Amanufacturing unit currently operates at 80 percent of its capacity. the profit function for the unit at the optimum output, x, is given by p(x) = -0.1x^2 + 80x − 60. if the function f(x) models the current capacity of the unit, the composite function giving the unit's current profit function is a. f(p(x))=-0.064x^2+6.4x-60 b. p(f(x))=-0.64x^2+0.64x-60 c. p(f(x))=-0.064x^2+64x-60 d. p(f(x))=-0.64x^2+6.4x-60 e. f(p(x))=-0.064x^2+64x-60 if the optimum output is 500 units, the current profit is $ a.15,400 b.15,940 c.16,060 d.16,600

Option D

Step-by-step explanation:

Let the manufacturing unit operates with the maximum capacity = x

Since manufacturing unit currently operates at 80%

So function f(x) that models the current capacity of the unit will be

f(x) = (0.80)x

Given profit function for the unit at optimum output is

p(x) = ( -0.1) x² + 80x - 60

so composite function giving the unit's current profit function will be

p[f(x)] = (-0.1) (0.8x)² + 80(0.80x) - 60

         = -(0.1) (0.64x²) + 80 (0.08x) - 60

         = - 0.64x² + 6.4x - 60

Option D will be the answer.

answer: the distance

step-by-step explanation:

to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) use the formula d (x2 x1)2 (y2 y1)2. to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) use the formula

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.