In this problem,p is in dollars and x is the number of units. If the demand function for a product is p = 28/(x + 1) and the supply function is p = 1 + 0.2x, find the consumer's surplus under pure competition. (Round your answer to two decimal places.

Answers

Answer 1

Given the demand function :

\(p=\frac{28}{x+1}\)

And the supply function:

\(p=1+0.2x\)

So,

\(\begin{gathered} \frac{28}{x+1}=1+0.2x \\ \\ (1+0.2x)\cdot(x+1)=28 \\ 1\cdot(x+1)+0.2x\cdot(x+1)=28 \\ x+1+0.2x^2+0.2x=28 \\ 0.2x^2+1.2x+1=28 \\ 0.2x^2+1.2x-27=0 \end{gathered}\)

using the general rule to solve the quadratic equation:

a = 0.2 , b = 1.2 , c = -27

so,

\(x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{-1.2\pm\sqrt[]{1.2^2-4\cdot0.2\cdot(-27)}}{2\cdot0.2}\)\(\begin{gathered} x=\frac{-1.2\pm\sqrt[]{23.04}}{0.4} \\ \\ x=\frac{-1.2\pm4.8}{0.4} \\ \\ x=\frac{-1.2+4.8}{0.4}=\frac{3.6}{0.4}=9 \\ OR \\ x=\frac{-1.2-4.8}{0.4}=-15 \end{gathered}\)

So, the answer is x = 9


Related Questions

Find the distance between the two points in simplest radical form (-6,8) and (-1,-4)

Answers

Answer:

13

Step-by-step explanation:

d) = √(-1 - -6)2 + (-4 - 8)2

= √(5)2 + (-12)2

= √169

= 13

Answer:

13

Step-by-step explanation:

We use the distance formula to find the distance between two points

d = sqrt ( (x2-x1)^2 + y2-y1) ^2)

Where ( x1,y1) and ( x2,y2) are the two points

d = sqrt( ( -1 - -6) ^2 + ( -4 - 8) ^2)

   = sqrt ( ( -1+6) ^2 + ( -12) ^2)

  = sqrt( 5^2 + 144)

 = sqrt ( 25+ 144)

 = sqrt ( 169)

 = 13

please help i’m stuck on my geometry hw. :(

please help im stuck on my geometry hw. :(

Answers

Answer:

the reflection line would be x=k, so it would be (4,7) I believe, I may not be correct since I haven't done these for a while.

Step-by-step explanation:

Please help me at least one of them number it!

Please help me at least one of them number it!

Answers

Answer:

1) y+6 or 6+y 2) 12 x n = x 3) 24 + b = x 4) x - 18 5) n - 5 6)a / 3 or 3 / a

Step-by-step explanation:

Find value of b and A

Answers

Answer:

Hi

Step-by-step explanation:

Please paste your question so I can solve it

Thanks

The die shown below is a perfect cube with sides of length s.



What is the distance from point A to point B?
Responses

s√2
s √ 2

s√3
s √ 3

2s
2 s

s√5

Answers

The distance from the point A to point B is s√3

What is the distance from point A to point B?

From the question, we have the following parameters that can be used in our computation:

Perfect cube with sides of length s.

The distance from point A to point B is calculated as

Distance^2 = s^2 + s^2 + s^2

When evaluated, we have

Distance^2 = 3s^2

Take the square roots of both sides

Distance = s√3

Hence, the distance = s√3

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-1000 2/3 is not real fraction. True or false

Answers

True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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A population of llamas on a tropical island can be modeled by the equation 0.035 500 t P e  , where t
represents the number of years since the llamas were first introduced to the island.

Answers

Answer:

Question itself was incorrectly pasted in/worded here. Didn't make sense. (To me at least.) After doing some research I found this:

Please check the attachment. Hope this helps and have a nice day!

A population of llamas on a tropical island can be modeled by the equation 0.035 500 t P e , where trepresents

An engineer is monitoring the liquid level in two tanks as they are being filled. The volume of the tank A after x minutes is represented by the equation y=75x +110. For tank B the engineer has created a table, shown below, from measurements taken while the tank is being filled

Answers

The two tanks differ in terms of Filling rates and initial volumes.

We can work with the equation for tank A, which represents a linear relationship between the volume of liquid in the tank (y) and the time it has been filling (x).

The equation y = 75x + 110 tells us that the tank A is filling at a constant rate of 75 units per minute, starting with an initial volume of 110 units.

To analyze the data for tank B, we would need to know the volumes of the tank at different times as it is being filled.

If the relationship for tank B is also linear, we could find the equation that represents it by using two points from the table and the slope-intercept form of a linear equation (y = mx + b). Once we have both equations, we can compare them to see how the two tanks differ in terms of filling rates and initial volumes.

