Determine the maximum profit if the marginal cost and marginal revenue are given by C'(x) = 20+ x/20 and R'(x) = 40 and fixed cost is $100.00.

Step-by-step explanation:

C= 2πr

Given,

Diameter= 9

so, radius = 9÷2 = 4.5

C= 2 x π x 4.5

= 28.3 (3.s.f)

If the commission rate is ​%6.5 for the real estate agency, the real estate agency made $20,475 on the house. The agent earned $4,095 in commission.

First, let's determine the commission earned by the real estate agency. To do this, we'll multiply the house price ($315,000) by the commission rate (6.5%).

$315,000 * 6.5% = $20,475

The real estate agency made $20,475 on the house.

Next, let's determine the commission earned by the agent. We'll multiply the commission earned by the real estate agency ($20,475) by the agent's commission rate (20%).

$20,475 * 20% = $4,095

The agent earned $4,095 in commission.

So, the real estate agency made $20,475 on the house, and the agent earned $4,095 in commission.

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To enclose his garden, Jayden needs 24 feet of wood assuming his rectangular-shaped garden has sides of 6 feet each.

Jayden needs wood to enclose his garden. He measured one side of his garden and found that it is 6 feet long.

To calculate how many feet of wood Jayden needs to enclose his garden, we need to know the length of all sides of the garden.

Assuming that the garden is rectangular in shape, we need to know the length of the other side as well.

Let's say the other side is also 6 feet long. In this case, we can calculate the total length of wood required by using the formula for the perimeter of a rectangle, which is:

                   Perimeter = 2 x (Length + Width)

Here, the length and width of the garden are both 6 feet.

So, we can substitute these values in the formula and get:

                   Perimeter = 2 x (6 + 6) = 2 x 12 = 24 feet

Therefore, Jayden needs 24 feet of wood to enclose his garden.

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the area of the circle is 615. 4 m²

The formula that is used to calculate the area of a circle is expressed with the equation.

We have the equation as;

A = πr²

Such that the parameters are given as;

From the diagram shown, we have that;

A = unknown

r = 14m

Now, substitute the values, we get;

Area = 3.14 ×14²

Find the square value

Area = 3.14(196)

Multiply the values

Area = 615. 4 m²

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The length of side AB is also 12 units.

What is a rhombus?

A rhombus is a four-sided quadrilateral with all sides of equal length. It is also known as a diamond or a lozenge. In a rhombus, opposite sides are parallel, and opposite angles are equal. Additionally, the diagonals of a rhombus bisect each other at right angles, meaning they intersect at a 90-degree angle and divide each other into two equal segments.

Since a rhombus has all sides of equal length, we know that YZ = AB. Therefore, if YZ = 12, we have:

AB = YZ = 12

So the length of side AB is also 12 units.

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The length of the shorter diagonal is approximately 7.07 units.

A rhombus is a four-sided polygon in which all sides are equal in length. It is also called a diamond shape because it is often used for diamond-shaped figures. In this case, we are given that the perimeter of the rhombus is 88. Since all sides of the rhombus are equal, we can divide the perimeter by 4 to find the length of one side.

88 ÷ 4 = 22

Therefore, each side of the rhombus measures 22 units.

We are also given that two of the angles in the rhombus are acute angles measuring 40° each. Since all angles in a rhombus are equal, we can find the measure of the other two angles by subtracting the sum of the acute angles from 360.

360 - 2(40) = 280

Each of the other two angles measures 140°.

To find the length of the shorter diagonal, we can use the formula:

Shorter diagonal = (2 × Area) / Length of longer diagonal

The area of a rhombus can be found by multiplying the length of the longer diagonal by the length of the shorter diagonal and then dividing by 2.

Area = (diagonal1 × diagonal2) / 2

We know that the longer diagonal is twice the length of the shorter diagonal.

Longer diagonal = 2 × Shorter diagonal

Substituting these values into the formula, we get:

Shorter diagonal = (2 × (22 × Shorter diagonal × sin 40°)) / (2 × Longer diagonal)

Simplifying, we get:

Shorter diagonal = (22 × Shorter diagonal × sin 40°) / Longer diagonal

Plugging in the values we know, we get:

Shorter diagonal = (22 × Shorter diagonal × sin 40°) / (2 × Shorter diagonal)

Shorter diagonal = 11 × sin 40°

Using a calculator, we can find that:

Shorter diagonal ≈ 7.07

Therefore, the length of the shorter diagonal is approximately 7.07 units.

