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.


Related Questions

Urgently need help please

Answers

Answer:

Most likely D

Step-by-step explanation:

common knowledge

PLEASE HELP!! Which equations represent a proportional relationship? If yes, give the constant of Proportionality.

Answers

Answer:

The constant of proportionality is the constant value of the ratio of two proportional quantities x and y, typically the equation is Y=KX.

Step-by-step explanation:

t a certain vineyard it is found that each grape vine produces about 10 lb of grapes in a season when about 500 vines are planted per acre. For each additional vine that is planted, the production of each vine decreases by about 1 percent. So the number of pounds of grapes produced per acre is modeled by
A(n) = (500 + n)(10 − 0.01n)
where n is the number of additional vines planted. Find the number of vines that should be planted to maximize grape production.

Answers

Answer: Grape production is maximized for 150 vines planted

Step-by-step explanation:

If you multiply a matrix and its inverse together, you will always get the identity
matrix.
True
False

Answers

Answer:

True

Step-by-step explanation:

If you multiply a matrix (such as A) and its inverse (in this case, A–1), you get the identity matrix I. And the point of the identity matrix is that IX = X for any matrix X (meaning "any matrix of the correct size", of course).

Answer:

Yes

Step-by-step explanation: And 1 is the identity, so called because 1x = x for any number x. It works the same way for matrices. If you multiply a matrix (such as A) and its inverse (in this case, A–1), you get the identity matrix I.

Find the value of the unknown​

Answers

Answer:

20°

Step-by-step explanation:

Step 1:

4n = 80°          Vertical ∠'s

Step 2:

n = 80° ÷ 4        Divide

Answer:

n = 20°

Hope This Helps :)

A sample of employees of Worldwide Enterprises is to be surveyed about a new health
care plan. The employees are classified as follows:
Classification Event Number of Employees
Supervisors A 120
Maintenance B 50
Production C 1,460
Management D 302
Secretarial E 68
(a) What is the probability that the first person selected is:
(i) either in maintenance or a secretary?
(ii) not in management?

(c) Are the events in part (a)(i) complementary or mutually exclusive or both

Answers

Using the probability concept, it is found that:

a) i) There is a 0.059 = 5.9% probability that the first person selected is either in maintenance or a secretary.

ii) There is a 0.849 = 84.9% probability that the first person selected is not in management.

b) The events are neither complementary nor mutually exclusive.

A probability is the number of desired outcomes divided by the number of total outcomes.

Item a:

In this problem, there is a total of 120 + 50 + 1460 + 302 + 68 = 2000 people.

Of those, 50 + 68 = 118 are either in maintenance or a secretary, hence:

[tex]p = \frac{118}{2000} = 0.059[/tex]

There is a 0.059 = 5.9% probability that the first person selected is either in maintenance or a secretary.

Item ii:

2000 - 302 = 1698 people are not in management, hence:

[tex]p = \frac{1698}{2000} = 0.849[/tex]

There is a 0.849 = 84.9% probability that the first person selected is not in management.

Item b:

If a person is either in maintenance or a secretary, they are also not in management, hence the events are neither complementary nor mutually exclusive.

To learn more about the probability concept, you can take a look at https://brainly.com/question/24437717

Following are the solution to the given points:

For point a:

i)

[tex]\to P(B \cup E) = P(B) + P(E) - P( B\cap E)[/tex]

Where [tex]P(B \cap E) = 0[/tex] because they are both separate occasions It is impossible to be a member of both departments.  

[tex]\to P(B\cup E) =\frac{50}{120 + 50 + 1460 + 302 + 68} +\frac{68}{120 + 50 + 1460+ 302 +68}\\\\[/tex]

                    [tex]=\frac{50}{2000} +\frac{68}{2000}\\\\=\frac{50+68}{2000} \\\\=\frac{118}{2000} \\\\=\frac{ 59}{1000} \\\\=0.059\\[/tex]

ii)

[tex]\to P(D^c) = 1 - P(D)[/tex]

               [tex]=1- (\frac{302}{120+50+1460+302+68})\\\\=1- (\frac{302}{2000})\\\\=1- (\frac{ 151}{1000})\\\\= 1- 0.151 \\\\= 0.849\\\\[/tex]

For point b:

Please find the attached file.

For point c:

Events in a. I are mutually incompatible since [tex]P(B \cap E) = 0[/tex]. One would be a part of the both departments.

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A ramp that is used to load a truck makes supplementary angles with the ground. The ramp has an incline (<1) of 28. What is the measure of <2?

