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# The number of electric scooters e that a factory can produce per day is a function of the number of hours h it operates and is given by e(h) = 290h, 0 <= h <= 10. The daily cost c to manufacture e electric scooters is given by the function c(e) = 0.05e^2 + 65e + 1000. (a) Find (c @ e)(h). (b) Evaluate (c @ e)(13).

Question
Composite functions
asked 2021-03-05
The number of electric scooters e that a factory can produce per day is a function of the number of hours h it operates and is given by $$\displaystyle{e}{\left({h}\right)}={290}{h},{0}\le{h}\le{10}.$$
The daily cost c to manufacture e electric scooters is given by the function $$\displaystyle{c}{\left({e}\right)}={0.05}{e}^{{2}}+{65}{e}+{1000}.$$
(a) Find $$\displaystyle{\left({c}\circ{e}\right)}{\left({h}\right)}.$$
(b) Evaluate $$\displaystyle{\left({c}\circ{e}\right)}{\left({13}\right)}.$$

## Answers (1)

2021-03-06
The composition of the function c(e) and e(h) is denoted by $$\displaystyle{\left({c}\circ{e}\right)}{\left({h}\right)}$$ is given by the formula,
$$\displaystyle{\left({c}\circ{e}\right)}{\left({h}\right)}={c}{\left({e}{\left({h}\right)}\right)}$$
(a) Compute the composite function as,
$$\displaystyle{e}{\left({h}\right)}={290}{h},{0}\le{h}\le{10}$$
$$\displaystyle{c}{\left({e}\right)}={0.05}{e}^{{2}}+{65}{e}+{1000}$$
$$\displaystyle{\left({c}\circ{e}\right)}{\left({h}\right)}={c}{\left({e}{\left({h}\right)}\right)}$$
$$\displaystyle={c}{\left({290}{h}\right)}$$
$$\displaystyle={0.05}{\left({90}{h}\right)}^{{2}}+{65}{\left({290}{h}\right)}+{100}$$
$$\displaystyle{3920}{h}^{{2}}+{18850}{h}+{1000},{0}\le{h}\le{10}$$
(b) The composite function $$\displaystyle{\left({c}\circ{e}\right)}{\left({h}\right)}$$ is not defined for h = 13.
Hence, the function $$\displaystyle{\left({c}\circ{e}\right)}{\left({13}\right)}$$ cannot be evaluated.

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This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
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Let's compare the percentage of unarmed shot for each race.
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Think of it this way. If you went to a college that was 90% female and 10% male, then females would most likely have the highest percentage of A grades. They would also most likely have the highest percentage of B, C, D and F grades
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