Samantha uses 3 cups of flour to bake 15 cupcakes. If she uses 5
cups of flour, how many cupcakes
can Samantha bake?

25 cupcakes

Step-by-step explanation:

set up a proportion then cross-multiply:

3/15 = 5/c

3c = 75

c = 25

25 cupcakes

Step-by-step explanation:

1. What is the ratio?

3 cups of flour to 15 cupcakes (3:15)

2. Quotient

What is the quotient of 15 and 3? 5

3. 5 x 5

25

25 cupcakes

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.