1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Marizza181 [45]
3 years ago
12

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

roduce 5 systems in one hour of production, and h represent the number of hours in production
Part a] write functions c(n) and n(h) to model this situation, explain what they represent

Part b] Then write a function c(n(h)) to represent the coat incurred in h hours. Show the work or explain the reasoning used to determine the answer

Part c] Find c(n(100)).

Part d] interpret your solution to part c
Mathematics
1 answer:
kvv77 [185]3 years ago
5 0

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: <em>"the cost of working for 100 hours is $130000"</em>

The given parameters are:

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

<u>(a) Functions c(n) and n(h)</u>

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}

<u>(b) Function c(n(h))</u>

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}

<u>(c) Find c(n(100))</u>

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}

<u>(d) Interpret (c)</u>

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

You might be interested in
What is the volume of the cone using pi/3.14 using the numbers 2and 3
k0ka [10]

Answer:

V=π*r^(2)*h/3

Step-by-step explanation:

8 0
3 years ago
What is y+2=⅞(x-3) in standard form?
Alla [95]
The answer is 7x - 8y = 37
8 0
3 years ago
What 2 numbers multiply to make -48 and combine to make 2?<br> ____ and ___
Mumz [18]
-6x8 equals -48 and adds to give you positive two
7 0
2 years ago
Read 2 more answers
Solve for x. 5(x – 10) = 30 – 15x
klio [65]
You can start by distributing the 5 to everything in the parenthesis.
5x-50=30-15x

Then get rid of your x values from one side, I chose to subtract 5x

-50 = 30 - 20x

Then subtract 30

-80=-20x
/-20
4=x

You can check by plugging your x into the equation to make sure it's right!

6 0
3 years ago
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!! I CANNOT RETAKE THIS!!<br><br> Simplify.
NNADVOKAT [17]

Answer:  \frac{2x(5x + 1)}{4x - 1}

<u>Step-by-step explanation:</u>

\frac{4x^{3}-12x^{2}}{4x^{2}+7x - 2} ÷ \frac{2x^{2}-6x}{5x^{2}+11x + 2}

= \frac{4x^{2}(x - 3)}{(4x - 1)(x + 2)} ÷ \frac{2x(x - 3)}{(5x + 1)(x + 2)}

= \frac{4x^{2}(x - 3)}{(4x - 1)(x + 2)} x \frac{(5x + 1)(x + 2)}{2x(x - 3)}

= \frac{2x(5x + 1)}{4x - 1}

8 0
3 years ago
Other questions:
  • Suppose x=0.5(300-x). what is the value of x?
    8·1 answer
  • 1. is the number written in scientific notation? if not, explain. 4.8 x 100^7 a) no; it is not written as a number times a power
    9·1 answer
  • 38=2a+54 solve equation check your answer
    9·1 answer
  • Is y=19x-5 a proportional relationship?
    6·1 answer
  • 5(2x - 8) + 15 = -15<br><br> the steps to solve the equation and explain each step.
    13·2 answers
  • Help me please thank you
    13·1 answer
  • I am tired of this so here is the last time and i'm gonna waste my points since nobody in the world actually cares
    6·1 answer
  • What is the area of this composite figure??
    7·1 answer
  • PLEASE HELP ME I WILL MARK BRAINLIST IF YOU SHOW YOUR WORK !!
    15·2 answers
  • Help me pleaseeeeeeee
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!