In interval estimation, the t distribution is applicable only when a. the population has a mean of less than 30.

b. the sample standard deviation is used to estimate the population standard deviation.

c. the variance of the population is known.

d. the mean of the population is unknown.

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.