The profit function p(x) of a tour operator is modeled by p(x) = −2x2 + 900x − 40000, where x is the average number of tours he arranges per day. What is the range of the average number of tours he must arrange per day to earn a monthly profit of at least $60,000?
between 200 and 250; exclusive
between 200 and 250; inclusive
less than 250
more than 200

Answers

Answer 1

Solving the quadratic function, it is found that the range is of:

between 200 and 250; inclusive

The profit for x tours is modeled by the following equation:

[tex]p(x) = -2x^2 + 900x - 40000[/tex]

It is concave down, so the monthly profit will be of at least $60,000 between the two roots when [tex]p(x) = 60000[/tex]. Thus:

[tex]60000 = -2x^2 + 900x - 40000[/tex]

[tex]2x^2 - 900x + 10000 = 0[/tex]

Simplifying by 2:

[tex]x^2 - 450x + 50000 = 0[/tex]

Which has [tex]a = 1, b = -450, c = 50000[/tex]

Then:

[tex]\Delta = (-450)^2 - 4(1)(50000) = 2500[/tex]

[tex]x_{1} = \frac{-(-450) + \sqrt{2500}}{2} = 250[/tex]

[tex]x_{2} = \frac{-(-450) - \sqrt{2500}}{2} = 200[/tex]  

At least $60,000 includes $60,000, thus the interval is inclusive, and the correct option is:

between 200 and 250; inclusive

A similar problem is given at https://brainly.com/question/25181401


Related Questions

Calculate the value of x and state the geometric relationship

Answers

They are same side interior angles and same side interior angles are supplementary (add up to 180 degrees).
So, 6x+12+4x+18=180
Combine like terms:
10x+30=180
Subtract 30 from both sides:
10x=150
Divide both sides by 10:
x=15.

Therefore, the angles are same-side interior angles and x=15.

5
Beena has a holiday in a villa in France.
The total cost of her travel is £349
Beena is on holiday for 2 weeks.
The cost of the villa is 650 euros per week.
While on holiday, Beena has 7 art lessons.
The cost of each art lesson is 45 euros.
Using an exchange rate of 1.12 euros = £1
(a) work out the total cost of Beena's travel, villa and art lessons.
Give your answer in pounds (£).

Answers

Answer:

The answer is 25 because they're both the same.

Mark me as brainliest please.

Step-by-step explanation:

The total cost of Beena's travel, villa and art lessons = £1790.97

What is  multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

The total cost of her travel is £349

Beena is on holiday for 2 weeks.

The cost of the villa is 650 euros per week.

i.e. 2*650

  =1300 euros

  =1300/1.12

  =£1160.71

While on holiday, Beena has 7 art lessons.

The cost of each art lesson is 45 euros.

i.e. total cost = 7*45

                     =315

                     =315/1.12

                     =£281.25

[Using an exchange rate of 1.12 euros = £1]

Hence, The total cost of Beena's travel, villa and art lessons = £1790.97

To learn more on multiplication click:

brainly.com/question/5992872

#SPJ2

please help don,t undertan

Answers

Answer:

substract.

Step-by-step explanation:

eg. 5 before 17 = 17-5

so 5 before 17= 12

same for others

can anyone helpp meeee???

Answers

Answer:

Look at the photo.................

Someone plz help me :(

Answers

Answer:

28 miles

Step-by-step explanation:

12:3

7:x

12÷3=4

4 miles per hour

7•4=28

Answer: Maria will run 28 miles in 7 hours.

Explanation: Since she ran 12 miles in 3 hours, we can simply do 12m/3 and get a pace of 4m or 4 miles per hour. Then multiply 4 by 7 because thats how many hours she has to run. The answer is 28.

Please help me in transformations

Answers

Answer:

A

Step-by-step explanation:

Answer:

Reflection over y = 1

Step-by-step explanation:

I need to solve for x

Answers

Answer:

x = 10

Step-by-step explanation:

The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles. The two non-adjacent interior angles opposite the exterior angle are sometimes referred to as remote interior angles.

In the given problem, the exterior angle is < JUV, and its corresponding remote interior angles are < V and < W.

Establish the following equation according to the exterior angle theorem:

< V + < W = < JUV

88° + (5x + 1)°  = (14x - 1)°

Solve for x algebraically:

88° + 5x + 1  = 14x - 1

89 + 5x = 14x - 1

89 + 1 + 5x = 14x - 1 + 1

90 +  5x = 14x

90 + 5x - 5x = 14x - 5x

90 = 9x

90/9 = 9x/9

10 = x

Therefore, the value of x = 10.

A number is first increased by 20 and then doubled. The result is less than 5 times the number

Answers

Answer:

25=x

Step-by-step explanation:

2x+20=3x-5 (x=25)

What is the equation of the line that passes through the point (-6, -7) and has a slope of 0

Answers

Answer:

x = - 6

Step-by-step explanation:

A line with a slope of zero is a horizontal line parallel to the x- axis with equation

x = c ( where c is the value of the x- coordinates the line passes through )

The line passes through (- 6, - 7 ) with x- coordinate - 6 , then

x = - 6 ← equation of line

is the answer C, E, A, B, or D?​

Answers

Answer:

the answer is B hope this helps

please mark mw brainalist

Anyone please help me to solve this problem Fast fast plz plz
please.​

Answers

[tex] - \frac{2}{ \sqrt{2} } \\ \\ in \: \: alternate \: \: form \\ \\ = - 0.7070107[/tex]

hope it helps

Which transformations will map octagon PQRSTVWZ onto itself?

Answers

Answer:

Rotation, Reflection and Translation.


1. What is the difference between
checking account and a savings
account?
a

Answers

Answer: A checking account is the account you take money out of. A savings account is where you put money to save it.

