Write the equation of the line that passes through the origin and is parallel to y + 9 = -(x - 2) in standard form.

a) To derive the own-price elasticity, we start with the linear demand curve x = a - bp. The own-price elasticity of demand (e) is defined as the percentage change in quantity demanded divided by the percentage change in price. Mathematically, it is given by the formula e = (dx/dp) * (p/x), where dx/dp represents the derivative of x with respect to p.

Differentiating the demand equation with respect to p, we get dx/dp = -b. Substituting this into the elasticity formula, we have e = (-b) * (p/x).

Since x = a - bp, we can substitute this expression for x in terms of p into the elasticity formula: e = (-b) * (p / (a - bp)).

b) To find the price at which e = 0, we set the derived elasticity equation equal to zero and solve for p: (-b) * (p / (a - bp)) = 0. This equation holds true when the numerator, (-b) * p, is equal to zero. Therefore, the price at which e = 0 is when p = 0.

c) To find the price at which e = -os, we set the derived elasticity equation equal to -os and solve for p: (-b) * (p / (a - bp)) = -os. This equation holds true when the numerator, (-b) * p, is equal to -os times the denominator, (a - bp). Therefore, the price at which e = -os is when p = a / (b(1 + os)).

d) To find the price at which e = -1, we set the derived elasticity equation equal to -1 and solve for p: (-b) * (p / (a - bp)) = -1. This equation holds true when the numerator, (-b) * p, is equal to the negative denominator, -(a - bp). Therefore, the price at which e = -1 is when p = a / (2b).

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Main Answer: A normalized binary number typically consists of three parts:

Supporting Question and Answer:

What is a sign bit in a normalized binary number?

The sign bit is the leftmost bit of a normalized binary number and indicates whether the number is positive or negative .A value of 0 indicates a positive number, while a value of 1 indicates a negative number.

Body of the Solution: A normalized binary number typically consists of  the following three parts:

Final Answer: A normalized binary number typically consists of three parts:

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Rate of change of x with respect to \(\alpha\) when \(\alpha =\frac{\pi }{3}\) is 5ft/s.

Since the ladder is 10ft long resting against a vertical wall.

Let the angle between the top of the ladder and the wall is \(\alpha\) .

And let the distance from the bottom of the ladder to the wall is x.

Thus we need to find the rate of change of x with respect to \(\alpha\)  when \(\alpha =\frac{\pi }{3}\)

Consider L to be the length of the ladder.

Then, L = 10ft

Thus, we get the relation between the angle and distance x i.e.

x = L \(\sin \alpha\)

On differentiating the above equation,

\(\frac{dx}{dt} =L \cos \alpha\)

Now after putting the values \(\alpha =\frac{\pi }{3}\) in above equation, we get,

\(=(10)\cos(\frac{\pi }{3} )=(10)(\frac{1}{2} )=5\)

Therefore, \(\frac{dx}{dt} =5\) ft/s

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Answer:

number 2 is c, number 3 is c

To simplify the expression COS X - cos x sin2x, we can use the trigonometric identity COS(A-B) = COS A COS B + SIN A SIN B.

Applying this identity, we get COS X - cos x sin2x = COS X - COS X SIN X COS X, Factoring out COS X, we get COS X (1 - SIN X), Therefore, the simplified expression is COS X (1 - SIN X), However, none of the given options match this expression. The closest option is sec²x, but this is not equivalent to COS X (1 - SIN X).
To simplify the expression cos(x) - cos(x)sin^2(x), we can factor out the common term cos(x): cos(x)(1 - sin^2(x)).

Now, recall the Pythagorean identity sin^2(x) + cos^2(x) = 1. We can rearrange it to find: 1 - sin^2(x) = cos^2(x), Substitute this into our expression: cos(x)(cos^2(x)), This is the simplified form of the given expression.

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It will take 2 hours 24 minutes time to two trains to meet.

Let a train starts from A towards to B with velocity v1 = 90 miles/hour

and another train starts it's journey from B towars A with velocity               v2 = 110 miles/hour

Let after  time t hour they meet at C.

