Emilio's Publishing prints and sells cookbooks to stores for $4.50 each. Their weekly profits can be modeled by the quadratic function P(x) = −0.1x2 + 15x + 120, where P(x) is profit and x is the number of $0.05 price increases. Use the graph to answer the question.

Graph of function p of x equals negative 0.1 x squared plus 15 x plus 120. The graph has the x-axis labeled as number of price increases, and the y-axis labeled as profit. The curve begins at (0, 120), increases to (75, 682.5), and decreases through (157.614, 0).

Approximately what amount should the company sell each cookbook for to maximize profit? (1 point)
$8.25
$9.50
$10.20
$17.00

Emilio's Publishing Prints And Sells Cookbooks To Stores For $4.50 Each. Their Weekly Profits Can Be

Answers

Answer 1

Using the vertex of the quadratic equation, it is found that the profit will be maximized when each cookbook is sold for $8.25.

What is the vertex of a quadratic equation?

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

[tex]x_v = -\frac{b}{2a}[/tex]

[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]

Considering the coefficient a, we have that:

If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.

In this problem, the function is modeled as follows, considering x as the price divided by $0.05.

P(x) = -0.1x² + 15x + 120.

The coefficients are a = -0.1 < 0, b = 15, c = 120, hence the x-value of the vertex is given by:

[tex]x_v = -\frac{15}{2(-0.1)} = \frac{15}{0.2} = 75[/tex]

75 increases of $0.05, hence the price will be of:

4.5 + 75 x 0.05 = $8.25.

Hence, the profit will be maximized when each cookbook is sold for $8.25.

More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967


Related Questions

HELP QUICK THIS IS EASY IM JUST DUM
A bakery uses 33.2 pounds of flour to make 1,000 hot dog buns. Min
says, “To determine how many pounds of flour are in one bun, divide
33.2 by 1,000. The shortcut is to add 3 zeros to the left side of the
number, so each bun has 0.000332 pound of flour in it.” Explain and
correct Min’s error.

Answers

Answer:

0.0332

Step-by-step explanation:

Min put too many zeros in front of 33.2. 33.2 with 3 zeros in front is 0.0332

Ok so it will be 6 bc the sum of it and yea the g p are love me bc my love is in address

PLEASEEEEE HELPPPPPPP ASAPPPPPPPPPP

Answers

Answer:

Its is 405 gallons

Step-by-step explanation:

If you need an explanation lmk!!!

Answer:

405 gallons

Step-by-step explanation:

The formula to find the amount of water is g=9m-0.17, so 45 is gonna go into the m spot

g=9(45)-0.17

g=405-0.17  <-After you multiply 9 and 45

g=404.83

Now you must round to nearest whole which is 405

I hope this helps

HELPP this is due tomorrow

254 people were surveyed regarding their favorite gemstone 54%chose diamonds 6%chose saphires 30% chose emeralds 10% rubies. How many people did not choose emeralds or rubies?

Answers

Answer:

152.4

Step-by-step explanation:

30%+10%=40%

100%-40%=60%

254*0.60=152.4

TO ALL AMAZING MATHMATICIANS PLS HELP ASAP, please do not put links in I won't click them and I know they're not the correct answer. Please these are urgent and I know its kind of tedious but i need help. Thank you so much to the kind smart person who ends up answering this.

Answers

Answer:

firast divide it by the nearest decimal, then convert your answer into simplest form and you will have your answer.

Step-by-step explanation:

Answer:

can you guys please teach me how to do that

how many students are involved in the school music program but not school sports

Answers

Answer:

45% of the school because some will sign up

find the value of x

Answers

Answer:

82•5°

Step-by-step explanation:

[tex]28 + 68.5 + x = 180[/tex]

[tex]x = 180 - 97.5[/tex]

[tex]x = 82.5[/tex]

Here,

let the forth degree of the quadrilateral be y

Then,

90° +90° +68.5° + y =360° (all the interior angle of a quadrilateral is 360°)

or, 248.5+ y=360°

or, y = 360° - 248.5°

or, y= 111.5°

Again, the second angle of the triangle be a

Then,

a=111.5(vertically opposite angle)

Lastly,

29° + 111.5° + x = 180°(all the interior angle of a triangle is 180°)

or, 140.5° + x = 180°

or, x =180° - 140.5°

or, x=39.5°

Q. Find the Volume

3.4
5.2
7.1
Answer choices

A. 105
B. 112.5
C. 125.5
D. 110

Answers

Answer:

[tex]\boxed{\sf{125.5m^{3} }}[/tex]

Step-by-step explanation:

To determine a volume, you need a volume formula.

Volume:

[tex]\Longrightarrow:\sf{V=l*w*h}[/tex]

L stands for length: 7.1W stands for width: 5.2H stands for height: 3.4

Multiply these numbers from left to right.

[tex]\sf{7.1m*5.2m*3.4m=\boxed{\sf{125.5m^{3}}}[/tex]

Therefore, the correct answer is 125.5m³.

I hope this helps you! Let me know if my answer is wrong or not.