Answers

Answer:

Step-by-step explanation:

two angles are said to be supplementary if their sum is 180 degrees

Hence <1 + <2 = 180

Given

<1 = 28

Required

<2

Substitute into the formula

28+<2 =180

<2 = 180-28

<2= 152

Hence the measure of <2 is 152 degrees

456x5 is what I can’t figure this out please help!!

Answers

Answer: 2,280

456 times 5

Answer:

2280

Step-by-step explanation:

Multiply 5 times 2325 it ain't that hard g just use google lol

Graph the line of the slope of 1/4 and includes the point (0,2)

Answers

Answer:

I'm on Edulastic.com taking a 100 Q test and this question is on it!

Step-by-step explanation:

Imao im fgging confused

The graph of the required line [tex]\bold{y=\frac{x}{4}+2}[/tex] is given below.

Slope point form of equation of line: -

An equation of line with slope m and passing through point (p, q) is:

(y - q) = m × (x - p)

We have been given the slope of the line m = 1/4,

and a point (p, q) = (0, 2)

Using the slope-point form equation of line would be,

⇒ (y - 2) = 1/4 × (x - 0)

⇒ (y - 2) = 1/4(x)    

⇒ y = x/4 + 2                          ...............................(1)

So, the equation of the line is [tex]y=\frac{x}{4} +2[/tex].

To plot the line we need at least  two coordinate points.

We have been given a point (0, 2).

We need to find another point.

Substitute x = -4 in equation (1),

⇒ y = (-4)/4 + 2

⇒ y  = -1 + 2

⇒ y = 1

So, another point on the line would be (-4, 1).

Now, we plot points (0, 2) and (-4, 1) on coordinates plane.

Then the graph of the line [tex]\bold{y=\frac{x}{4}+2 }[/tex] is as shown in figure.

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Help? Please? This is algebra math

Answers

Answer:

You count the blocks and then put the amount of blocks before:)

(That sounds confusing but it sounds harder than it is)

The answer would be 3xy + 4x

Step-by-step explanation:

How many xy blocks are there? yea there's 3 so you do 3xy

you can't add xy and x blocks together because xy is a different unit than x (xy is x times y) so then you'd count the other x blocks seperately

(I'm sorry if I'm wrong on this lol)

FIRST RIGHT GETS BRAINLIEST

Answers

5+9=14 i hope this helps!

PLEASE HELP!!! The sum of 2 consecutive itegers is 294. Write an equation for the integers.

Answers

Answer:

147

Step-by-step explanation:

Divide 294 by 2

three numbers that have 2, 4, and 8 as factors. What other factors do these numbers have in common?

Answers

8, 16, 24, 32, 7992, and 8008 all have 2, 4, and 8 as factors

Hello Can someone help me please???

What is the factored form of 5x2 – 19x + 12?
A.) (5x – 3)(x – 4)
B.) (5x – 4)(x – 3)
C.) (5x – 12)(x – 1)
D.) (5x – 1)(x – 12)

Answers

B. (5x-4)(x-3)
Explanation: Multiply using distributive property to get 5x^2-19x+12

Answer:

pretty sure its B

Step-by-step explanation:

hope this helps ;)

Which statement correctly describes the relationship between the graph of f(x) and the graph of g(x)=f(x)−4?



The graph of g(x) is the graph of​​ ​f(x)​ translated 4 units down.

The graph of g(x) is the graph of ​f(x)​ translated 4 units right.

The graph of g(x) is the graph of ​​f(x)​ translated 4 units up.

The graph of g(x) is the graph of f(x) translated 4 units left.

Answers

Answer:

The graph of g(x) is the graph of​​ ​f(x)​ translated 4 units down.

Explanation:

Given the function f(x) and g(x) = f(x)-4

This means that the function g(x) is 4 less than the function g(x) i.e the function g(x) is reduced by 4. Since the negative values on a graph are located from the origin down the negative y axis and towards the negative x axis, we can conclude that the graph g(x) translated 4 units down. of f(x). This is translated along the y axis because the function g(x) serves as the output for all values on input variable x.

The g(x) can be written as a function of y i.e we can rewrite it as y = f(x)-4.

Hence the correct option is The graph of g(x) is the graph of​​ ​f(x)​ translated 4 units down.

John's sister is twice his age. In 5 years the sum of their ages will be 31. How old are John and his sister now? Briefly explain how you arrived at your answer.

Answers

Like usual, we can solve this question using an equation. Let’s assume that John’s age is x, and his sister’s age is y.

x = 2y

To figure out John’s age, we need to know his sister’s age. He’s 2 times older than his sister.

x + y = 27

The sum of their ages is 27, and we can substitute the value of x here to figure out y.