Hence, we get  AC + CB = AB

                    ⇒  v1t + v2t = 480

                    ⇒ (v1 + v2) t = 480

                    ⇒ (90 + 110) t = 480

                    ⇒ t = 480/200 = 48/20 = 12/5 hours

                     ∴ t = \(2\frac{2}{5}\) hours

                          = 2 hour (2/5 × 60) mins

                    ∴ t  = 2 hours 24 minutes time

So, after 2 hours 24 minutes time they meet each otherv at C, where                 AC = v1t  = 90 × 12/5 = 216 miles.

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According to the graph the value of the Dog Walking Service would be $0.75 per minute.

To know the value per minute of the Dog Walking Service offered by Linda we must carry out the following mathematical procedure:

If every 20 minutes is worth $15, how much is each minute worth?

To do this we must follow the following rule of three:

Additionally, we must take into account that according to the graph, the value per minute decreases if we contract more hours of service. For example, with 40 minutes of service it would be worth 0.5 each minute.

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Answer:

No

Step-by-step explanation:

Distributing the 1st expression, we get 3j + 4.

Distributing the 2nd expression, we get 3j + 2.

3j + 4 does not equal 3j + 2

Answer:

120 cm

Step-by-step explanation:

To solve this problem, we can use the equation:

(length of arc) / (circumference of circle) = (degrees in arc) / (degrees in circle)

In this equation, we only have one unknown, circumference of circle. So, if we plug in the values we do know, we can find the circumference of circle C.

(length of arc) / (circumference of circle) = (degrees in arc) / (degrees in circle)

length of arc = 10

circumference of circle = x

degrees in arc = 30°

degrees in circle ALWAYS equals 360°

\(\frac{10}{x}=\frac{30}{360} \\\)

30x = 3600

x = 120

So, the circumference of the circle is 120 cm.

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9514 1404 393

Answer:

  more than half are being used

Step-by-step explanation:

Perhaps easiest to understand is the most straightforward: figure the total number of seats and the number of seats being used. Check to see if that is more than half.

The 1 first-class carriage has usage of ...

  (3/8)(64 seats) = 24 seats.

The 6 standard carriages have usage of ...

  (7/13)(6 · 78 seats) = 252 seats.

The total number of seats used is ...

  24 + 252 = 276 . . . . seats used

__

The total number of seats on the train is ...

  1·64 +6·78 = 532 . . . . seats on the train

Half of the seats on the train will be ...

  532/2 = 266 seats . . . . half the seats

The 276 used seats are more than half of the total number. More than half the seats are being used.

_____

Alternate solution

Another way to look at this is to compare utilization to 1/2 in each carriage class.

  In first class 1/2 -3/8 = 1/8 of 64 seats = 8 seats fewer than 1/2 the seats are being used.

  In standard class, 7/13 -1/2 = 14/26 -13/26 = 1/26 of 78 seats = 3 seats more than 1/2 the seats are being used. There are 6 standard class carriages, so 6·3 = 18 more than half the seats in the standard-class carriages are being used.

This number is 10 more than the 8 under-utilized seats in first class, so more than half the train seats are being used.

K2/3 = 12Hence, K = (12)3/2 = 20.784 Profit maximizing value of K is 20.784.

Given the production function, (K, L) = 12K1/3L1/2 - 4K – 1, where K > 0,1 ≤ 20, L = π. We need to find the profit-maximizing level of K.

Profit maximization occurs where Marginal Revenue Product (MRP) is equal to the Marginal Factor Cost (MFC).To determine the optimal value of K, we will derive the expressions for MRP and MFC.

Marginal Revenue Product (MRP) is the additional revenue generated by employing an additional unit of input (labor) holding all other factors constant. MRP = ∂Q/∂L * MR where, ∂Q/∂L is the marginal physical product of labor (MPPL)MR is the marginal revenue earned from the sale of output.

