Dr. Leona Williams, a well-known plastic surgeon, has a reputation for being one of the best surgeons for reconstructive nose surgery. Dr. Williams enjoys a rather substantial degree of market power in this market. She has estimated demand for her work to be: Q = 480 – 0.2P where Q is the number of nose operations performed monthly and P is the price of a nose operation. What is the inverse demand function for Dr. Williams’ services? What is the marginal revenue function?
The average variable cost function for reconstructive nose surgery is estimated to be:
AVC = 2Q2 – 15Q + 400
where AVC is the average variable cost (measured in dollars), and Q is the number of operations per month. The doctor’s fixed cost per month is $8,000. If the doctor wishes to maximize her profit, how many nose operations should she perform each month?
What price should Dr. Williams charge to perform a nose operation?
How much profit does she earn each month?

Answer: the correct value of x in this will be 6.

Step-by-step explanation: According to the equation given ,

f(x) = 64

so , f(x) = 11x - 2 now putting the value of f(x) in this equation

therefore , 64 = 11x - 2

now solving the equation , 11x= 64+2

11x = 66

x = 66/11

x = 6

thus, the value of x obtained from the equation is 6

Answer:

136/5

Step-by-step explanation:

18 9/10 + 8 3/10

change to improper fraction

=189/10 + 83/10

Adding, you have:

=272/10

2 can further divide both numbers

= 136/5

The equation of the line perpendicular to -2y = 5x + 8  and passes through (10, -1) is y = 2 / 5 x - 5.

Linear equation can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the equation is perpendicular to  -2y = 5x + 8  and passes through (10, -1).

Perpendicular lines have slopes that are negative reciprocals of one another.

Therefore,

-2y = 5x + 8

y = - 5 / 2 x - 4

Therefore,

slope = 2 / 5

Let's find the y-intercept using (10, -1)

-1 = 2 / 5(10) + b

-1 = 20 / 5 + b

b = -1 - 4

b = -5

Therefore, the equation of the line is y = 2 / 5 x - 5

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By calculating, The value of given expression 8 · (2 + 3 )²- 4² is 184

What is Algebraic expression ?

Algebraic expressions are the concept of expressing numbers the use of letters or alphabets with out specifying their actual values. The fundamentals of algebra taught us a way to explicit an unknown price using letters along with x, y, z, etc. those letters are known as right here as variables.

An algebraic expression can be a combination of both variables and constants. Any cost this is positioned before and extended by using a variable is a coefficient.

Given expression ,

= 8 · (2 + 3 )²- 4²

= 8. (5)^2 - 4^2

=8.25 - 16

= 200 - 16

= 184

so, the value of expression is 184.

Therefore, The value go given expression 8 · (2 + 3 )²- 4² is 184

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The scale factor of the two triangles is 1/4 or 4

You should understand that scale factor is the ratio of any two corresponding lengths.

Looking at the triangles, the larger triangle has sides

The smaller triangle has sides

Scale factor = (Larger length)/ (Smaller length) or (Smaller length/(Larger length)

This is an indication that the triangles have scale factors of:

Scale factor = 12/3 = 4 or

Scale factor = 3/12 = 1/4

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a. The profit function P(x) is 10x - 5000.

b. The break even point is at 500 units.

c. If 350 units were sold, the loss was Rs. 1500.

d. The graph of the functions are attached below.

The solutions are obtained using the profit function.

What is profit function?

A profit function is a mathematical relationship that represents the difference produced when the cost function is subtracted from the revenue function. The graph of a profit function shows the optimal combination of revenues and expenses to produce the maximum profit.

a. We are given cost of raw material as Rs. 15 and the fixed cost is Rs. 5000. The product is sold for Rs.25 per unit.

This means that R(x) = 25x

We know that TC= FC + VC(x)

So, TC = 5000 + 15x

Therefore, the profit function will be

⇒Profit = R(x) - TC

⇒Profit = 25x - 5000 - 15x

⇒Profit = 10x - 5000

b. For break even, the profit should be 0.

