Final answer:
To find two possible values for the unknown number x, given the range of the set is 61, x can either be the smallest value (-13) or the largest value (78) in the set.
Step-by-step explanation:
Calculating Possible Values of x
Given the numbers 46, 30, 17, x, 48, 38, 27, and 40, and knowing that the range is 61, we can find two possible values for x. The range is the difference between the largest and smallest numbers in a set. To achieve a range of 61, x must either be the minimum or maximum value in the set.
If x is the smallest value, we subtract the range from the current maximum value: 48 - 61 = -13. Since the smallest given value is 17, and -13 is not in the list, x must be -13 for the range to be 61. Conversely, if x is the largest value, we add the range to the current minimum value: 17 + 61 = 78. Therefore, x can also be 78 to satisfy the range of 61.
Thus, the two possible values for x are -13 and 78.