MRP = (∂/∂L) (12K1/3L1/2) * MRLMPPL = 6K1/3L-1/2MR = P = 10Therefore, MRP = 6K1/3L1/2 * 10 = 60K1/3L1/2The Marginal Factor Cost (MFC) is the additional cost incurred due to the use of one additional unit of the input (labor) holding all other factors constant.

MFC = Wages = 5 Profit maximization occurs where MRP = MFC.60K1/3L1/2 = 5K1/3Multiplying both sides by K-1/3L-1/2, we get;60 = 5K2/3L-1Therefore,K2/3 = 12Hence, K = (12)3/2 = 20.784Profit maximizing value of K is 20.784.

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In the analysis of variance procedure (ANOVA), "factor" refers to the independent variable(b).

In the analysis of variance procedure (ANOVA), "factor" refers to the independent variable. ANOVA is used to determine if there is a significant difference between the means of two or more groups, and the factor is the variable being studied that is believed to have an effect on the outcome. Variance is a measure of the variability or spread of the data, and ANOVA compares the variance between groups to the variance within groups to determine if there is a significant difference. The different levels of a treatment are also referred to as levels of the factor.

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The percentage change when a price of 200 is increased to 210.99 is 5.495%.

A percentage is a relative number that represents a hundred parts of any quantity.

The initial price is 200.

And the final price is 210.99.

The formula for the percentage change is,

Percentage change = [(Final value - Initial value)/Intitial value] * 100

Putting the given values in the above formula, we get

= [(210.99 - 200)/200] * 100

= [10.99/200] * 100

= 0.05495 * 100

= 5.495

Hence, the percentage change when a price of 200 is increased to 210.99 is 5.495%.

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1.) true

2.) false

3.) false

4.) true

5.) true

6.) False

7.) true

8.) false

Answer:

1. True

2. False

3. False

4. True

5. True

6. False

7. True

8. False

The product of (4z² + 7z – 8) and (–z + 3) is -4z³ + 5z² + 29z - 24

(4z² + 7z – 8) and (–z + 3)

= -4z³+ 12z² - 7z² + 21z + 8z - 24

= -4z³ + 5z² + 29z - 24

Therefore, the product of (4z² + 7z – 8) and (–z + 3) is -4z³ + 5z² + 29z - 24

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Answer:

f(-3)=10

Explanation:

Given the function:

When x = -3

To find the surface area of an object, we need to calculate the area of all its faces and add them up.

Assuming that "W" stands for the width, "l" for the length, and "h" for the height, the surface area of the object would be:

Area of the bottom face = length x width = 17' x 21' = 357 square feet

Area of the top face = same as the bottom face = 357 square feet

Area of the front and back faces = height x width = 19' x 17' = 323 square feet (each)

Area of the left and right faces = height x length = 19' x 21' = 399 square feet (each)

Therefore, the total surface area of the object would be:

357 + 357 + 323 + 323 + 399 + 399 = 2158 square feet.

So, the surface area of the object is 2158 square feet.

The speeds for each of the given distance and times are;

A) 45 miles per hr

B) 22 miles per hr

C) 30 miles per hr

D) 50 miles per hr

E) 65 miles per hr

To convert the given values of distance and time to speed in miles per hour, we will just divide the time by the distance. Speed = distance/time

A) 135 miles in 3 hours. Thus;

Speed = 135/3 miles per hour = 45 miles per hr

B) 22 miles in 1 hour. Thus;

Speed = 22/1 miles per hr = 22 miles per hr

C) 7.5 miles in 1/4 hour. Thus;

Speed = 7.5/(1/4) miles per hour = 30 miles per hr

D) 100/3 in 2/3 hour. Thus;

Speed = (100/3 ÷ 2/3) = 50 mph

E) 97.5 in 1.5 hours. Thus;

Speed = 65 miles per hr

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The statement "If dy/dt=f(t)g(y), the equilibrium solutions can be obtained by finding the solutions to f(t)=0" is not entirely correct.

