Final answer:
By adding the known numbers in the sequence and dividing by the total count, we find the mean. After testing the provided options, we determine that option B) 35 is the correct mean (average) value.
Step-by-step explanation:
To find the mean (average) value of the sequence 9, 45, 42, 31, 42, x, we first need to add all the numbers together, including the unknown x, and then divide by the total number of values in the sequence.
The sum of the known values is 9 + 45 + 42 + 31 + 42 = 169. Since we are looking for the mean of 6 numbers, we divide this sum by 6.
The equation to find x, given the mean (average) value, would be (169 + x) / 6 = mean.
As the options A) 9 B) 35 C) 39 D) 42 are provided for the mean, we can substitute each into the equation to see which one solves the equation correctly.
Using option B) 35 as the potential mean, we would have: (169 + x) / 6 = 35. Multiplying both sides by 6 gives 169 + x = 210, and subtracting 169 from both sides gives x = 210 - 169, which results in x = 41.
Since we could find a value of x that makes the mean 35, option B) 35 is the correct answer.