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Answer: 1  ÷ 2

Step-by-step explanation: I think this is what you mean?

Answer:

We are given that:

- f(x) = x² - 2x - 4

- g(x) = x - 1We want to find fx for which f(x) = g(x) - 4, or in other words:

- f(x) = x - 1 - 4

- f(x) = x - 5

We can solve forTo find the value of x for which f(x) = g(x) - 4 (which is what I assume you meant by "f(x) = (x) = m - 4"), we can set up the following equation:

f(x) = g(x) - 4

Substituting the given expressions for f(x) and g(x), we get:

x² - 2x - 4 = x - 1 - 4

Simplifying, we have:

x² - 3x - 3 = 0

We can solve for x using the quadratic formula:

x = (-(-3) ± sqrt((-3)² - 4(1)(-3))) / (2(1))

x = (3 ± sqrt(21)) / 2

Therefore, the two values of x for which f(x) = g(x) - 4 are:

- x = (3 + sqrt(21)) / 2

- x = (3 - sqrt(21)) / 2

The population increased by a percentage of 5%.

The population of Sanibel, Florida in 2016 can be determined using the given population model P = 6191 * 1.05^t, where t represents the number of years since 2016. To find the population in 2016, we set t to 0 since there are 0 years since 2016.

Step 1: Set t to 0 in the equation:
P = 6191 * 1.05^0

Step 2: Calculate the population P:
P = 6191 * 1
P = 6191

So, the population in Sanibel, Florida in 2016 was 6,191.

Regarding the percent population increase each year, the given model uses an exponential growth formula with a constant factor of 1.05. The factor (1.05) represents a 5% increase in the population each year.

In summary, the population in Sanibel, Florida in 2016 was 6,191, and the population increases by 5% each year. This exponential growth model demonstrates how the population continues to grow at a steady rate, contributing to the overall population increase in the area.

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Answer:

C.

Step-by-step explanation:

3 = 1.5 * 2

9 = 1.5 * 6

15 = 1.5 * 10

33 = 1.5 * 22

The height of the feeder is approximately 4 inches.

We can use the formula for the volume of a cone, which is V = (1/3)π[tex]r^{2}[/tex]h, where V is the volume, r is the radius, and h is the height. We know that V = 113.04 and r = 3, so we can solve for h:

113.04 = (1/3)*π*([tex]3^{2}[/tex])h

113.04 = 9πh

h = 113.04 / (9π)

h ≈ 4 inches

The y- intercept of a direct equation is the point where the line crosses the y- axis. It's the value of y when x is equal to 0.   To graph a direct equation, you can  compass the y- intercept on the y- axis, and  also use the  pitch to find other points on the line.

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The missing corresponding side length in Figure B is 30 meters.

Perimeter is the total length of the boundary of a two-dimensional shape. It is found by adding up the lengths of all the sides of the shape.

Since Figure A and Figure B are similar, their corresponding side lengths are proportional.

Let's represent the missing side length in Figure B with x. Then, we can set up a proportion to solve for x:

18 / (72 - 3 × 18) = x / (120 - 3 × x)

Here, 72 - 3 × 18 represents the sum of the other three sides in Figure A, and 120 - 3 × x represents the sum of the other three sides in Figure B.

Simplifying the left-hand side, we get:

18 / (72 - 3 × 18) = 18 / 18 = 1

Substituting this into the proportion, we get:

1 = x / (120 - 3 × x)

Multiplying both sides by (120 - 3 × x), we get:

120 - 3 × x = x

Simplifying and solving for x, we get:

4x = 120

x = 30

Therefore, the missing corresponding side length in Figure B is 30 meters.

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The triangles ABC and EDF are similar, and x = r × w/u.

As per the question, we have angle A in triangle ABC congruent to angle F in triangle EDF, angle C in triangle ABC congruent to angle D in triangle EDF, and angle B in triangle ABC congruent to angle E in triangle EDF.

Therefore, the triangles are similar by the Angle-Angle (AA) similarity theorem.

To find the expression for x, we can use the fact that the corresponding sides of similar triangles are proportional.

In this case, we have:

x/w = u/r (corresponding sides of similar triangles)

Solving for x, we get:

x = r × w/u

Therefore, x = r × w/u, and it can use this expression to solve for x in triangle ABC and EDF.