Therefore,

⇒10x - 5000 = 0

⇒10x = 5000

⇒x = 500

So, the break even will be at 500 units.

c. We are given x=350

Putting this value in profit function, we get

⇒Profit = 10(350) - 5000

⇒Profit = 3500 - 5000

⇒Profit = -1500

So, there is loss of Rs. 1500.

d. The red line represents the cost function and the blue line represents the revenue function.

The break even point is the point where the two lines are meeting.

The area below the break even is the loss area and above it is the profit area.

Hence, the solutions are obtained.

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When the number of people is 16, the water lasts for 6 days, which is found using unitary method.

What is the unitary method?

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit and then multiplying that value to determine the required value.

a) Let the amount of water present = L

Initially, this amount was considered for 12 people for 8 days.

For 12 people,

8 days = L

1 day = L/8

So the water required for one person for one day = (L/8) / 12 = L/96

But now 4 more people joined the trek,

So for 16 people, water used in one day = (L/96)*16 = L/6

Now the water will last for 6 days since,

                   (L/6 * 6) = L

b) The assumption that is made while solving the question is that the water required by each person is considered the same(L/96) even if the number of persons increases.

Therefore the water lasts for 6 days when the whole group consists of 16 people.

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Answer:

First choice: 5x²+21x-20

Step-by-step explanation:

This is easy to answer if you realize that there is only one way an x² term can appear in the result and that is by the multiplication of 5x and x which results in 5x².

The only choice which has 5x² as a term is the first:  5x²+21x-20

However, it is important to know the FOIL method to multiply two terms together

FOIL stands for First Outer Inner Last and is a technique for multiplying two terms of the form (a+b) and (c+d)

In (a + b) (c + d),

First terms are a and c so their product is ac

Outer terms are a and d so their product is ad

Inner terms are b and c with product bc

Last terms are b and d with product bd

The result is the sum of all these terms

Let's take (5x - 4)(x + 5)
F: 5x·x = 5x²

O: 5x · 5 = 25x

I: -4 ·x = -4x

L: -4·5 = -20

Adding up these individual terms we get

5x² +25x - 4x - 20 = 5x²+21x-20

So first choice is the correct answer

The average annual cumulative rainfall is 1  inch per month. During month of August average rain fall is greatest because slope in this month is maximum.

In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.

The graph does not represent cumulative rainfall as a function of day.

Because they have average all values for month Total cumulative rainfall is 12 inches.

Total period is 12 month

So, average annual cumulative rainfall is

12/12 =1 inch per month

Average rainfall in the month of December= (average cumulative rainfall in December - average cumulative rainfall in November)

= 12-11

= 1 inch

Therefore, during month of August average rain fall is greatest because slope in this month is maximum.

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Richard is incorrect, As if two angles are same then the 3rd angle must be same too using angle sum property and therefore ΔJFH ≅ ΔJGH with AAA congruency.

Two triangles are congruent if they have the same shape and size. Congruent triangles have all corresponding angles and sides congruent, meaning they are equal in measure.

A triangle can be shown to be congruent to another triangle by using one or more of the following criteria:

SSS (Side-Side-Side) Congruence: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

SAS (Side-Angle-Side) Congruence: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

ASA (Angle-Side-Angle) Congruence: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

HL (Hypotenuse-Leg) Congruence: If the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Richard is incorrect, As if two angles are same then the 3rd angle must be same too using angle sum of property and therefore ΔJFH ≅ ΔJGH

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Answer:

That is correct.

Step-by-step explanation:

The greater the absolute value of a negative number, the lesser (farther left from zero) it is. The greater the absolute value of a positive number, the greater (farther right from zero) it is.

