solve In 2010, the percentage of assisted living residents who had both heart disease and depression was 9%, the percentage with only heart disease was 25%, and the percentage with either condition was 48%. What percentage of assisted living residents had only depression

The percentage of assisted living residents had only depression

P(D) =0.32

Step-by-step explanation:

Explanation:-

Given  the percentage of assisted living residents who had both heart disease and depression was 9%

Let The event 'H' be the event of heart disease and 'D' be the event of depression

P(H ∩D) = 9% =0.09

The  percentage with only heart disease was 25%

P(H) = 0.25

The percentage with either condition was 48%.

P(H∪D) = 48%=0.48

By addition theorem on probability

            P(D) = 0.48 -0.16

            P(D) = 0.32  

The percentage of assisted living residents had only depression

P(D) =0.32

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.