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The measure of the angle is 50.7° and the measure of its complementary angle is 39.3°.

Let x be the measure of the angle and y be the measure of its complementary angle.

Then we have:

x = y + 11.4 (since the angle measures 11.4° more than its complementary angle)

x + y = 90 (since the two angles are complementary)

Substituting the first equation into the second equation, we get:

(y + 11.4) + y = 90

2y + 11.4 = 90

2y = 78.6

y = 39.3

Substituting y = 39.3 into the first equation, we get:

x = y + 11.4 = 50.7

So, we have

x = 50.7

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Sophie will pay money equivalent to $100 for 15m at the same store.

The term "money" in mathematics refers to a form of payment, such as bills, coins, and demand deposits, that is used to purchase goods and services. Money is used to pay for the worth or price of an item or service.

A country's monetary system is referred to as its currency.

In the case of Gareth,

Money paid for 9 m of climbing [tex]=\$60[/tex]

Money paid per m of climbing [tex]=\$60\div9[/tex]

Thus, money paid by Sophie for 15 m of climbing [tex]= 15 \times (60\div9)[/tex]

[tex]\boxed{\bold{= \$100}}[/tex]

Hence Sophie will pay money equivalent to $100 for 15m at the same store.

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Answer:

$100

Step-by-step explanation:

We know that for 9m of rope, Gareth had to pay $60.

The question is asking us to find out how much Sophie will pay for 15m of rope.  To do this, we have to find out how much is paid per meter of rope.

[tex]60/9\\=6\frac{2}{3}[/tex]

For the sake of not using fractions, let's keep it as an improper fraction: 60/9

So, we can write an equation for the price of 15m of rope:

(60/9)·15

=100

So, Sophie will pay $100 for 15m of rope.

Hope this helps! :)

John needs approximately 1,814.4 mm² of tape to cover the pepper shaker. Rounded to the hundredths, the answer is 1,814.40 mm².

To calculate the amount of tape needed to cover the pepper shaker, we need to find the lateral area of the cylinder. This is given by the formula L = 2πrh, where r is the radius and h is the height.

Substituting the values given, we get L = 2π(9 mm)(32 mm) = 1,814.4 mm².

Therefore, John needs approximately 1,814.40 mm² of tape to cover the pepper shaker.

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No journal entry is required for the land since it is not depreciated.

To record depreciation expense for buildings and equipment for the year ended December 31, 2021, we need to calculate the depreciation amounts for each asset based on their respective methods.

For the building, we will use the double-declining-balance method. The annual depreciation expense is calculated as (2 / 20) x $442,000 = $44,200. Since depreciation has already been recorded for 2019 and 2020, the accumulated depreciation balance for the building as of December 31, 2020 is $83,980. Therefore, the 2021 depreciation expense for the building is $44,200 - $83,980 = $(-39,780). We record this as follows:

Building Depreciation Expense: $39,780
 Accumulated Depreciation - Building: $39,780

For the equipment, we will use the straight-line method. The annual depreciation expense is calculated as ($245,000 - $13,000) / 10 = $23,200. Since depreciation has already been recorded for 2019 and 2020, the accumulated depreciation balance for the equipment as of December 31, 2020 is $46,400. Therefore, the 2021 depreciation expense for the equipment is $23,200, and we record it as follows:

Equipment Depreciation Expense: $23,200
 Accumulated Depreciation - Equipment: $23,200

No journal entry is required for the land since it is not depreciated.
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The volume of water a cone with a diameter of 6 inches and a height of 21 inches can hold is 198 cubic inches. So, the correct answer is B) 198 cubic inches.

To find the volume of water a cone with a diameter of 6 inches and a height of 21 inches can hold, we will use the formula for the volume of a cone: V = (1/3)πr²h.

Given a diameter of 6 inches, the radius (r) is 3 inches. The height (h) is 21 inches, and we will use 3.14 as an approximation for π.

V = (1/3) * 3.14 * (3²) * 21
V = (1/3) * 3.14 * 9 * 21
V = 3.14 * 3 * 21
V = 197.82 cubic inches

Rounding to the nearest whole number, the volume of water the cone can hold is approximately 198 cubic inches. Therefore, the answer is B) 198 cubic inches.