Thus,

-6 < -2 < 0 < 4 < 8

and

-5.5 < -5.2 < -5 < -2.5 < 5.5

Notice also how it is easier to compare numbers when they are converted to the same form—in this case decimal form.

Answer:

----------------------------

Given expression:

Simplify it in steps below:

Answer:

[tex] \sf \: 98h - 56k [/tex]

Step-by-step explanation:

Given expression,

→ 9(7h - 4k) + 10k - 5(6k - 7h)

Let's simplify the expression,

→ 9(7h - 4k) + 10k - 5(6k - 7h)

→ 63h - 36k + 10k - 30k + 35h

→ (63h + 35h) + (-36k + 10k - 30k)

→ (98h) + (-56k)

→ 98h - 56k

Hence, answer is 98h - 56k.

Answer:

5 and 6

Step-by-step explanation:

sqrt of 32= 4sqrt2 = 5.656

The function that describes the height of the ball as a function of time t (in seconds) can be represented as:

h(t) = -16t^2 + 64t + 40

Where h(t) is the height of the ball in feet above the ground, t is the time in seconds, and the -16t^2 represents the acceleration due to gravity. The 64t represents the initial velocity of the ball, and 40 is the initial height of the ball above the ground.

Check the picture below.

Answer: 1/24

Step-by-step explanation:

1st even = 3/6 (2,4,6)

2nd Prime = 3/6 (2,3,5)

3rd multiple of 5 = 1/6 (5)

3/6 x 3/6 x 1/6 = 9/216

9/216 = 1/24

Answer:

vendor sold 90 sodas and 45 hot dogs

Step-by-step explanation:

Let x = number of sodas sold

Let y = number of hot dogs sold

We have x = 2y (1)
( The number of sodas sold was two times the number of hot dogs sold)

We also have x + y = 135 (2)

( sold a combined total of 135 sodas and hot dogs.)

Substituting x = 2y we get

2y + y = 135

3y = 135

y = 135/3

y = 45

Therefore x = 135 - 45

x = 90

Therefore vendor sold 90 sodas and 45 hot dogs

(a) Average velocity = -7(5^2-1^2) + 70(5-1) = -90 m/s.

(b) Average velocity = -7(4^2-1^2) + 70(4-1) = -62 m/s.

(c) Average velocity = -7(3^2-1^2) + 70(3-1) = -34 m/s.

(d) Average velocity = -7(1+h)^2 + 70(1+h-1) = -7h^2 + 70h m/s.

(a) Average velocity = -7(5^2-1^2) + 70(5-1) = -7(25-1) + 70(4) = -7*24 + 280 = -168 + 280 = -88 m/s.

(b) Average velocity = -7(4^2-1^2) + 70(4-1) = -7(16-1) + 70(3) = -7*15 + 210 = -105 + 210 = -95 m/s.

(c) Average velocity = -7(3^2-1^2) + 70(3-1) = -7(9-1) + 70(2) = -7*8 + 140 = -56 + 140 = -16 m/s.

(d) Average velocity = -7(1+h)^2 + 70(1+h-1) = -7(1+h)^2 + 70h = -7(1+h)^2 + 70h m/s. The average velocity of an object over a given period of time is calculated by taking the difference between the final and initial positions, and dividing it by the amount of time elapsed. In this exercise, we are given the position of an object along a line as a function of time, s(t) = -7t^2 + 70t. To solve each part, we can plug in the given time intervals into the function, and calculate the difference between the initial and final positions. We then divide this difference by the amount of time elapsed to find the average velocity. For example, in part (a), the average velocity is calculated as -7(5^2-1^2) + 70(5-1) = -90 m/s. In part (b), the average velocity is calculated as -7(4^2-1^2) + 70(4-1) = -62 m/s. In part (c), the average velocity is calculated as -7(3^2-1^2) + 70(3-1) = -34 m/s. Finally, in part (d), the average velocity is calculated as -7(1+h)^2 + 70h m/s

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I learned to save for the future and spend responsibly. In my adult life I will continue to save and be mindful of my spending habits. I will change my attitude towards money and become more frugal.