Step-by-step explanation:

Saving you put money in to save and not use/touch and Checking you put money in and you can use

Which property is illustrated by the equation below?
(7+6) +4= 7+ (6 + 4)
associative property
O commutative property
distributive property
O identity property

Answers

Answer:

We conclude that the question illustrates associative property.

Transpose for p
w = p + cg


Make h the subject
m = r - h + 4d

Answers

The result of making the required variable the subject in both equation are :

p = w - cgh = - (m - r - 4d)

Making p the subject in w = p + cg :

w = p + cg

Subtract cg from bith sides

w - cg = p + cg - cg

p = w - cg

2.)

Make h the subject m = r - h + 4d

m = r - h + 4d

Subtract r from both sides

m - r = r - h + 4d - r

m - r = - h + 4d

Subtract 4d from both sides

m - r - 4d = - h

Divide both sides by - 1

h = - (m - r - 4d)

Learn more : https://brainly.com/question/18796573

Use substitution to solve 2x2=5+y and 4y= -20+8x2

Solve the first equation for Y and substitute it into the second equation. The resulting equation is?

Answers

Step-by-step explanation:

First

2 × 2 = 5 + y

y = -1

And

4y = -20 + 8 × 2

4 × (-1) = -4

-4 = -4

Is this what you wanted?

A fishing boat radioed the Coast Guard for a helicopter to pick up a sick crew member. At the time of the message, the boat is 660 kilometers from the helicopter and heading toward it. The average speed of the boat is 30 kilometers per hour, and the average speed of the helicopter is 300 kilometers per hour. How long will it take the helicopter to reach the boat

Answers

The answer for this question is 6,000

Find 6.8x1.9 using partial products. Draw an area model to show the partial
products.

Answers

Answer: i do not now this one

Step-by-step explanation:

helppppppppppppppppp meeeeeeeee

Answers

Answer:

1.392 km²

Step-by-step explanation:

8.352÷6

please mark me brainliest

help please, im confused​

Answers

Answer:

same sir sorry can't help you ok bye sorry

Please HELPPPPPPPPPP

Answers

Answer:

1.3

2.6

3.24

Step-by-step explanation:

Hope it helps

A) 3
B)6
C)6/1=6
I hope I helped

Which statement BEST compares the growth of the two functions shown in the table?
A
The value of the exponential function will never be greater than the linear
function
B)
The value of the linear function will never be greater than the exponential
function
The value of the linear function will eventually be greater than the
exponential function
D)
The value of the exponential function will eventually be greater than the
linear function

Answers

Answer will be (D)

The value of the exponential function will eventually be greater than the

linear function.

and

B)

The value of the linear function will never be greater than the exponential

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question in the picture. HELP! please

Answers

Answer:

1) 4*4x-4*3 and 16x-12

2)15y and 8y+7y

Answer:

16x-12 & 4(4x)-4(3)

15y & 8y+7y

Step-by-step explanation:

36.05 rounded off to the nearest tens place

Answers

Answer:

36.1

Step-by-step explanation:

if the 100s place is 5 or above add 1 to the tens place. if it's 5 or below the tens will stay the same.

What is the value of x in the equation 3(2x + 8) = 0? (4 points) Group of answer choices −8 −4 4 8

Answers

Answer:

-4

Step-by-step explanation:

Start with 3(2x + 8) = 0.

Distribute the 3 to the 2x and 8 in the parentheses.

That will give you 6x + 24 = 0.

Subtract 24 from both sides, which will get x by itself and leave you with 6x = -24.

Divide both sides by 6 to get x = -4.

That is your answer.

Hope this helped.

3(2x + 8)= 0
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24-24
0-24
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X = -4

-7 + - 20 please help me i really don't understand

Answers

Answer:

-27

Step-by-step explanation:

-7 + - 20

let's not forget that a + and a - is equal to a - therefore all the question really says is ...

-7-20

which is now easier to do and is equal to

= -27

Hope this helped you, have a good day bro cya)

find the missing number so that the equation has no solutions. 5x+1-3x=_x+13

Answers

Answer:

You may just add 2 in the spot. Moreover, you get no solution.

Step-by-step explanation:

Hope this helped!

Help me with this pls!!!

Answers

Answer:

B) $1.25

Step-by-step explanation:

1. First, let's take two points. In this case, we're going to take (4,5) and (8,10). We took 2 points, so we can verify the unit rate/cost per pound of pineapple.

2. To find the cost per pound of pineapple, we have to divide the cost (the y-coordinates) by the pound (x-coordinates)

5 ÷ 4 = 1.2510 ÷ 8 = 1.25

3. Now, since we can verify with 2 coordinates that the cost per pound is $1.25, the answer is B) $1.25.

Hi, I need help with this math . What is inpendent and dependent variable in question?
Here's the question: The formula for the surface area of a right rectangular prism is a=2LW+2HW+2H , where l, w, and h represent length, width, and height , respectively, which term of this formula is not dependent on the height?
1) A
2) 2LW
3) 2HW
4) 2LH

Answers

Answer:

Answer is option 2 (as it doesn't contain H)

Step-by-step explanation:

If you like my answer than please mark me brainliest

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The term in the formula which isn't dependent on height is :

2.) 2LW

Hi, I need help with this question and I don't it is right or wrong answer pls correct me and explain.

Answers

Answer:

x=5.5

Step-by-step explanation:

2x+3.50=14.50

2x=14.50-3.50

2x=11

x=11/2

x=5.5

Option B

Let's Find x

[tex]\\ \sf\longmapsto 2x+3.50=14.50[/tex]

[tex]\\ \sf\longmapsto 2x=11[/tex]

[tex]\\ \sf\longmapsto x=11/2=5.5[/tex]

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