Answer:
Nate needs to score at least 92 points on the fifth test to have an average of at least 90.
Explanation:
To calculate the least number of points Nate needs on the fifth test to have an average of at least 90, we can use the concept of averages.
Nate has already taken four tests with scores of 85, 91, 89, and 93. Let's denote the score he needs on the fifth test as "x."
To find the average, we sum up all the scores and divide by the total number of tests.
Average = (Sum of scores) / (Number of tests)
We want the average to be at least 90, so we can set up the following inequality:
(85 + 91 + 89 + 93 + x) / 5 ≥ 90
Now, we can solve for "x":
(85 + 91 + 89 + 93 + x) / 5 ≥ 90
(358 + x) / 5 ≥ 90
Multiply both sides of the inequality by 5:
358 + x ≥ 450
Subtract 358 from both sides of the inequality:
x ≥ 450 - 358
x ≥ 92
Therefore, Nate needs to score at least 92 points on the fifth test to have an average of at least 90.