2y + y = 27

We can now simplify this, and get y by itself.

3y = 27

Now, we can divide by 3 to get the y by itself.

y = 9

We now know that John’s sister is 9.

Now, using our original equation, we can substitute in the value of y.

x = 2(9)

We can simplify this.

x = 18

John’s age is 18!

Hope this helps.

In the given picture, y/x =4 and z/x =3. Find x.

Answers

Answer:

Step-by-step explanation:

x=22.5 degrees

[tex]\frac{y}{x} =4[/tex]

[tex]\frac{z}{x} =3[/tex]

[tex]y = 4x[/tex]

[tex]z=3x[/tex]

[tex]x +3x+4x=180[/tex]

[tex]8x=180[/tex]

[tex]\frac{8x}{8} =\frac{180}{8}[/tex]

[tex]x=22.5[/tex]

What is the value of x in the equation below? 1/3(12x-24)=16
2
6
8
10

Answers

Hope this helps with your problem !!

Daniel has to carry 32 boxes to his room. He can
carry 4 boxes on each trip. How many trips will
Daniel take? Show your work?

Answers

32 divided by 4= 8
So 8 trips in total

Daniel will take 8 trips.

What is division?

The division is one of the four basic mathematical operations, the other three being addition, subtraction, and multiplication.

Now it is given that,

Number of boxes = 32

Number of boxes can be carried in each trip  = 4

So, Number of trips = Number of boxes / Number of boxes can be carried in each trip

⇒ Number of trips = 32/4

⇒ Number of trips = 8

this is the required number of trips Daniel will take.

Thus, Daniel will take 8 trips.

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Consider the following data on x = weight (pounds) and y = price ($) for 10 road-racing bikes.

Brand Weight Price ($)
A 17.8 2,100
B 16.1 6,250
C 14.9 8,370
D 15.9 6,200
E 17.2 4,000
F 13.1 8,500
G 16.2 6,000
H 17.1 2,580
I 17.6 3,500
J 14.1 8,000

Required:
Use the F test to determine whether the weight for a bike and the price are related at the 0.05 level.

Answers

Answer:

There is a significant relation between weight and price

Step-by-step explanation:

              Brand Weight(x)          Price ($) (y)

A                  17.8                        2100

B                   16.1                        6,250

C                   14.9                        8,370

D                   15.9                        6,200

E                   17.2                        4,000

F                   13.1                         8,500

G                   16.2                        6,000

H                   17.1                         2,580

I                   17.6                          3,500

J                   14.1                         8,000

Null Hypothesis : [tex]H_0: \mu =0[/tex]

Alternate Hypothesis : [tex]H_a: \mu \neq 0[/tex]

Given : SST=51956800 SSE= 7312286.84 n = 10

SSR = SST-SSE

SSR=51956800-7312286.84

SSR=44644513.16

Level of significance =[tex]\alpha = 0.05[/tex]

[tex]F=\frac{\frac{SSR}{m}}{\frac{SSE}{n-k}}[/tex]

Where m = no. of restrictions

k = No. of independent variables

[tex]F=\frac{\frac{44644513.16}{1}}{\frac{ 7312286.84}{10-2}}[/tex]

F=48.843

Degree of freedom 1 = 1

Degree of freedom 2 = 10-2=8

Using calculator

p-value is .000114.

p value < α

So, we reject the null hypothesis .

Hence There is a significant relation between weight and price

write an equation for the line Below​

Answers

Answer:

y=-1/2x

Step-by-step explanation:

Answer:

y=-1/2x

Step-by-step explanation:

shown in graph

On average, Starla drinks 5/6
of a 12 ounce glass of water in 1/3
of an hour.
How much water does she drink in an hour?
O 10 ounces
12 ounces
20 ounces
30 ounces

Answers

30 ounces 5th grade math

A fuel company supplies fuel in two different-sized tankers. The first tanker can supply x cubic feet of fuel in one trip and the second tanker can
cubic feet of fuel in one trip. The first tanker makes M trips daily and the second taker makes n trips daily. What does
Mx +Ny represent in expression
Mx +NY,
M+N
total fuel, in cubic feet, supplied by the two tankers in one trip
total fuel, in cubic feet, supplied by the two tankers in one day
o
total fuel, in cubic feet, supplied by the two tankers in one week
total fuel, in cubic feet, supplied by the two tankers in one month

Answers

Answer:

A. Total fuel, in cubic feet, supplied by the two tankers in one trip.

Step-by-step explanation:

First option: A. Total fuel, in cubic feet, supplied by the two tankers in one trip.