In a differential equation of the form dy/dt = f(t)g(y), the equilibrium solutions are the constant solutions where dy/dt = 0. These occur when g(y) = 0.

To find the equilibrium solutions, we need to solve g(y) = 0. Once we have found these solutions, we can determine their stability by analyzing the sign of f(t) near these equilibrium values. If f(t) is positive near an equilibrium value, the solution is unstable (i.e., solutions near the equilibrium will move away from it). If f(t) is negative near an equilibrium value, the solution is stable (i.e., solutions near the equilibrium will move towards it).

So, while f(t) = 0 may be useful in some cases for finding equilibrium values, it is not the correct approach for finding all equilibrium solutions in a differential equation of the form dy/dt = f(t)g(y). The equilibrium solutions are found by solving g(y) = 0.

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Answer:

\(\huge\boxed{ f^{-1}(x) = \sqrt[3]{-x-9}}\)

Step-by-step explanation:

\(f(x) = -x^3-9\)

Put f(x) = y

\(y = -x^3-9\)

Interchange x and y

\(x = -y^3-9\)

Solve for y

\(x = -y^3-9\)

Add 9 to both sides

\(-y^3 = x+9\)

Divide both sides by -1

\(y^3 = -x-9\)

Take cube root to both sides

\(y = \sqrt[3]{-x-9}\)

Put \(y = f^{-1}(x)\)

\(\boxed{f^{-1}(x) = \sqrt[3]{-x-9}}\)

\(\rule[225]{225}{2}\)

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The inverse function of the given function is  \(f^{-1} (x)\)=∛-x-9.

The given function is f(x)=-x³-9.

To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.

Now, replace f(x)=y.

y=-x³-9

Interchange the variables.

That is, x=-y³-9

Solve for y.

That is, y³=-x-9

⇒y=∛-x-9

Solve for y and replace with \(f^{-1} (x)\).

\(f^{-1} (x)\)=∛-x-9.

Therefore, the inverse function of the given function is  \(f^{-1} (x)\)=∛-x-9.

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Answer:

B. (x-5)²+(y+1)² = 49

Step-by-step explanation:

An equation of a circle with center (h, k) and radius r is

\( \large \boxed{ {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} }\)

We have all given information we need. Our h is 5 - Our k is -1 and our radius is 7

Substitute these values in

\( \large{ {(x - 5)}^{2} + {(y - ( - 1))}^{2} = {7}^{2} } \\ \large{ {(x - 5)}^{2} + {(y + 1)}^{2} = {7}^{2} } \\ \large{ {(x - 5)}^{2} + {(y + 1)}^{2} = 49 }\)

So the answer is B choice.

Answer:

I would use a timeline to illustrate the following: Comparing the events of a story to what was going on in the world at the time the story was written.

A timeline is a graphic organizer that shows the order in which events happened. It can be used to compare events in a story to events in the real world.
To create a timeline, you will need to identify the events that happened in the story and the events that happened in the real world. You can then arrange the events in chronological order. You can also add additional information to the timeline, such as the dates of the events and the people who were involved.

Here is an example of a timeline that compares the events of the story "The Great Gatsby" to the events that were happening in the world at the time the story was written:

The Great Gatsby

The World in 1922

Summary:
A timeline can be a helpful tool for understanding the historical context of a story. By comparing the events of a story to the events that were happening in the world at the time the story was written, you can gain a deeper understanding of the story's meaning and significance.

Answer:

I would use a timeline to illustrate the following: Comparing the events of a story to what was going on in the world at the time the story was written.

A timeline is a graphic organizer that shows the order in which events happened. It can be used to compare events in a story to events in the real world.

To create a timeline, you will need to identify the events that happened in the story and the events that happened in the real world. You can then arrange the events in chronological order. You can also add additional information to the timeline, such as the dates of the events and the people who were involved.

Here is an example of a timeline that compares the events of the story "The Great Gatsby" to the events that were happening in the world at the time the story was written:

The Great Gatsby

1922: The story takes place.

