Let C(x) represent the cost of producing x items and p(x) be the sale price per item if x items are sold. The profit P(x) of selling x items is P(x)=x p(x)-C(x) (revenue minus costs). The average profit per item when x items are sold is P(x)/x and the marginal profit is dP/dx. The marginal profit approximates the profit obtained by selling one more item given that x items have already been sold. Consider the following cost functions C and price functions p. Complete partsâ (a) throughâ (d) below.
a. Find the profit function P.
b. Find the average profit function and marginal profit function.
c. Find the average profit and marginal profit if x=a units are sold.
d. Interpret the meaning of the values obtained in part (c).
C(x)=â0.02x^2 +50x+100, p(x)=100, a=500

Answer:

y=-108x3-342x2-240x+50

Step-by-step explanation:

First start with the factors

(3x+5)(3x+5)(6x-1) The multiplicity of 2 means there are 2 of that same factor.

Next, figure out how to get it to go through the point (0,50) Plug in these points, solve for a

50=a(3(0)+5)(3(0)+5)(6(0)-1)

50=a(5)(5)(-1)

50=-25a Divide both sides by -25

-2=a Plug this in

y=-2(3x+5)(3x+5)(6x-1) Now multiply the factors out. Will start by FOILING the first 2 factors

y=-2(9x2+30x+25)(6x-1) Now multiply the remaining factors together

y=-2(54x3+180x2+150x-9x2-30x-25) Combine like terms

y=-2(54x3+171x2+120x-25) Distribute the -2

The conditional probability for this problem is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For this problem, we have that 5 students play soccer, and of those, 2 play basketball, hence the conditional probability is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

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The transformation of f(x) to p(x) is that (a) the graph is reflected and shifted down

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

The functions f(x) and g(x)

In the function equations, we can see that

f(x) = x²

p(x) = -f(x) - 3

So, we have

Vertical Difference = 0 - 3

Evaluate

Vertical Difference = - 3

This means that the transformation of f(x) to p(x) is that f(x) is reflected and shifted down 3 units to p(x).

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The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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Answer:

n>1

Step-by-step explanation:

Answer:

                             ‎‎‎                  ‎‎‎‎‎‎‎       ‎‎‎

Answer:

1) 7/8     8/7

2) 4.4

3) 3.7

4) 2.8

Step-by-step explanation:

Length of bottom side of Figure A: 8 cm

Length of bottom side of Figure B: 7 cm

From Figure A to Figure B, the scale factor is 7/8.

7/8

8/7

5 × 7/8 = 35/8 = 4.375

4.4

3.2 × 8/7 = 3.657...

3.7

3.2 × 7/8 = 2.8

2.8

Step-by-step explanation:

2x=8

x=8÷2

x=4

x=5+3

×=8

Answer:

f(x) = x + 4

Step-by-step explanation:

\(y - 8 = (x - 4) \\ \\ y - 8 = x - 4 \\ \\ y = x - 4 + 8 \\ \\ y = x + 4 \\plug \: y = f(x) \\ \\ \implies \: f(x) = x + 4\)

The numerical value of x in angle ABD is 9 as angle ABC is divided into two equal halves.

An angle bisector divided an angle into two equal halves.

From the diagram:

Line BD divides angle ABC into two equal halves.

Angle ABD = ( 3x - 7 ) degrees

Angle DBC = 20 degrees

Since angle ABD and DBC are equal haves;

Angle ABD = Angle DBC

Plug in the values:

( 3x - 7 ) = 20

Solve for x:

3x - 7 = 20

Add 7 to both sides:

3x - 7 + 7 = 20 + 7

3x = 27

x = 27/3

x = 9

Therefore, the value of x is 9.

Option A)9 is the correct answer.

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Answer: x=3\(\sqrt{2\). y=3\(\sqrt{2\)

Step-by-step explanation: This is a 45-45-90 triangle. Both of the legs, x and y, are congruent. To find the length of the legs, divide 6, the hypotenuse, by \(\sqrt{2\). 6/\(\sqrt{2\)=3\(\sqrt{2\).

The misleading about the data shown on the figure is the clas width

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

The histogram

On the histogram, we have the following readings

From the above, we can see that

The above readings are not consistent i.e. the class widths are not equal

Hence, the misleading about the data shown on the figure is the clas width

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Answer:

Step-by-step explanation:

Cross multiply,

74* b = 600 * 100

74b = 60000

b = 60000/74 = 810.8

Answer: 1/8

Step-by-step explanation:

First make the bottom half the same:

3/4*2/2=6/8

We don’t need to change the first portion since they have a common factor

7/8-6/8=1/8

Answer:

17 quarters 25 dimes

Step-by-step explanation:

quarters 25 cents

dimes 10 cents

$6.75 total.