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An engineer is monitoring the liquid level in two tanks as they are being filled. The volume of the tank

What the means of lathi charges

Answers

Answer:

the police tactic of charging a crowd with lathis or batons in order to disperse it

What value of x is in the solution set of the inequality 2(3x – 1) ≥ 4x – 6? –10 –5 –3 –1

Answers

Answer:

-1

Step-by-step explanation:

What value of x is in the solution set of the inequality 2(3x 1) 4x 6? 10 5 3 1

Answer:

-1 is the answer

Step-by-step explanation:

Sharon types for other people. She charges $1.25 per page for double-spaced pages and $1.75 per page for space-and-a-half pages. How much total pay would she receive for a 25 page double spaced report and a 15 page space-and-a-half report?

Answers

Answer: Double Spaced Pages = $31.25 Space And A Half Pages = $26.25

Step-by-step explanation:

Multiplication

Double-Spaced Pages

1.25 x 25 = 31.25

Space And A Half Pages

1.75 x 15 = 26.25

Urgent

ALMN is reflected about the line y = 3.

Urgent ALMN is reflected about the line y = 3.

Answers

Answer:

B

Step-by-step explanation:

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed). ... the line y = x is the point (y, x). The reflection of the point (x,y) across. the line y = -x is the point (-y, -x).

the base company has assets other than investment securities, that cost $50,000. The current market value of the assets is $75 million. The assets will be recorded and reported as assets at

Answers

As the company asset other than investment securities cost $50,000 and market value of the assets is $75 million. The assets will be recorded and reported as at $75,050,000.

How are asset recorded and reported?

An asset is a resource with monetary value that an individual, corporation, or country owns or controls with the expectation of future benefit. An asset is anything that can generate cash flow, reduce expenses, or increase sales in the future, whether it's manufacturing equipment or a patent.

A company's assets are reported on its balance sheet. They are divided into four categories: current, fixed, financial, and intangible. They are purchased or created in order to increase the value of a company or to benefit its operations.

The reported asset of the company will be:

= $50,000 + $75 million

= $75,050,000

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What order should you simplify like terms in? E.g. \(16-4\sqrt{5} -4\sqrt{5} +5\) A video said to Simplify the numbers first as they will be positive?
But in \(6+3\sqrt{5} +2\sqrt{5}+5\) You simplify the surds first.

Answers

Answer:

It does not matter, since, from your second case, \(5\sqrt5 +11 = 11+5\sqrt5\).

In general is a matter of personal preference but in general I like to start with a positive number (I like \(\sqrt2 -1\) more than \(-1+\sqrt2\) since if there's an equal sign before I'm guaranteed to have the two signs mesh together in a few steps).

If everything you are adding together is positive, I just go first come first served and pick a new term in order it appears in the previous passage.

Need help find answers

Need help find answers

Answers

Answer:

JMK= 54 degrees,  JKH=45 degrees, HLK=90 degrees, HJL=45 degrees, LHK=45 degrees, JLK=45 degrees

Step-by-step explanation:

can you help me please

can you help me please

Answers

Hence the correct option is to translate down 2 unit

Transformations can be non-rigid (when the preimage's size or shape is unaltered) or stiff (where the size is changed but the shape remains the same). These are the fundamental guidelines that this concept abides by. It is a straightforward approach to alter 2D forms.

Planar transformations and spaces can be distinguished from one another using the dimensions of the operand sets.

We have the parent function f(X)= x

and transformed function is g(x)= -3f(x+5)-2

the parent function f(x) is translated dawn 2 units and stretched by 5 .

Hence the correct option is to translate down 2 unit

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find the sum of the interior angles of a rectangular polygon of 18 sides​

Answers

Sum of the interior angles of a rectangular polygon of 18 sides​ IS 2880°

Given,

Rectangular polygon of 18 sides.

The sum of the measures of the interior angle of any polygon is the number of sides minus 2 multiplied by 180.

Then,

S=(n-2)*180°

n = Number of sides

So,

S=(18-2)(180°)

S=16(180°)

S=2880°

A polygon with 18 sides has an interior angle sum of 2880 degrees.

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(4-i)-(3-i) in standard form

Answers

Answer:

ifeywifheb

Step-by-step explanation:

hkefewib

convert 9,78 h to hours, minutes and seconds​

Answers

In hours it’s 9 hours and 78 minutes

PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!

PLS HURRY I AM GIVING BRAINLIEST!!!the question is in the photo!!

Answers

Jordan spend 25 minutes writing each dayNoHow much time does Jordan spend writing each dayFrom the question, we have the following parameters that can be used in our computation:D + W = 75W + 25 = DSo, we haveW + W + 25 = 75EvaluateW = 25This means that Jordan spends 25 minutes on writing is it possible?Based on the answer in (a), the truth statement is No

Calculate.
12C4
Note: Cr=
n
n!
r!(n−r)!

