A company has determined that its profit for a product can be described by a linear function.
The profit from the production and sale of 150 units is $455, and the profit from
250 units is $895.
(i) What is the average rate of change of the profit for this product when
between 150 and 250 units are sold?
(ii) Write the equation of the profit function for this product.
(iii) How many units give break-even for this product?
(b) You are the CEO for a lightweight compasses manufacturer. The demand
function for the lightweight compasses is given by p = 40 − 4q
2where q
is the number of lightweight compasses produced in millions.It costs the company $15
to make a lightweight compass.
(i) Write an equation giving profit as a function of the number of lightweight compasses
produced.
(ii) At the moment the company produces 2 million lightweight compasses and makes a profit
of $18,000,000, but you would like to reduce production. What smaller number of
lightweight compasses could the company produce to yield the same profit?

Answers

Answer 1

Step-by-step explanation:

(a)(i) The average rate of change is:

(895 − 455) / (250 − 150)

4.4

(a)(ii) Since the profit is linear, the slope of the line is equal to the average rate of change.  Using point-slope form:

y − 455 = 4.4 (x − 150)

Simplifying to slope-intercept form:

y − 455 = 4.4x − 660

y = 4.4x − 205

(a)(iii) The break-even point is when the profit is 0.

0 = 4.4x − 205

4.4x = 205

x = 46.6

(b)(i) The "demand function" is the selling pice of the compasses:

p = 40 − 4q²

where p is the price in dollars and q is the quantity in millions of units.

Profit is revenue minus cost.

P = R − C

P = pq − 15q

P = (p − 15) q

P = (25 − 4q²) q

P = 25q − 4q³

where P is the profit in millions of dollars and q is the quantity in millions of units.

(b)(ii) Find values of q when P = 18.

18 = 25q − 4q³

4q³ − 25q + 18 = 0

We know that q=2 is a root of this equation.  Using grouping:

4q³ − 8q² + 8q² − 25q + 18 = 0

4q² (q − 2) + (q − 2) (8q − 9) = 0

(q − 2) (4q² + 8q − 9) = 0

4q² + 8q − 9 = 0

Solve with quadratic formula.

x = [ -b ± √(b² − 4ac) ] / 2a

q = [ -8 ± √(8² − 4(4)(-9)) ] / 2(4)

q = (-8 ± √208) / 8

q = (-8 ± 4√13) / 8

q = (-2 ± √13) / 2

Since q is positive, q = (-2 + √13) / 2, or approximately 0.803.


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Answer:

Step-by-step explanation:

1. yes

2. no

3. -10 and 5

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5. 3x+3

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9. 10x -5

Answer:

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Step-by-step explanation:

A parachutists speed during a free fall reaches 153 miles per hour. What is this speed in feet per second? at this speed, how many feet will the parachutist fall during 15 seconds of free fall? in your computations, use the fact that 1 mile is equal to 5280 feet. do not round your answer

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153 miles x 5280 feet per mile = 807,840 feet per hour.

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The height of the rocket after t seconds is given by the equation h(t) = -16t² + 42t

What is an equation?

An equation is an expression that shows the relationship between two or more variables and number.

1 mile = 5280 feet, 1 hour = 3600 seconds

153 miles per hour = (153 * 5280) / (3600) ft/s = 224.4 ft/s

After 15 seconds, height = 224.4 ft/s * 15 s = 3366 ft

The speed of the parachute is 224.4 ft/s, while after 15 seconds the distance fell was 3366 ft.

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Answer:

x will equal to 4

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Pass necessary journal entries in the books of Narender for the month of March 2006

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Please explain this question as I can't 'Pass necessary journal entries in the books of Narender for the month of March 2006'

The late fee at the library is based on the number of days a book is late. Carter paid $1.08 for a book that was 9 days late. If his sister Sydney had a fee of $1.92 for a late book, how many days late was the book?​

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Answer:

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Step-by-step explanation:

1.08 $:9 days

1.92 $: x

1.08 x: 17.28

x = 16

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Answer:

☆<《HOPE IT WILL HELP YOU 》>☆

Step-by-step explanation:

capital of Peru is Lima

Evaluate the expression of X = 3

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Answer:

x=3

Step-by-step explanation:

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3) You paid $5 for a bucket of popcorn and $1.25 per candy bar. How many candy bars
can you buy to spend no more than $10?

Answers

4 dollars flat $4.00

Step-by-step explanation:

1.25x4= 5$ 5$+5$=10$

Answer:

4 candy bars

Step-by-step explanation:

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What is 2/5 + 1/4+7/10

Answers

Answer:

1 7/20

Step-by-step explanation:

Answer:

27/20 or 1 7/20

Step-by-step explanation:

1) make the denominators the same

2/5 multiplied by 4 on top and bottom =8/201/4 multiply by 5 = 5/207/10 multiply by 2 = 14/20

2) add the numerators

8+5+14=27

3) the denominator stays the same

27/20

4) simplify it to 1 7/20

a group a friends share 3 1/2 slices of cake. each friend get half a slice of cake. how many friends shared the slices of cake.

