Answer the following questions:

Each week, Heather’s company has $5000 in fixed costs plus an additional $250 for each system produced. The company is able to p

kvv77 [185]

The question is an illustration of composite functions.

Functions c(n) and h(n) are $\mathbf{c(n) = 5000 + 250n}$ and $\mathbf{n(h) = 5h}$
The composite function c(n(h)) is $\mathbf{c(n(h)) = 5000 + 1250h}$
The value of c(n(100)) is $\mathbf{c(n(100)) = 130000}$
The interpretation is: "the cost of working for 100 hours is $130000"

The given parameters are:

$5000 in fixed costs plus an additional $250
5 systems in one hour of production

(a) Functions c(n) and n(h)

Let the number of system be n, and h be the number of hours

So, the cost function (c(n)) is:

$\mathbf{c(n) = Fixed + Additional \times n}$

This gives

$\mathbf{c(n) = 5000 + 250 \times n}$

$\mathbf{c(n) = 5000 + 250n}$

The function for number of systems is:

$\mathbf{n(h) = 5 \times h}$

$\mathbf{n(h) = 5h}$

(b) Function c(n(h))

In (a), we have:

$\mathbf{c(n) = 5000 + 250n}$

$\mathbf{n(h) = 5h}$

Substitute n(h) for n in $\mathbf{c(n) = 5000 + 250n}$

$\mathbf{c(n(h)) = 5000 + 250n(h)}$

Substitute $\mathbf{n(h) = 5h}$

$\mathbf{c(n(h)) = 5000 + 250 \times 5h}$

$\mathbf{c(n(h)) = 5000 + 1250h}$

(c) Find c(n(100))

c(n(100)) means that h = 100.

So, we have:

$\mathbf{c(n(100)) = 5000 + 1250 \times 100}$

$\mathbf{c(n(100)) = 5000 + 125000}$

$\mathbf{c(n(100)) = 130000}$

(d) Interpret (c)

In (c), we have: $\mathbf{c(n(100)) = 130000}$

It means that:

The cost of working for 100 hours is $130000

Read more about composite functions at:

brainly.com/question/10830110

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3 years ago

A collection of coins nickels and quarters is worth $1.25 . There are 13 coins in all. How many of each are there?

yulyashka [42]

3 quarters (75cents) and 10 nickels (50cents) = 1.25$

7 0

3 years ago

What is the arithmetic sequence of -1.2, 0.6 , 1.8 , 3.0

zlopas [31]

-1.2 ( a negative number is always smaller than positive number)

0.6

1.8

3.0

4 0

3 years ago

The number of popcorns sold at a movie theatre was 8 less than three times the number hotdogs. How many hotdogs did the theatre

serg [7]

Answer:

200

Step-by-step explanation:

If the theater sold 8 more popcorns, the total would be 600, and it would be exactly 3 times the number of hotdogs. The theater sold 1/3 of 600, or 200 hotdogs.

6 0

3 years ago

How do you solve this: In ?PQR, PQ = 39 cm and PN is an altitude. Find PR if QN = 36 cm and RN = 8 cm.

ikadub [295]

Answer:

PR = 17 cm

Step-by-step explanation:

Given :

In ΔPQR,

PQ = 39 cm

PN is an altitude.

QN = 36 cm