10 points & ! show process : )

in a math class there are five equally weighted tests. a student has grades of
94, 92, 78, and 97 on the first four tests. to earn an a in the class, the students
must have an average of at least 90. what must the student get on the fifth test
to earn an a in the math class?

the student needs at least an 89 on the fifth test to earn an a in the math
class.

Step-by-step explanation:

From the problem statement, the average needs to be , the total number of students is , and the sum is , where is the grade the final student gets.

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66answer:

step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.