Saving money for the future requires discipline and dedication. One of the easiest ways to start saving is to create a budget and stick to it. Make sure to include a line item for savings in your budget and allocate a specific amount each month to save.

Additionally, set up automatic transfers from your checking account to your savings account to ensure money is put into savings each month. It's also important to find ways to minimize expenses. Cutting back on eating out, reducing your cell phone bill, and shopping for discounts are all great ways to save money.

Finally, look into investing your money in stocks, bonds, and other investments to help your savings grow. Saving money for the future takes time, but it is possible with the right strategies.

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The standard deviation of Y is $432.00 and this can be determined by using the formula of standard deviation and the given data.

Given :

A company sells concrete in batches of 5 cubic yards.

The probability distribution of X, the number of cubic yards sold in a single order for concrete from this company, is shown in the table below.

The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76.

There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by  (Y = 75X - 100).

The formula to obtain the standard deviation is given below:

SD(Y) = SD(75X - 100)

Simplify the above expression by substituting the value of SD(X) and SD(100) in the above expression.

SD(Y) = 75SD(X) - SD(100)

SD(Y) = 75 SD(X) - 0

SD(Y) = 75×5.76

SD(Y) = $432

Therefore, the correct option is B.

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-12a is  a cubic function in exercises when Relative minimum (4,2).

What in mathematics is a relative maximum?

A point (x,y) on the graph of the function whose y-coordinate is larger than all other y-coordinates on the graph at locations "near to" is known as a relative maximum point (x,y). ( x , y ) .

  f'(x) = 3ax² + 2bx + c

(3,3) and (5,1 ) are print of  relative maximum

   so,    f'(3) = f'(5) = 0

  3a(3)² + 2b(3) + c = 0

or   27a + 6b + c = 0

and   3a(5)² + 2b(5) + c = 0

       75a + 10b + c = 0   ...................... 2

the  Inflection point occurs at point where f''(x) = 0

     d/dx ( 3ax² + 2bx + c ) ∫x = 4 = 0

       because (4,2) is point of  Inflection .

           6a(4) + 2b = 0

          24a + 2b = 0

          b = -12a

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Answer:  1⅗

Step-by-step explanation:  We can write 8 divided by 5 as 8/5.

As 8/5 is an improper fraction, when we divide 8 by 5, we get 1 as quotient and 3 as remainder.

To convert an improper fraction into a mixed fraction, we take quotient 1 as a whole part and in the fractional part remainder 1 as the numerator, and divisor 5 as the denominator.

The GCF of 5 and 1 is 1. So, divide both the numerator and denominator by the GCF to simplify and convert it to a mixed fraction.

Thus, 8 divided by 5 as a fraction in simplest form is 1⅗.

The answer to the question is d) c and l; f and h.

The concept of opposite numbers on the number line can be expressed mathematically by the equation -x = y, where x is the original number and y is the opposite number. This equation can be used to calculate the opposite of any number. For example, if the number 5 is located at point a on the number line, the opposite of 5 is located at point k and can be calculated by substituting 5 for x in the equation and solving for y. -5 = y, therefore y = -5. The opposite of 5 is therefore -5. To calculate the opposite of any of the other numbers marked on the number line, the same equation can be used. The answer to the question is d) c and l; f and h.

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Answer:

No!

Step-by-step explanation:

(1 5/2)

is a mixed fraction so you will change it to proper fraction.

the solution is

=7/2 or 3.5

You will multiple two by one and add by five given 7/2.

Answer:

all of them are 17

Step-by-step explanation:

7+9=16

16+1+0=17

9+7=16

16+1+0=17

1+0+9=10

10+7=17

7+1=8

8+9+0=17

hope this helped!

The domain is discrete and the range is continuous, which can be an accurate statement regarding the two terms.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input.