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I would say she has to walk 17 dogs, im not sure if that's correct though

Let's assume that Lucinda needs to walk "x" more dogs to have at least $80. Then, the amount of money she will earn from walking those "x" dogs can be calculated by multiplying the number of dogs by the amount of money earned per dog, which is $3:

Amount of money earned from walking "x" dogs = $3x

To determine how many more dogs Lucinda needs to walk to have at least $80, we can write the following inequality:

$30 + $3x ≥ $80

Simplifying the inequality, we get:

$3x ≥ $50

Dividing both sides by 3, we get:

x ≥ 16.67

Since we can't walk a fraction of a dog, we need to round up to the nearest whole number. Therefore, Lucinda needs to walk at least 17 more dogs to have at least $80.

The area of the circle is approximately 202.03 square feet

If the circumference of a circle is 50.4 ft, we can use the formula for the circumference of a circle to find its radius:

C = 2πr

C = circumference

r = radius

r = C / (2π)

Substituting C = 50.4 ft, we get:

r = 50.4 / (2π)

Using a calculator, we can approximate this value to be:

r =25.2/π ft

A circle's area can be calculated using the following formula:

A = πr²

Substituting r = 25.2/π ft, we get:

A = π(25.2/π)²

= 635.04/3.14

= 202.03

Therefore, the area of the circle is approximately 202.03 square feet.

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Answer:

7776 outcomes

Step-by-step explanation:

To get the total number of outcomes we multiply the total number of possibilities for each roll. Since there are 5 rolls, the total number of outcomes will be:

6 x 6 x 6 x 6 x 6 = 7776 outcomes

The true statements are:

The initial cost for manufacturing records is $454, regardless of the number of records ordered.

In addition to the initial cost, each record costs $0.90 to manufacture.

Each record costs a total of $454.90 to manufacture.

As according to the question the function f(x)= 454+0.9x gives the cost, in dollars, of manufacturing x vinyl records.

Hence the incorrect statements are:

"The initial cost for manufacturing records depend on the quantity ordered".

"in addition to the initial cost, each record costs $454 to manufacture".

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The fire had burned half the area (2,400 acres) one week before it measured 4,800 acres.

How to evaluate Days (d) and Burned area (y), the area burned in the fire, and the area the fire has burned a week before it measured 4,800 acres?

a. To complete the table, we substitute the values of d and evaluate the expression for y.

Days (d)      Burned area (y)

0                      0

1                      23,040

2                      92,160

3                      207,360

4                         368,640

b. When d = -1, the value of y = (4,800)^(2*(-1)) = (4,800)^(-2) = 3.255e-8. This value is very small, indicating that the burned area was negligible or not measurable at this point in time.

When d = -3, the value of y = (4,800)^(2*(-3)) = (4,800)^(-6) = 1.130e-34. This value is extremely small, indicating that there was essentially no burned area at this point in time.

c. To determine the number of days before the fire measured 4,800 acres, we need to solve the equation y = (4,800)^2 for d.

4,800^2 = (4,800)^2d

1 = 2dlog(4,800)

d = log(4,800) / (2log(4,800)) = 0.5

Therefore, the fire had burned half the area (2,400 acres) one week before it measured 4,800 acres. This is because the area burned increases quadratically with time, so the area burned one week before is the square root of the area measured at the time.

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The dimensions of the square are 6 inches by 6 inches.

Let's assume that the side of the square is equal to x inches. Then, the area of the square can be expressed as x^2 square inches. The perimeter of the square is equal to 4 times the length of the side, or 4x inches.

According to the problem, the area of the square is 12 more than its perimeter, so we can write:

x^2 = 4x + 12

This is the equation we can use to find the dimensions of the square. To solve for x, we can rearrange the equation:

x^2 - 4x - 12 = 0

Then, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -4, and c = -12.

Plugging in these values, we get:

x = (-(-4) ± √((-4)^2 - 4(1)(-12))) / 2(1)

x = (4 ± √64) / 2

x = (4 ± 8) / 2

Therefore, the two possible solutions are:

x = 6 or x = -2

Since the side of a square cannot be negative, the only valid solution is x = 6.

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The volume of the oblique prism is approximately 55.424 cm³.

The volume of the cube is given as 64 cm³, which means that each side of the cube has a length of 4 cm.

To find the volume of the oblique prism, we need to know the area of the base and the height. The base of the oblique prism is a parallelogram, and we can find its area using the formula:

area = base × height

where the base is the length of one side of the parallelogram, and the height is the perpendicular distance between the base and the opposite side.

