Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Write a linear model for the amount of boxes, b, as a function of the number of hours since they opened, h. Use your model to predict the number of boxes in stock at the end of an 8 hour shift.

Sagot :

MrRoyal

Question:

A company produces boxes of DVDs at a rate of 52 boxes per hour they begin to produce boxes when they first opened for the day and after 3 hours have 400 boxes in stock.

- How many boxes were in stock when they opened?

- Write a linear model for the amount of boxes, b, as a function of the number of hours since they opened, h.

- Use your model to predict the number of boxes in stock at the end of an 8 hour shift.

Answer:

1. [tex]Initial = 244[/tex]

2. [tex]b = 244 + 52h[/tex]

3. 660 boxes

Step-by-step explanation:

Given

[tex]Rate = 52\ per\ hour[/tex]

[tex]Total\ boxes\ in\ 3\ hours = 400[/tex]

Solving (a): Initial Number of boxes

First, we calculate the number of boxes made in 3 hours

[tex]Boxes = Rate * Hours[/tex]

[tex]Boxes = 52 * 3[/tex]

[tex]Boxes = 156[/tex]

If they had 400 boxes at the 3rd hour.

Then, the number of boxes when they opened is:

[tex]Initial = 400 - 156[/tex]

[tex]Initial = 244[/tex]

Solving (b): Linear function

[tex]b = boxes[/tex]

[tex]h = hours[/tex]

Since, we have the rate and the initial number of boxes.

The linear function is:

[tex]Boxes = Initial + Rate * Hours[/tex]

i.e.

[tex]b = 244 + 52 * h[/tex]

[tex]b = 244 + 52h[/tex]

Solving (c): Boxes at the end of the 8th hour

We have:

[tex]b = 244 + 52h[/tex]

In this case:

[tex]h = 8[/tex]

Substitute 8 for h

[tex]b = 244 + 52 * 8[/tex]

[tex]b = 244 + 416[/tex]

[tex]b = 660[/tex]

Hence, there are 660 boxes at the end of the 8th hour

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.