Mr. Bryant gave all of his classes the same quiz consisting of 3 true/false questions. His grading scheme is shown in the table. If all the students guess on all the questions, which is CLOSEST to the average number of points a student is likely to be awarded on the quiz?

stethere all not eveanp-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.