Answer:Average score for 3 tests is 83.67

Step-by-step explanation:sorry if im wrong

Answer:

the horizontal and vertical lines passing through the point (1,6)

y-6=

x-1=

Step-by-step explanation:

Answer:

x=1 and =

Step-by-step explanation:

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

Answer:

Your answer is correct

Step-by-step explanation:

Use the rules of exponents to simplify the expression.

To raise a power to another power, multiply the exponents.

Multiply 6 by 2.

The correct option is the third.

The surface area of the cylindrical pottery vase is 177.55 in².

Given that a cylindrical pottery vase has a diameter of 4.3 inches and a height of 11 inches, we need to find the surface area of the vase,

SA of a cylinder = 2π×radius(h+r)

= 2×3.14×2.15(2.15+11)

= 177.55 in²

Hence, the surface area of the cylindrical pottery vase is 177.55 in².

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Answer:

Length of rectangle = 15 feet

Width of rectangle = 6 feet

Step-by-step explanation:

Given:

Perimeter of rectangle = 42 ft

Length of rectangle = 2[Width of rectangle] + 3

Find:

Value of length and width

Assume:

Width of rectangle = w

SO,

Length of rectangle = 2[w] + 3

Perimeter of rectangle = 2[l + b]

42 = 2[2w + 3 + w]

2[3w + 3] = 42

6w + 6 = 42

6w = 42 - 6

6w = 36

w = 36 / 6

w = 6

So,

Width of rectangle = 6 feet

Length of rectangle = 2[w] + 3

Length of rectangle = 2[6] + 3

Length of rectangle = 12 + 3

Length of rectangle = 15 feet

Answer:

x  =24

Step-by-step explanation:

Call the angle in the lower right corner y

The outside angles add to 180 degrees for the large triangle

41+ 94+ y = 180

135 + y = 180

y = 180-136

y =45

The small triangle in the lower right also has angles that add to 180

y+ 111+x = 180

45+111+x = 180

156 + x = 180

x = 180-156

x =24

Answer:

x = 24

Step-by-step explanation:

Angles on a straight line add up to 180 degrees.

a + 111 = 180

180 - 111 = a

a = 69

Angles in a quadrilateral add up to 360 degrees.

69 + 41 + 94 + c = 360

204 + c = 360

c = 360 - 204

c = 156

Angles on a straight line add up to 180 degrees.

x + 156 = 180

x = 180 - 156

x = 24

Answer:0.0001

t means there is a 1% chance you will see a flood like the one on the FEMA flood map each and every year. Since 1% is also "1 out of 100", the term "100-year flood" was adopted because that's easier to talk about than rattling off a bunch of statistics

Step-by-step explanation

Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.

Step-by-step explanation:

To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.

Answer:

the afternoon is the right one

Given

To find

Let the purchase value be P,

ATQ,

P -3 x 0.1P = Rs 43,740

P-0.3P = Rs 43,740

0.7P = Rs 43,740

P = Rs 43,740/0.7

P = Rs 62,486 (approx)

Hence, the purchase value of the machine would be Rs 62,486

Answer:

To convey the sense that Alfonso is concerned about how others perceive him.

Answer:

To convey the sense that Alfonso is concerned about how others perceive him.Step-by-step explanation:

Answer:

a

 \(P(r n L) =  0.12\)  

b

 \(P(L) = 0.225\)

c

  \(P(\= r | L) = 0.4667 \)

Step-by-step explanation:

The chance that it will rain is  \(P(r ) = 0.30 \)

 The chance that it does not rain is \(P(\= r ) = 1 - P(r )  \)

                                                             \(P(\= r ) = 1 -0.30  \)

                                                              \(P(\= r ) = 0.70  \)

The probability that the bus run late if it rains is  \(P(L | r) = 0.4\)

 The probability that the bus run late if it does not rain is   \(P(L | \= r) = 0.15\)

  Generally the probability that it will rain and the bus will be late is mathematically represented as

     \(P(r n L) = P(L | r) * P(r)\)

=>  \(P(r n L) = 0.4 * 0.30\)

=>  \(P(r n L) = 0.12\)  

Generally the probability that the bus will be late is mathematically represented as

     \(P(L) = P(r) * P(L|r) + P(L | \= r) * P(\= r)\)

=>  \(P(L) = 0.30 * 0.4 +0.15*0.70\)

 =>  \(P(L) = 0.225\)

Generally given that the bus ran late,  the probability that the bus it was not raining is mathematically represented as

      \(P(\= r | L) = 1- P(r | L )\)

Here  \(P(r | L ) = \frac{P(r n L)}{P(L)}\)

=>   \(P(r | L ) = \frac{0.12}{0.225}\)

=>   \(P(r | L ) = 0.533 \)

So

      \(P(\= r | L) =  1- 0.533\)

   =>   \(P(\= r | L) =  0.467 \)