Since the parallelogram is tilted at an angle of 60°, we need to find the perpendicular height by using trigonometry. The height of the parallelogram is given by:

height = (side length) × sin(60°)

height = 4 × sin(60°)

height = 4 × 0.866 = 3.464

Therefore, the area of the base is:

area = (side length) × height

area = 4 × 3.464 = 13.856 cm²

To find the volume of the oblique prism, we multiply the area of the base by the height of the prism. Since the height of the prism is also 4 cm (the same as the side length of the cube), we have:

volume = area of base × height

volume = 13.856 × 4 = 55.424 cm³

Therefore, the volume of the oblique prism is approximately 55.424 cm³.

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The cost to manufacture 2000 headphones as the number of headphones varies inversely with the cost of manufacture is $32

Let x = number of headphones

y = cost of manufacturing headphones

The cost of manufacturing a certain type of headphones is inversely proportional to the number of headphones.

The equation for inversely proportional is

x₁ y₁ = x₂ y₂

x₁ = 8000 , y₁ = 8 , x₂ = 2000 y₂ = ?

Putting the value in the equation we get ,

8000 × 8 = 2000 × y₂

64000/2000 = y₂

y₂ = 32

Cost of manufacturing 2000 headphones is 32 .

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1.  The proportion of students at the school who write with their left hand is 2/15 OR 13.3%

2. The estimated number of students who write with their left hand is 77 students

3. The estimated number of students in the different class of 18 students who write with their left hand is 2

From the question, we are to estimate the proportion of students who write with their left hand

To estimate the proportion of students at the school who write with their left hand, we need to count the number of students in the sample who write with their left hand and divide by the total number of students in the sample.

From the given sample, there are 2 students who write with their left hand and 13 students who write with their right hand. So the estimated proportion of students who write with their left hand is:

2/15 = 0.133

OR

13.3%

2.

To estimate the number of students at the school who write with their left hand, we can multiply the proportion by the total number of students in the school

That is,

2/15 x 580 = 77.33

Thus, about 77 students write with their left hand

3.

To estimate how many students in a different class of 18 students write with their left hand, we can apply the proportion to the new sample:

2/15x 18 = 2.4

Hence, about 2 students in the different class write with their left hand.

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The value of x in the intersecting chord is determined as 18.6.

The value of x is calculated by applying intersecting chord theorem, which states that the angle at center is equal to the arc angle of the two intersecting chords.

m ∠EDF  = arc angle EF

50 = 5x - 43

The value of x is calculated as follows;

5x = 50 + 43

5x = 93

divide both sides by 5;

5x/5 = 93/5

x = 18.6

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The particular solution of the given differential equation with the initial condition f(6) = -2.

To find the particular solution of the given differential equation dy/dx = (x-3)/y with the initial condition f(6) = -2, we first need to solve the differential equation. This is a first-order separable equation, so we can rewrite it as:

y dy = (x - 3) dx

Now, integrate both sides:

∫y dy = ∫(x - 3) dx

(1/2)y^2 = (1/2)x^2 - 3x + C

Now, apply the initial condition f(6) = -2:

(1/2)(-2)^2 = (1/2)(6)^2 - 3(6) + C

(1/2)(4) = (1/2)(36) - 18 + C

2 = 18 - 18 + C

C = 2

So the particular solution is:

(1/2)y^2 = (1/2)x^2 - 3x + 2

This is the particular solution of the given differential equation with the initial condition f(6) = -2.

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To determine whether the series Σ(1) с converges or diverges, we can use the root test. The root test states that if the limit of the absolute value of the nth root of the terms of the series approaches a value less than 1, then the series converges. If the limit approaches a value greater than 1, the series diverges. If the limit equals 1, the test is inconclusive and another test should be used.

Using the root test, we have:

lim┬(n→∞)⁡〖|1^(1/n) c| = lim┬(n→∞)⁡|c| = |c|〗

If |c| < 1, then the limit approaches a value less than 1 and the series converges. If |c| > 1, then the limit approaches a value greater than 1 and the series diverges. If |c| = 1, then the test is inconclusive.

Therefore, the series Σ(1) с converges if |c| < 1, and diverges if |c| > 1. If |c| = 1, then another test should be used to determine convergence or divergence.
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