Which sentence is correct?
OA) -3 > 2
OB) -3 <-6
OC) -3>-8
OD) -3>-2



HELP IM BEING TIMED I WILL GIVE BRAINLIEST

Answers

Answer:

OC is correct

Step-by-step explanation:

The greater answer is always gonna be the closest one to zero on the number line.

Hopefully this helps!

20 Points, Part A What percentage of the time margins are at least 0.6 second? Part B What is the most common margin of victory? (Screenshot)

Answers

Answer:

20%

0.5

Step-by-step explanation:

There are 20 margins, so you have to count how many are 6.0 or higher. There are 4 margins that fit this so you divide the 4 margins by 20, then multiply the quotient by 100. That's how you get 20%.

The most common time was 0.5.

In a survey, 125 people were asked to chose one card out of five cards labeled 1 to 5. The results are shown in the table. Compare the theoretical probability and experimental probability of choosing a card with the number 3
.

Answers

Answer:

There is no table, so I'll just calculate the theoretical.

125/5=25.

So, 20% to get a card with the number 3

Helppp mee plsssssss

Answers

Answer:

Option 3 (left object volume = right object volume)

For explanation:

The volume of a slanted cylinder is nothing but the same volume as the volume of the right circular cylinder of the same height

I hope my answer helps you.

What is the slope of the line represented by the equation y=- 1/2x+1/4

Answers

Step-by-step explanation:

This equation is known as slope-intercept form.

Parts of the slope-intercept form equation:

[tex]y=mx+b[/tex]

m represents the slope.

b represents the y-intercept.

In the equation, [tex]-\frac{1}{2}[/tex] is in the placement of m.


We can conclude that [tex]-\frac{1}{2}[/tex] is our slope.

Learn more about the slope of a line:

https://brainly.com/question/12551131

Simplify the expression: 4a+8−2a−4+7b
Expression:__

Answers

Answer:

2a+7b+4

Step-by-step explanation:

collect like terms:

4a-2a=2a

8-4=4

then put the equation back together

What is the value of the 9 3/4- 2 1/5 +1/2

Answers

Answer:

93 will the answer

Step-by-step explanation:

yes htey are good

Please help fast i I’ll give brainliest

Answers

Answer:

The answer is B. 1/4^8

Step-by-step explanation:

Every time the power it to the negative it inverse it.

An example, 2^-2 = 1 / 2^2

So, 4^-8 = 1 / 4^8

Which situation could be represented by the expression 1.40x?

Answers

B is the correct answer because length times width is the formula for a rectangle, and if the side lengths are 1.40 and x, then that satisfies the requirements

Answer:

B. the area of a rectangle with side lengths 1.40 and x

Step-by-step explanation:

To find the area of a rectangle, multiply the length by the width.

If 1.40 is the length, x is the width.

1.40×x=1.40x

So B is the correct answer.

Element x decays radioactively with a half life of 12 minutes. if there are 580 grams
of element x, how long, to the nearest tenth of a minute, would it take the element to
decay to 68 grams?

Answers

Answer:

37.1

Step-by-step explanation:

37.1

Ms Alvarez’s math class surveyed 10 students in 6th grade and 10 students in 7th grade

Answers

Answer: Would the total be 20 Students? What exactly is the question

Step-by-step explanation:

10 + 10 = 20

Padraig is a financial advisor. he earned a salary of $80,000 last year and sold stocks for $5,000. which of the following types of income did padraig have? i earned income ii passive income iii capital gains income a. i and ii b. i and iii c. ii and iii d. iii please select the best answer from the choices provided a b c d

Answers

The earned income is $80,000 and the capital income is $5,000. Then the correct option is B.

What is capital gain?

A profit in the value of an asset then an investor can make a profit by selling an asset. Then selling price of an asset must be greater than the cost of an asset.

Padraig is a financial advisor.

He earned a salary of $80,000 last year and sold stocks for $5,000.

A salary of $80,000 is known as earned income because of employment bases.

$5,000 is a capital gain because this is obtained from the selling of stocks.

The income gained by the interest income, rental income, or dividend income is known as passive income.

More about the capital income link is given below.

https://brainly.com/question/14103167

Thrice a number subtracted from 10?​

Answers

Answer:

10-3x

Step-by-step explanation:

let the number=x

thrice the number becomes 3x

Please help with this and how to solve it.

Answers

Answer:

angle HMS = 62 degrees

x = 13 degrees

AT = 28

Step-by-step explanation:

angle SHM and angle HMS are both inside the triangle SMH.

We want to find the angle of HMS. We know that the sum of the angles in the triangle adds up to 180 degrees. There are two angles that we already know.

Angle SHM = 28 (given)

Angle HSM = 90 (because it is a right angle which is always 90 degrees, right angles are formed at two perpendicular lines)

Angle HMS = x (we let angle HMS be a variable as we don't know the value for it)

x + 90 + 28 = 180

x = 62 ddegrees

HMS is 62 degrees

TSA is a right angle in triangle AST because it is formed by two perpendicular lines. Right angles always equal 90 degrees.

10x - 40 = 90

10x = 130

x = 13 degrees

AT and HT are both congruent sides. We know this because the figure we are given is a kite. In a kite, we have two pairs of sides that are congruent to each other.  HT is congruent to AT while HM is congruent to AM.

