
-2
c)
1
d)
5
e)
6

Correct answer is option 'E'. Can you explain this answer?

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In a certain learning experiment, each participant had three trials an...

- **Understanding the Problem:**
The problem states that Anne received scores of 1 and -1 for her first two trials. Her final score is calculated as the sum of the first trial score, 2 times the second trial score, and 3 times the third trial score.
- **Calculating Anne's Final Score:**
Let's assume that Anne's first trial score is 1 and her second trial score is -1. Therefore, her final score can be calculated as follows:
Final Score = 1 + (2 * (-1)) + (3 * X) = 1 - 2 + 3X = -1 + 3X
Now, for the third trial, Anne can receive a score of either -2, -1, 0, 1, or 2.
- **Determining Possible Final Scores:**
We can calculate Anne's possible final scores by substituting the third trial scores into the equation:
- If the third trial score is -2: Final Score = -1 + 3(-2) = -1 - 6 = -7
- If the third trial score is -1: Final Score = -1 + 3(-1) = -1 - 3 = -4
- If the third trial score is 0: Final Score = -1 + 3(0) = -1 + 0 = -1
- If the third trial score is 1: Final Score = -1 + 3(1) = -1 + 3 = 2
- If the third trial score is 2: Final Score = -1 + 3(2) = -1 + 6 = 5
- **Identifying the Impossible Final Score:**
From the calculations above, we can see that Anne's final score can be -7, -4, -1, 2, or 5. The only score that could NOT be her final score is 6, which is not among the possible final scores calculated.
Therefore, option E - 6 is the correct answer as it is the only score that cannot be Anne's final score based on the given information.

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In a certain learning experiment, each participant had three trials and was assigned, for each trial, a score of either -2, -1, 0, 1, or 2. The participants final score consisted of the sum of the first trial score, 2 times the second trial score, and 3 times the third trial score. If Anne received scores of 1 and -1 for her first two trials, not necessarily in that order, which of the following could NOT be her final score?a)-4b)-2c)1d)5e)6Correct answer is option 'E'. Can you explain this answer?

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