Answers

Answer:

7

Step-by-step explanation:

3×2

6+1

7

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Answer:

7

Step-by-step explanation:

3 1/2 divided by 2 is 7

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Answer:

What is the question?

Step-by-step explanation:

I will change my  answer if you put a clear question up...

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Explanation
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Answer:

2.44949

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

10x

Step-by-step explanation:

If the question mark is an accident, the answer is 10x.

5x+6x-2x+x

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Hi :)

First add 5x and 6x
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Combine 11x and -2x to get 9x

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Hope this helps!

0.5f - 2.3g

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Answers

Hi there & welcome to brainly !

Answer:

[tex] \huge{ \bold{ \boxed{ \tt{1.4}}}}[/tex]

Step-by-step explanation:

[tex] \text{Given : f \: = \: 12 \: g = 2}[/tex]

[tex] \text{To \: find : Value \: of \: given \: expression}[/tex]

[tex] \text{Let's \: start}[/tex] :

[tex] \text{0.5f \: - 2.3g}[/tex]

Here, The values of f and g are 12 and 2 respectively. Plug the given values :

↦ [tex] \text{0.5 ∗ \: 12 - 2.3 ∗ 2}[/tex]

Multiply : 0.5 and 12

↦ [tex] \text{6 - 2.3 \: ∗ \: 2}[/tex]

Multiply : 2.3 and 2

↦ [tex] \text{6 - 4.6}[/tex]

Subtract 4.6 from 6

↦ [tex] \text{ \boxed{1.4}}[/tex]

Hope I helped!

Best regards! :D

~[tex] \text{TheAnimeGirl}[/tex]

The solution of the given expression will be; 1.4

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given that  0.5f - 2.3g where f = 12 and g = 2

Now substitute 12 in for f and 2 in for g and solve;

0.5(12)  -2.3(2)

6 - 4.6

=1.4

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The complete question is;

Evaluate the expression: 0.5f - 2.3g where f = 12 and g = 2

Let xy=6 and x2 + y2 = 23 what is the value of (x+y)??

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Answer:

I'll assume that x2 = x^2 and y2 = y^2 and the answer is sqrt{35}.

Step-by-step explanation:

This problem invovles completing the square, so if I square (x+y), I get

x^2+2xy+y^2, and since xy = 6, 2xy = 12, 23+12 = 35, and your answer is sqrt{35}.

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Answer:

A, B, C

Step-by-step explanation:

It's correct, I took the activity before the quiz and got it right.

Happy to help :3

what is the value of 2.5x+17+21x-25=180

Answers

Answer:

x=8

Step-by-step explanation:

2.5x+17+21x−25=180

Simplify 2.5x+17+21x−25

23.5x−8=180

Move all terms not containing x to the right side of the equation.

23.5x=188

Divide each term by 23.5 and simplify.

x=8

Hope this helps! :) Plz mark as brainliest

Which set of ordered pairs does not represent a function?

Group of answer choices

{(6, 0), (-9, 5), (1, -5), (0, 0)}

{(4, 6), (6, 8), (3, 2), (-6, 8)}

{(-9, -7), (-8, -7), (8, 2), (9, -5)}

{(-8, 6), (-8, 5), (-9, 4), (-5, 3)}

Answers

Answer:

the last one

Step-by-step explanation:

No points on a function can have the same x value, can you give me brainliest

9+10
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Answer: 19 XD

Step-by-step explanation: u add

Rewrite the following equation in slope-intercept form.
17x + 18y = -6

Answers

Answer:

y= -17/18x-1/3

Step-by-step explanation:

The slope-intercept form of the equation is y = (-17/18)x -1/3.

What is linear equation?

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

A linear equation 17x + 18y = -6.

To find the slope-intercept form:

Simplifying,

17x + 18y = -6

18y = -6 -17x

y = -17/18x -1/3

Therefore, y = (-17/18)x -1/3 is the slope-intercept form.

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what is a point-slope equation of the line with slope -10 that goes through the point (1,4)

Answers

Answer:

The answer is

[tex]y - 4 = - 10(x - 1)[/tex]

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

[tex]y - y_1 = m(x - x_1)[/tex]

where

m is the slope

( x1 , y1) is the point

So we have the final answer as

[tex]y - 4 = - 10(x - 1)[/tex]

Hope this helps you

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Answers

Answer:

Option B. 4<=x<=6 is the solution set.

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