So,

8x - 4 = 2x + 20

Subtraact 2 x from both sides

6x - 4 = 20

Add 4 to both sides

6x = 24

Divide 6 on both sides.

x = 4

Plug x back to AT.

AT = 2(4) + 20 = 28

These are two similar triangles.
What does x equal?

Answers

Answer:

112

Step-by-step explanation:

So, we know that a triangle's sides must add up to have a sum of 180. If you add up your given lengths and you should get 47, not including x. Then if you look at the left side/the one without a given length and it should be identical to the 21, so you know that side is 21. So now add 21 to 47, you should get 68. Finally, you subtract 68 from 180 like this: 180-68, and it should equal 112. So you're answer is 112.

find the circumference

Answers

Answer:

18πm

Step-by-step explanation:

The area is πr^, so to find just the radius, take the square root of 81.

This means the radius is 9, and because the formula for the circumference is 2πr, simply double it and multiply by π to get 18π.

If you found this helpful, I would appreciate if you gave me the brainliest award :D

What is the correct answer?​

Answers

Answer:

D. 81/m^7.

Step-by-step explanation:

(3m ^ -4)^3(3m^5)

= (3/ m^4) ^3 (3m^5)

= 3^3/ m^12)(3m^5)

= 81/m^7.

the correct answer is D !

What is the equation of the line of the graph?


Question 12 options:


y= 2x + 1



y= -x -2



y= x + 2



y= -2x + 1

Answers

Answer:

y = x+2

Step-by-step explanation:

y = mx +c

y-intercept is +2

so y = mx + 2

the slope of the line is one across one up so

y = x+2

Answer:

Step-by-step explanation:

At y-intercept, x =0

So, from the graph, y-intecept = b = 2

Equation of the line: y =mx +b

y = mx + 2

Choose any point on the line and substitue in the above equation and we get the slope(m)

(-2 ,0)

0 = m*(-2) + 2

0 = -2m + 2

-2 = -2m

-2/-2 = m

m= 1

Equation of the line: y = x + 2

what is the perimeter of a 12 inch by 13 inch triangle

Answers

Answer:

Perimeter = 30 in

Step-by-step explanation:

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

a = ab = 12 inc = 13 in

Substitute given values into the formula and solving for a:

⇒ a² + 12² = 13²

⇒ a² + 144 = 169

⇒ a² = 25

⇒ a = 5 in

Therefore, perimeter = a + b + c

                                   = 5 in + 12 in + 13 in

                                   = 30 in

Final Answer:

[tex]\fbox{perimeter \: of \: triangle = 30 \: in.}[/tex]

Step by Step explanation:

Data achieved from diagram:

The given triangle is a right angle triangle

Hypotenuse of triangle = 13 in.

Base of triangle = 12 in.

To find:

Perimeter of triangle = ?

Solution:

We need length of all three sides (Altitude) of triangle,

let's find out the measure of length of Altitude using Pythagoras theorem!

[tex]{Hypotenuse}^2 = {Base}^2 + {Altitude}^2 \\ {13}^{2} = {12}^{2} + {A}^{2} \\ {A}^{2} = 169 - 144 \\ {A}^{2} = 25 \\ {A} = \sqrt{25 } \\ \fbox{A = 5 \: in.}[/tex]

Now we have all three sides of triangle,

[tex]perimeter \: of \: triangle = Hyp. + Base + Alt. \\perimeter \: of \: triangle = 13 + 12 + 5 \\ \fbox{perimeter \: of \: triangle = 30 \: in.}[/tex]

Thanks for joining brainly community!

What are the measures of the interior angles of the triangle?

m∠1 =
°

m∠2 =
°

m∠3 =
°

Answers

Answer:

Step-by-step explanation:

a and b are parallel lines. So, alternate interior angles are congruent.

∠2 = 64.8°

∠3 = 30.5°

Sum of all angles of triangle  = 180

∠1 + ∠2 + ∠3 = 180

∠1 + 64.8 + 30.5 = 180

           ∠1  + 95.3 = 180

                       ∠1 =  180 - 95.3

                        ∠1  =  84.7°

Guys guys GUYS guys guYs HELPhelp helppp

Answers

Answer:

A is 3 x 3 = 9 so thats one multiple and the ones that have the same put in the middle

Step-by-step explanation:

Use the graph to complete the follow statement. _____ cm of rain fell in total on Tuesday.

Answers

I don’t know the answer is 19 I guess

8, 14.5, 21, 27.5, 34, 40.5 What’s the next number in the sequence

Answers

Answer:

47

Step-by-step explanation:

Determine if the sequence is arithmetic or geometric.

The difference between each term in the sequence is constant, so this is an arithmetic sequence.

To calculate the common difference, subtract one term from the next term:

14.5 - 8 = 6.5

21 - 14.5 = 6.5

27. 5 - 21 = 6.5

34 - 27.5 = 6.5

40.5 - 34 = 6.5

So the common difference is 6.5

To find the next term in the sequence, add 6.5 to the last term given:

40.5 + 6.5 = 47

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