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We need 232 mL of Compound A

Step-by-step explanation:

We know the ratio

A    : B    : total

4       3      4+3

4      3        7

We want 406

406 /7 =58

Multiply each part by 58

A       : B        : total

4*58    3*58     7*58

232      174       406

We need 232 mL of Compound A

$30.32

step-by-step explanation:

65.00*.12=2.80

65.00-2.80=57.20

57.20*1.06=60.632

60.632/2=30.316

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.