Answers

Answer:

495

Step-by-step explanation:

using the definition

n\(C_{r}\) = \(\frac{n!}{r!(n-r)!}\)

where n! = n(n - 1)(n - 2) ... × 3 × 2 × 1

then

12\(C_{4}\)

= \(\frac{12!}{4!(12-4)!}\)

= \(\frac{12!}{4!(8!)}\)

cancel 8! on numerator/ denominator

= \(\frac{12(11)(10)(9)}{4!}\)

= \(\frac{11880}{4(3)(2)(1)}\)

= \(\frac{11880}{24}\)

= 495

John is buying a new work uniform. He used a 25% off coupon on a pair of boots that were $80. He also bought a belt that was 15% off. In total, John spent $120.25.

How much was the original price of the belt?

Answers

Answer:

$70.88

Step-by-step explanation:

He bought the boots for $80*75% = $80*0.75 = $60

Let x = the original price of the belt

He spent x * 85% = 0.85x for the belt

total cost = 60 + 0.85x = 120.25

0.85x = 120.25 - 60 = 60.25

x = 60.25/0.85 = $70.88

Select the correct answer.
Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x - 11)?
A. It is the graph of f(x) where the slope is increased by 11.
It is the graph of f(x) translated 11 units to the left.
It is the graph of f(x) translated 11 units up.
It is the graph of f(x) translated 11 units to the right.
B.
C.
OD.

Answers

The correct answer is C. It is the graph of f(x) translated 11 units to the left.

The correct answer is:

C. It is the graph of f(x) translated 11 units to the left.

When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.

In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.

The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.

Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.

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PLS HELP ME WITH THIS QUESTION PLS SHOW YOUR WORKING OUT

PLS HELP ME WITH THIS QUESTION PLS SHOW YOUR WORKING OUT

Answers

The maximum volume of the cylinder is approximately 1257 cubic centimeters.

What is the maximum volume of the cylinder?

The volume V of a right circular cylinder with radius r and height h is given by:

V = πr²h

Substituting the given expressions for the radius and height of the cylinder, we get:

V = πx²(800/πx - x)

Simplifying the expression, we get:

V = 800x - πx³

To find the maximum value of V, we need to find the value of x that maximizes V. We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

dV/dx = 800 - 3πx² = 0

3πx² = 800

x² = 800/3π

x ≈ 6.43

Substituting this value of x back into the expression for V, we get:

V ≈ 1257

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76890 million in standard form

Answers

Answer:

76890000000 to 7.689 ×10^10

Step-by-step explanation:

Write a division problem that has a quotient of 12.
At least one of the numbers you give must be a proper fraction. The other can be a proper fraction, whole number, or
improper fraction. Neither the dividend nor the divisor can be 12.

Answers

12%12 that’s ur answer

Choose the correct equation for the parabola based on the given information. Given: Focus:(4,-3) Vertex: (-2,-3) a. 24(y+3) = (x+2)^2 b. 24(x+2)=(y+3)^2 c. 6(x-4)= (y+3)^2 d. 6(y+3)=(x-4)^2

Answers

Answer:  b.  24(x + 2) = (y + 3)²

Step-by-step explanation:

Vertex: (-2, -3)

Focus:  (4, -3)

                  ↓

                same y-value so equation will be y²

Equation: a(x - h) = (y - k)²

a = 4p where p is the distance from Vertex to Focush is the x-coordinate of the Vertexk is the y-coordinate of the Vertex

Given: h = -2,  k = -3,   a = 4[4 - (-2)] --> a = 24

Input those values into the equation:  24(x + 2) = (y + 3)²

 

Which graph has a y-intercept of 2 and a slope of - 1/3?

Which graph has a y-intercept of 2 and a slope of - 1/3?

Answers

it is the fourth graph the numbers are 24

In the figure, the angles are formed by a transversal and two parallel lines. Which angles seem to be congruent?

In the figure, the angles are formed by a transversal and two parallel lines. Which angles seem to be

Answers

The angles are formed by a transversal and two parallel lines in the figure. By applying congruent angles and vertical opposite angle property, ∠1 ≅∠3 ≅ ∠5 ≅ ∠7; ∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8. Therefore option B is correct.

Congruent angles are identical to each other and have the same measure. The angles formed by the transversal in corresponding corners are called corresponding angles and they are congruent.

Therefore, ∠1 ≅ ∠5, ∠3 ≅ ∠7----------(1)

At a vertex if two angles are opposite to each other, then they are vertically opposite angles, they are equal and congruent to each other.

Therefore, ∠1 ≅ ∠3, ∠5 ≅ ∠7----------(2)

Combining (1) and (2), we get:

∠1 ≅∠3 ≅ ∠5 ≅ ∠7
Similarly we can find,

∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8.

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Find f(5) in the piecewise function

Find f(5) in the piecewise function

Answers

Your example is of f(5) so we will be using the 2nd example :
6x-28
>> 6(5)-28=2
So , f(5)=2
The question is giving you hints just check the value of f(x) and see which rule implies
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