1920: The Eighteenth Amendment to the United States Constitution is ratified, prohibiting the manufacture, sale, and transportation of alcoholic beverages.

1929: The stock market crashed, leading to the Great Depression.

The World in 1922

The Roaring Twenties: A Period of economic prosperity and cultural change in the United States.

The Jazz Age: A period of artistic and cultural innovation, characterized by the rise of jazz music and dance.

The Lost Generation: A group of American writers and artists who lived in Europe during the 1920s.

A timeline can be a helpful tool for understanding the historical context of a story. By comparing the events of a story to the events that were happening in the world at the time the story was written, you can gain a deeper understanding of the story's meaning and significance.

Step-by-step explanation:

Answer:

1/2= 5/10

5/10 - 3/10 = 2/10 or 1/5

so planet X is 1/5 of a light-year closer

Step-by-step explanation:

Answer:

5/10

Step-by-step explanation:

Simplified

The histogram depicts that the number shipments that had more than 20 light bulbs broken is D. 12.

A histogram simply means a graphical representation that is used to organize a group of data points into ranges.

From the complete question, the histogram shows that the number shipments that had more than 20 light bulbs broken is 12. This can be interpreted based on the ranges shown in the histogram.

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The resultant force would be the vector sum of 5 N and 3 N in the same direction. The resultant force is 8 N in the direction of Jan. The correct option is D) 8 N in all directions.

To calculate the resultant velocity of the plane, we need to consider the vector sum of the plane's velocity and the tailwind velocity.

A) If the plane is traveling at 100 km/h North with a 5 km/h tailwind, the resultant velocity would be the vector sum of 100 km/h North and 5 km/h tailwind in the same direction. Therefore, the resultant velocity is 105 km/h North.

B) If the plane is traveling at 95 km/h North with a 5 km/h tailwind, the resultant velocity would be the vector sum of 95 km/h North and 5 km/h tailwind in the same direction. Therefore, the resultant velocity is 100 km/h North.

C) If the plane is traveling at 95 km/h South with a 5 km/h tailwind, the resultant velocity would be the vector sum of 95 km/h South and 5 km/h tailwind in opposite directions. Therefore, the resultant velocity is 90 km/h South.

D) If the plane is traveling at 100 km/h North with a 5 km/h tailwind, the resultant velocity would be the vector sum of 100 km/h North and 5 km/h tailwind in the same direction. Therefore, the resultant velocity is 105 km/h North.

Regarding the tug of war scenario:

The resultant force during a tug of war is the vector sum of the forces exerted by Jan and Margret.

If Jan pulls with a force of 5 N and Margret pulls with a force of 3 N:

The resultant force would be the vector sum of 5 N and 3 N in the same direction. Therefore, the resultant force is 8 N in the direction of Jan.

Hence, the answer is D) 8 N in all directions.

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The domain for the function in this problem is given as follows:

0 ≤ x ≤ 5.

The domain of the function in this problem is the number of hours, which is represented by numbers between 0 and 5, as the hours cannot be negative and they played for 5 hours, hence the interval is given as follows:

0 ≤ x ≤ 5.

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The number of men living in the village is 260.

A collection of many linear equations that include the same variables is referred to as a system of linear equations. A linear equation system is often composed of two or more linear equations with two or more variables.A linear equation with two variables, x and y, has the following general form:

                                           \(ax + by = c\)

Given:

Total inhabitants in the village: 817

Number of children: 241

There are 56 more women than men in the village

Total adults = Total inhabitants - Number of children

Total adults = 817 - 241

Total adults = 576

Let number of men in the village be 'x' and number of women in the village be 'y',

∴ y=x+56 (given) ..................(1)

Also, x+y=576 .................(2)

From equation (1) and (2),

x + (x + 56) = 576

2x + 56 = 576

2x = 576 - 56

2x = 520

x = 520 / 2

x = 260

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Answer:

Age of Kim's sister is 12 and that of kim is 24.

Step-by-step explanation: