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.

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Related Questions

Hi can someone plss help me with these 2 questions. Im really struggling with them.

Answers

Trees are important to one's health as they produce oxygen and reduce climate change. Also, bees pollinate our crops leading to more crop production and increase in revenue.

What is health?

It should be noted that health simply means the state of being free from illness or diseases.

In this case, trees are important for one's health as they help in the production of oxygen which are needed by human beings. Bees are also important for the generation of higher profits though the pollination of crops which leads to increase in crop production.

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The measures of the bases of a trapezoid are 14 and 20. What is the measure of the median of the trapezoid?

Answers

The median of the trapezoid is = 17

calculation of the median of a trapezoid

A trapezoid is a quadrilateral with one pair of opposite sides parallel. It has parallel sides which are known as the bases.

The base of the trapezoid(B1) =14

The base of the trapezoid (B2) = 20

To calculate the median = half the sum of the base of the trapezoid given.

Therefore,

14+20/2

34/2= 17

Therefore, the median of the trapezoid is = 17

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64.89% of 407.68cm

Give your answer rounded to 2dp

Answers

Answer: 264.54cm

Step-by-step explanation:

407.68x0.6489=264.543552264.543552 rounded to 2 decimal points is 264.54

(100 POINTS AND BRAINLIEST) Please use the answers that are given. Using the following data, calculate the mean absolute deviation
What is the mean absolute deviation for these data?
A: 9
B: 5.4
C: 5
D: 2.6

Answers

Answer:

There isn't any data, maybe you could put the rest of the question in the comment area.

PLEASE HELP WILL GIVE BRAINLIEST!!!!​

Answers

Answer:

Its The 3rd one you are correct in picture

Step-by-step explanation:

Q: Ribbon cost $1.44 for 3 m.
(1) What is the cost per meter?
(2) How much would 5 m of ribbon cost?
(3) How much ribbon could you buy for $12?

Answers

Answer:

1.44 divided by 3m will give $0.48/5 times 0.48 gives 2.412 times three divided by 1.44 gives$.25

Pls help !!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

D. Rhombus.

Step-by-step explanation:

This will be a quadrilateral with 4 equal sides.

The oppsoite angles will be equal   but they will not be 90 degrees as each triangle of the 3 dimensional figure is an equilateral triangle.

Therfore the cross section is a rhombus.

This is a 30-60-90 triangle.
What is the measure of x?
Rationalize the denominator.
[?]
х
X=
7

Answers

Answer:

x = [tex]\frac{2\sqrt{21}}{3}[/tex]

Step-by-step explanation:

For a 30-60-90 triangle:

Short leg = sLong leg = s√3Hypotenuse = 2s

Thus:

Short leg = √7/√3 = (√21)/3Long leg = √7Hypotenuse = x = 2(√21)/3

Answer:

2 21 3

Step-by-step explanation:

Please help will give brainliest

Which of the following are tangent to circle A? Select all that apply
see picture

Answers

Answer:

RS RT ST

Step-by-step explanation:

This is due to the facts that tangency means having contact at a single point or along a line without crossing. so the first 3 options are correct

Given P(A) = 0.55, P(B) = 0.42 and P(AUB) = 0.639, find the value of
P(An B), rounding to the nearest thousandth, if necessary.

Answers

Answer:

The probability of A and B, denoted as P(A ∩ B) is equal to 0.331.

Step-by-step explanation:

Recall our formula for the probability of A or B:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

We are given are variables already, which we can once again define:

P(A) = 0.55P(B) = 0.42P(A ∪ B) = 0.639

To find P(A ∩ B), we start by plugging in the values into our formula:

0.639 = 0.55 + 0.42 - P(A ∩ B)

We can add the RHS of the equation:

0.639 = 0.97 - P(A ∩ B)

Subtracting 0.97 on both sides, we get closer to our answer:

-0.331 = -P(A ∩ B)

To obtain our final answer, we can simply just divide both sides by -1:

0.331 = P(A ∩ B)P(A ∩ B) = 0.331

Therefore, the probability of A and B is equal to 0.331.

prove it equals 1
(Tanx - Cotx) + Sinx.Cosx

Answers

Step-by-step explanation:

(sinx/cosx - cosx/sinx) + sinxcosx

sin²x - cos²x = 1

I can't prove

I only know sin²x + cos²x = 1 : )

Factor 5x^2−14x+8.
PLS HELP IM STUCK

Answers

[tex]5x^2-14x+8\\\\=5x^2-10x-4x +8\\\\=5x(x-2) -4(x-2)\\\\=(x-2)(5x-4)[/tex]

Find the volume of a cone that has a diameter of 14 feet and a height of 11 feet. Use 3.14 for pi

Answers

Answer:

564.15 cubic ft

[tex] \: [/tex]

Step-by-step explanation:

In the question, it is given that a cone has a diameter of 14 feet and a height of 11 feet and we have to find the volume of the cone.

[tex] \: [/tex]

To Find the volume of the cone, we must know this formula :

[tex] \\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { Volume_{(cone) }= \dfrac{1}{3} \: \pi {r}^{2}h }}}}}}} \\ \\[/tex]

Where,

r refers to the radius of the cone. As the diameter is 14 ft, therefore the radius will 7 ft.

h refers to the height of the cone.

Now, we will substitute the values in the formula :

[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times {(7)}^{2} \times 11 }}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times 49 \times 11 }}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times 539 }}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 1692.46 }}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1692.46}{3} }}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \: \: \underline{ \boxed{ \frak{564.15 } }} }}}}}}} \: \: \bigstar \\ \\[/tex]

Therefore,

The volume of the cone is 564.15 ft³ .

Step-by-step explanation:

Given :-

Height of cone :- 11 feet Diameter of cone :- 14 feet , radius = 7 feet

To Find :-

Volume of cone

Solution:-

Formula for volume of cone = 1/3πr²h

putting the known values ,

Volume = 1/3×3.14×7²×11 cubic ft.

Volume = 564.15 cubic ft.

Abebi surveyed how many miles the students in her Algebra 1 class travel to get to school, and ended up with the following set of data: 4.75, 2.25, 3, 3.5, 1.75, 2.25, 1.5, 5, 4.5, 2.25, 2, 3, 2.65, 4.8, 3.5\

Match the measures of central tendency to the correct values.

Hint:

MEAN = Sum of the data/# of data values

MEDIAN = middle data value when values are listed least to greatest

MODE = value appearing the most times

RANGE = difference between the largest and smallest values

Answers

Answer:

Mean: 3.1

Median: 3

Mode: 2.25 appears 3 times

Range: 5 - 1.5 = 3.5

Mean = (4.75+2.25+3+3.5+1.75+2.25+1.5+5+4.5+2.25+2+3+2.65+4.8+3.5)/16

= 3.56625

Median = 3.50

Mode = 2.25

Range = 9.10

a
С
b
60°
45°
Find a, b, and c.

Answers

Answer:

Step-by-step explanation:

Past experience shows that Mr.Reisman will have 3 left-handed students in ever class of 25 math students. If Mr.Reisman teaches 125 students in one day, what is the most likely total number of left-handed students in his classes?

Answers

Answer:

15 students

Step-by-step explanation:

125/25=5

5x3=15

Find the area of the following triangle. Show each of the math steps that you use to find the area. Then explain how to go about finding the area of this particular triangle (explain each one of the steps that you showed with your math).

Answers

Right angled triangle

Base=B=2.4cmHeight=H=1.8cm

Area:-

[tex]\\ \rm\rightarrowtail \dfrac{1}{2}BH[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{1}{2}(2.4)(1.8)[/tex]

[tex]\\ \rm\rightarrowtail 1.2(1.8)[/tex]

[tex]\\ \rm\rightarrowtail 2.16cm^2[/tex]

Im so desperate
ms. davis sold $309.00 of books. at the end of the day, she earned $27.81 in commission for those sales. what is ms. davis' commission rate?​

question 8 options:

11%


9%


3.4%


2.81%

Answers

so Ms. Davis gets hmmm say "x" percent from sales as her commission, and we know she did in sales $309 and made $27.81.

if we take 309 to be the 100%, and x% of that is 27.81, what's "x"?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 309 & 100\\ 27.81& x \end{array} \implies \cfrac{309}{27.81}=\cfrac{100}{x} \\\\\\ 309x=2781\implies x=\cfrac{2781}{309}\implies x=9[/tex]

i do not know this answer

Answers

Answer: awnser is m= 1/6

Step-by-step explanation: m = add the terms which is  -1 -5m-4+6 m= 1-5m

step 2 then rerange the terms  to m= 1-5m to m = 5m + 1

step 3  add 5m to both sides m= -5m+1 to m + 5m= -5m + 1  + 5m

step 4  simplify and combine like terms 6m= 1

step 5 divide both sides by the same factor 6m= 1  6m/6 =  1/6

step 6 simplify Cancel terms that are in both the numerator and denominator so it is m= 1/6 is the correct awnser mark me brainliest please

2Answer: the answer is -5m+2
Step-by-step explanation: here are the steps .
-5m-4+6
-5m+2
Negative four plus six gives positive 2 because you will make 6 minus 4 and it will tale the sign of the bigger number so it positive two ( 2 ) so negative 5m plus two . -5m+2
HOPE IT HELPS. PLEASE GIVE BRAINLIEST. THANKS.

The soccer players were required to run 6 more laps per day than the tennis players for five straight days. If the soccer players ran 45 laps total during these days, how many laps did the tennis players run each day?

Answers

Answer:

3 laps per day

Step-by-step explanation:

Divide 45 laps by 5 days to get how many laps they ran per day

45/5 = 9 laps per day

The tennis players run 6 less laps per day than the soccer players so subtract 6 laps from 9 laps to get their daily laps

6-9 = 3 laps per day

express the following rational algebraic expression to its simple form.show your solution​

1. 25 ׳y³/ 75 ×⁴y⁴​

Answers

express the following rational algebraic expression to its simple form.show your solution

1. 25 ׳y³/ 75 ×⁴y⁴

Answer

1/3×y

when I think of a number, double it , then add seven , I get 23. Determine the number I first thought of

Answers

Answer:

8

Step-by-step explanation:

2x + 7 = 23

2x = 16

X = 8

What is the measure of each angle in the circle?

40°
60°
45°
36°

Answers

Answer:

i think it would be 45

hope im right

if not i can change it

Step-by-step explanation:

Answer:

45°

Step-by-step explanation:

The circle is divided into 8 equal arcs, each arc measuring an angle of:

360/8 = 45°

Hope this helps

How would we add -3 + (-9) on the number line?

Answers

Answer:

-12

Step-by-step explanation:

1. Create an Equation

-3-9

2. Solve

-3-9 <=== subtract -3 and -9 together to get your answer

-12

3. Check

-12+3 <=== create this equation or this one ===> -12+9 to check if we calculated correctly

-12+3= -9 -12+9= -3

this shows the answer is corrrect

when you are adding a positive number we would go right but -9 isn’t a positive it’s a negative so we would go left on the number line

What is the length of a car if the length on the scale madel car is 17 cm and the scale is 2 cm : 50 cm?

Answers

Answer:

x= 425

Step-by-step explanation:

A recipe for muffins calls for 1 1 over 3 cups of milk. a recipe for bread calls 2 over 3 cup of milk how much more milk is needed for the muffin recipe than the bread recipe

Answers

Answer:

The Muffin Recipe calls for 3 more cups of Milk than the Bread Recipe.

Step-by-step explanation:

11/3=

3[tex]\frac{2}{3}[/tex]

2/3

We can see that the difference is GREAT. So, now, let's subtract.

[tex]3\frac{2}{3} -\frac{2}{3} =3[/tex]

So hence, the Muffin Recipe calls for 3 more cups of Milk than the Bread Recipe!

----------------------------------------------------------------------------------------------------------"The beautiful thing about learning is that no one can take it away from you!"

B.B.King

Thanks!

Have a great night!

~ms115~

:D

The muffin recipe requires 2/3 cup more milk than the bread recipe.

What is subtraction?

Subtraction is a mathematical operation. Which is used to remove terms or objects in the expression.

To find out how much more milk is needed for the muffin recipe than the bread recipe,

we need to calculate the difference between the amount of milk required for each recipe.

The muffin recipe calls for 1 1/3 cups of milk, which is equivalent to 4/3 cups of milk.

The bread recipe calls for 2/3 cup of milk.

To find the difference between the two amounts of milk, we can subtract the milk required for the bread recipe from the milk required for the muffin recipe:

4/3 - 2/3 = 2/3

Therefore, 2/3 is the required fraction.

To learn more about subtraction;

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Write and solve an equation to find the value of x

Answers

Answer:

Equation: x+90=7x

Answer: x=15

Step-by-step explanation:

By looking at the image, I can tell that both of those angles are vertical.

Vertical angles mean that both of the angles would be equal. Therefore, we can set x+90 = 7x

You then subtract x from both sides, leaving us with 90 = 6x

From there, divide both sides by 6 to isolate 6 to 1, and you are left with 15= x or x=15, giving you your answer and equation.

The value of x is 15.

What is an angle measure?

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given that the two angle measures (x + 90)° and 7x°.

And both the angle measures are formed by opposite angles,

so,

x + 90 = 7x

Taking like terms to one side,

we get,

7x - x = 90

6x = 90

Divide by 6, and we get,

x = 90/6

x = 15

Therefore, x = 15°.

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What is the area of this figure?
18 ft
3 ft
15 ft
12 ft
9 ft
3 ft
square feet
Submit

Answers

Answer: Times it

Step-by-step explanation:

Answer:

90 square feet

Step-by-step explanation:

area of this figure = area of 1 rectangle + area of 2nd rectangle

= L×B + l × b

= 18 × 3 + 12 × 3

= 54 + 36

= 90 feet²

Please Help!!! Will Mark Brainliest!

Answers

Step-by-step explanation:

from my side it's blury, try to send it again

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

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