Simplify fully
x² – 9/3x²+8x-3 divided by x-3/x+2


Answers

Answer:

-(x(2x squared-8x+3))/(x-1)(x+3)

Step-by-step explanation:

This can't be simplified very far, but the answer is above. Hope it helps!

The simplified equation of x² – 9/3x²+8x-3 divided by x-3/x+2 is (x-3)(4x+1)/(3x-1)(x+2).

What is Simplification?

Simplification is the process of replacing a mathematical expression by an equivalent one, that is simpler. Therefore,

WE need to simplify the given;

[tex]\dfrac{x^{2}-9 }{3x^{2} +8x-3}+\dfrac{x-3}{x+2}[/tex]

3x² + 8x - 3 = (3x - 1)(x + 3)

x² - 9 = (x - 3)(x + 3)

Then;

[tex]\dfrac{(x-3)(x+3)}{(3x-1)(x+3)} +\dfrac{x-3}{x+2} =\dfrac{(x+2)(x-3)(x+3)+(x-3)(x+3)(3x-1)}{(3x-1)(x+3)(x+2)}[/tex]

Therefore,

[tex]\frac{(x+2)(x-3)(x+3)+(x-3)(x+3)(3x-1)}{(3x-1)(x+3)(x+2)}=\frac{((x+3)(x-3)((x+2)+(3x-1)))}{(3x-1)(x+3)(x+2)}[/tex]

[tex]\dfrac{((x+3)(x-3)((x+2)+(3x-1)))}{(3x-1)(x+3)(x+2)}=\dfrac{(x-3)((x+2)+(3x-1))}{(3x-1)(x+2))}[/tex]

[tex]\dfrac{(x-3)((x+2)+(3x-1))}{(3x-1)(x+2))} = \dfrac{(x-3)(x+2+3x-1)}{(3x-1)(x+2)}[/tex]

[tex]\dfrac{(x-3)(x+2+3x-1)}{(3x-1)(x+2)}=\dfrac{(x-3)(4x+1)}{(3x-1)(x+2)}[/tex]

Hence, The simplified equation of x² – 9/3x²+8x-3 divided by x-3/x+2 is (x-3)(4x+1)/(3x-1)(x+2).

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Misha’s hamster weighed 0.845 kilograms. About how much does it weigh, rounded to the nearest hundredth?
1 0.84 kilograms
2 0.8 kilograms
3 0.85 kilograms
4 1 kilograms

Answers

Answer:

0.85 kilograms

Step-by-step explanation:

The nearest hundredth can be defined as a place value used when rounding up numbers after the decimal.

The nearest hundredth can also mean rounding up to 2 decimal places.

We are asked to round up 0.845 to the nearest hundredth

The nearest hundredth is the second number after the decimal = 4

The third number after the decimal = 5, hence we add 1 to 4 , making it 5.

Hence:

0.845 kilograms to the nearest hundredth = 0.85 kilograms

I need help it wouldn’t let me put the song I wanted but whatever

Answers

Answer:

[tex]this \: proberbility \: is \: p(history)[/tex]

The probability of this is p(history)

This graph shows the solution to which inequality?
(3,-1)
(-3,-3)

Answers

Answer:

its c. y>1/3x-2

Step-by-step explanation:

Just took the quiz

lines of best fit (regression lines) must touch all dada points on a scatter plot

true or false ​

Answers

Answer:

False

Step-by-step explanation:

A regression line tries to average out all data points, so it may not touch any of them.

Given:
p: student achieves 90 percent on the geometry final.
q: student will receive a passing grade in geometry class.
Which statement is logically equivalent to q - p?
If a student achieves 90 percent on the geometry final, then the student will pass geometry class.
If a student passes geometry class, then the student achieved 90 percent on the geometry final.
If a student did not achieve 90 percent on the geometry final, then the student did not pass geometry class.
Olfa student did not pass geometry class, then the student did not achieve 90 percent on the geometry final.

Answers

the answer would be c

Answer:

c

Step-by-step explanation:

Leo has $28 to spend on pencils and paper for a school. Pencils cost $0.50 each and paper cost $1.50 each. Using x for pencils, and y for paper, write an inequality that represents what Leo can buy.​

Answers

Answer:

Please mark Brainliest if helpful...

0.5x+1.5y[tex]\leq[/tex]28

Step-by-step explanation:

X is the number of pencils, so multiply the price of one pencil by the number of them to get the total price of pencils-0.5xY is the number of paper, so multiply the price of one paper by the number of them to get the total price of paper-1.5yLeo has $28, so he can either spend $28 or less on pencil and paper, which means that his total cost should be less than or equal to 28
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