Jan has 35 teaspoons of chocolate mix and 45 teaspoons of french vanilla cocoa mix. she wants to put the same amount of mix into each jar, and she only wants one flavor of mix on each jar. she wants to fill as many jars as possible. how many jars of french vanilla cocoa mix will jan fill?

9 jars

Step-by-step explanation:

Given,

Number of teaspoons of chocolate coca mix = 35,

Number of teaspoons of french vanilla coca mix = 45,

∵ 35 = 5 × 7,

45 = 5 × 3 × 3

⇒ HCF(35, 45) = 5

Thus, the minimum number of teaspoons in each jar = HCF(35,45) = 5,

Therefore, the maximum possible number of jars = maximum number of jars of french vanilla + maximum number of jars of coca mix

=

= 9

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.