To determine the number of trout in a lake, a conservationist catches 194 trout, tags them and throws them back into the lake. Later, 56 trout are caught; 14 of
them are tagged. How many trout would the conservationist expect to be in the
lake?

18

step-by-step explanation:

ik this stuph and i am smart donkey

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.