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Not possible scores: 6, 15, 23, 31 and 58.
Step-by-step explanation:
We have been given that Juana threw five darts at a dartboard. The possible scores on the target were 2, 4, 6, 8, and 10. Each dart hit the target. We are asked to choose the total scores that can be quickly identified as "not possible".
Given scores: 38, 23, 58, 30, 42, 31, 26, 6, 14, or 15.
Since the maximum score is 10 and number of hits are 5, therefore, the maximum score can be hitting 10 each of the 5 times.
Since the maximum score is 50, therefore, 58 is an impossible score.
Since the minimum score is 2 and number of hits are 5, therefore, the minimum score can be hitting 2 each of the 5 times.
Since the minimum score is 10, therefore, 6 is an impossible score.
Since all scores on board are even, so the sum of 5 hits must be even, therefore, odd numbers like 15, 23, 31 are not possible scores.