A wedding planner uses 72 ivy stems for 18 centerpieces. When she arrives at the venue, she realizes she will only need 16 centerpieces. How many ivy stem should she use so that the ratio of ivy stems to centerpieces stays the same?

64 ivy stems

Step-by-step explanation:

A wedding planner uses 72 ivy stems for 18 centerpieces.

for only need 16 centerpieces ⇒ she will use x  ivy stems

Using the ratio and the proportional

ivy stems : centerpieces

    72       :         18

     x        :          16

Solve for x

∴ x = 16 * 72/18 = 64 ivy stems

So, she should us 64 ivy stems

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.