Final answer:
To determine the score needed on the sixth assignment for a mean of 85, add the first five scores, multiply the desired mean by six, and subtract the subtotal from this product. Adam needs to score 90 on the sixth assignment to achieve the mean of 85.
Step-by-step explanation:
To find the score on the sixth assignment that would result in a mean of 85, we first need to determine the total points Adam has earned on the first five assignments. We add up the scores 75, 88, 92, 94, and 71 to get a subtotal. Then we multiply the desired mean (85) by the total number of assignments (6) to find the grand total required for all six assignments. Finally, we subtract Adam's subtotal from this grand total to find out the score on the sixth assignment.
Let's perform these calculations step by step:
Add the scores of the first five assignments: 75 + 88 + 92 + 94 + 71 = 420.
Multiply the desired mean (85) by the total number of assignments (6): 85 * 6 = 510.
Subtract Adam's subtotal from the grand total: 510 - 420 = 90.
Therefore, the score Adam must earn on the sixth assignment to achieve a mean of 85 is 90.