After we enter an x value, the function outputs this sequence of values.

So, the parameters are as follows, taken from the query:

Downloaded Amount = $2.50

Added amount to each player = $1.50

Use x to indicate how many players there are.

The following representations are what we have.

Total amount = Amount to download + Amount to add each player * Number of players

Now, we obtain:

y = 2.50 + 1.50 * x

y = 2.50 + 1.5x

The number of players serves as the input to the aforementioned linear function.

The domain is discrete as a result.

The amount, though, can have decimal points

The range is continuous as a result.

Therefore, the domain is discrete and the range is continuous, which can be an accurate statement regarding the two terms.

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92 Square inches is the area of the shaded region shown below

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given a rectangle, that has a length of 12 inches and 9-inch width

Since,

Area = length * width

Area of the given triangle = 12 * 9

Area of the given triangle = 108 square inch

There is also one square inside this rectangle of side 4 inch

Since the area of square = side * side

Thus in our case,

Area of square = 4 * 4 = 16 square inch

As we can see in the figure:

Area of shaded region  = complete area of rectangle - area of square

Area of shaded region  = 108 - 16

Area of shaded region  = 92 square inch

Therefore, The area of the shaded region is 92 Square inches.

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Complete question:

Electric potential energy is the energy that is needed to move a charge against an electric field.

Completed question :

A point charge q1 , is held stationary at the origin. A second charge q2 is placed at a point a, and the electric potential energy of the pair of charges is -6.4 x [tex]10^{-8}[/tex] J. When the second charge is moved to point b, the electric force on the charge does 4.2 x [tex]10^{-8}[/tex] J of work. What is the electric potential energy of the pair of charges when the second charge is at point b?

Given data :

PE1 = -6.4 x [tex]10^{-8}[/tex] J

Work done = 4.2 x [tex]10^{-8}[/tex] J

PE1 = PE2 + Work done

PE2  = PE1 - Work done =

= -6.4 x [tex]10^{-8}[/tex] J - 4.2 x [tex]10^{-8}[/tex] J = -10.6 x [tex]10^{-8}[/tex] J

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The faster car is traveling at 149 mph, and the slower car is traveling at 142 mph.

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Least cost in the sales promotion is when (140, 70) i.e. Hats = 140 and pair of glasses = 70.

To determine if the data support the mixing of two potential sources or the fractionation of a single source, graphical approaches are frequently used.

To better interpret their data, researchers now employ a variety of graphical tools, including scatterplots, box plots, and histograms. Graphs are excellent for illustrating trends, patterns, and correlations between variables as well as for displaying and summarizing vast volumes of numerical data.

Value of cost at (140, 70) is 3 × 140+ 3 × 70

= $630

Consider any point on the feasible line, say (150, 60)

Cost = 3 × 150 + 3 × 60 =  $570

Cost is increasing towards the point (210, 0)

Thus, Least cost is when (140, 70) i.e. Hats = 140 and pair of glasses = 70.

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In order to accurately represent the surface, we would need to be able to plot the equation in 3-dimensions using 3-dimensional coordinates. Since this is not possible, the answer is dne.

In order to accurately represent the surface, we would need to be able to plot the equation in 3-dimensions using 3-dimensional coordinates. Since this is not possible, the answer is dne.

dne

Since 9x2 y2 9z2 is a 3-dimensional equation, it cannot be sketched on a 2-dimensional plane. Therefore, the answer is dne.

The equation 9x2 y2 9z2 is a 3-dimensional equation and cannot be represented on a 2-dimensional plane. Therefore, it is not possible to sketch the surface using this equation. As a result, the answer is dne. The equation contains three variables, x, y and z, and cannot be represented on a graph without the use of three axes. In order to accurately represent the surface, we would need to be able to plot the equation in 3-dimensions using 3-dimensional coordinates. Since this is not possible, the answer is dne.

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