E’(-18,-4),f’(-18,-10),g’(12,-10) center: (-6,-4), k=3/4Find the original coordinates

Marcus has 3 sticks of butter which he plans to equally split between 4 recipes. The fraction that represents the amount of butter in each recipe is obtained as follows:Firstly, we find the total amount of butter. 3 sticks of butter mean 3/1 sticks of butter.3/1 sticks of butter is equal to 12/4 sticks of butter.

(by multiplying both the numerator and denominator by 4)Thus, there are 12/4 sticks of butter to split between the 4 recipes. To find the amount of butter in each recipe, we divide the total amount of butter by the number of recipes. Amount of butter in each recipe = Total amount of butter / Number of recipes= (12/4) / 4= 12/4 × 1/4= 3/4Therefore, Marcus will use 3/4 of a stick of butter in each recipe.We have used 99 words in answering this question.

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the clown would need to buy 138 packs of balloons to have a total of 275 balloons for the party.

IfIf the balloons only come in packs of 2, we need to determine how many packs the clown would need to buy in order to have a total of 275 balloons.

To find the number of packs needed, we divide the total number of balloons (275) by the number of balloons in each pack (2).

275 balloons ÷ 2 balloons per pack = 137.5 packs

Since we cannot have a fraction of a pack, we round up to the nearest whole number.

Therefore, the clown would need to buy 138 packs of balloons to have a total of 275 balloons for the party.

Note: Rounding up to the nearest whole number ensures that the clown has enough balloons and avoids having a fractional number of packs.

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additional information to prove that the two triangles have all three corresponding sides and angles congruent. Hence option d is correct.

When we sa that two triangles are congruent, it means that they have all three pairs of corresponding sides and angles that are congruent

t. So, in order to know that the triangles are congruent using the SAS (Side-Angle-Side) method, we need to have additional information to prove that the two triangles have all three corresponding sides and angles congruent.

Option a): OP = OV. This is not sufficient to show congruence between the triangles using the SAS method. The given reason does not provide any angle information.

Option b): RO = TO or OP = OV. This is also not sufficient to show congruence using the SAS method. The given reason provides only two corresponding sides and no angle information.

Option c): RO = TO. This is not sufficient to show congruence using the SAS method. The given reason provides only one pair of corresponding sides and no angle information.

Option d): Angle R = Angle T. This is sufficient to show congruence using the SAS method. This given reason provides one pair of corresponding sides and an included angle that is congruent in both triangles. Thus, the two triangles have two pairs of congruent sides and a congruent angle between them, which satisfies the SAS condition.

From the above analysis, we can conclude that option (d) is the correct answer. To know whether two triangles are congruent using the SAS method, we need to have additional information to prove that the two triangles have all three corresponding sides and angles congruent

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the lengths of the three sides of the triangle are approximately:

Side one: 4.875 units

Side two: 19.5 units

Side three: 14.625 units

Let's denote the lengths of the sides of the triangle as follows:

Side one: x

Side two: 4x (since it is four times the length of side one)

Side three: 3x (since it is three times the length of side one)

The perimeter of a triangle is the sum of the lengths of all three sides. In this case, the perimeter is given as 39 units. We can set up an equation to solve for x:

x + 4x + 3x = 39

Combining like terms:

8x = 39

Dividing both sides by 8:

x = 39/8

Simplifying the fraction:

x = 4.875

Now, we can find the lengths of all three sides by substituting this value of x back into our expressions for each side:

Side one: x = 4.875 units

Side two: 4x = 4.875 * 4 = 19.5 units

Side three: 3x = 4.875 * 3 = 14.625 units

Therefore, the lengths of the three sides of the triangle are approximately:

Side one: 4.875 units

Side two: 19.5 units

Side three: 14.625 units

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A sample of n = 5 scores has a mean of M = 12. If one person with a score of X = 18 is added to the sample, the new mean, can be calculated as 14.

The initial sample of n = 5 scores has a mean of M = 12. To find the new mean after adding a score of X = 18 to the sample, we can use the formula for the mean: M = (sum of scores) / (number of scores).

The sum of the original scores is 5 * 12 = 60. When we add the score of 18, the new sum becomes 60 + 18 = 78. Since the total number of scores is now 6, the new mean is calculated as 78 / 6 = 13.

Therefore, the new mean after adding a score of 18 to the sample is 14.

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The correct answer is option (b) 15.125 ft², representing the amount of material required for the patch.

The amount of material required for the patch, which is in the shape of the region defined by the equation y = (1/2)x^3, can be determined by calculating the area under the curve.

The patch's shape is defined by the equation y = (1/2)x^3. To find the area under the curve, we need to integrate the equation with respect to x over the appropriate interval. In this case, we are not given specific limits of integration, so we assume the interval is from x = 0 to x = 3 (based on the curve's shape shown in the equation).

The integral for finding the area under the curve is: A = ∫[0 to 3] (1/2)x^3 dx.

Evaluating the integral, we get: A = [(1/2) * (1/4)x^4] evaluated from 0 to 3.

Plugging in the limits, we have: A = (1/2) * (1/4) * (3^4 - 0^4) = (1/2) * (1/4) * (81 - 0) = (1/2) * (1/4) * 81 = 15.125 ft².

Therefore, the correct answer is option (b) 15.125 ft², representing the amount of material required for the patch.

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For a triangle with base= 2 cm and perimeter= 10 cm, total area of the plastic triangles on the spinner is=18 square centimeters or 18 cm²

Let us assume that the two sides that are not the base of the triangle are x each.

Therefore, the perimeter of the triangle is: x + x + 2

Now,

     2x + 2 = 10 cm

=> x = 4 cm

Thus, we have a right triangle with sides 2 cm, 4 cm, and a hypotenuse of =√(2^2 + 4^2)

                                                                                                                             = √20

                                                                                                                             = 2√5.

The area of a triangle is= 1/2×(base)×(height).

For the plastic triangles, the base is 2 cm and the height is 2√5. Therefore, the area is given by:

=1/2(2)(2√5)

= 2√5 square centimeters.

The spinner has four plastic triangles, so the total area is:

=4(2√5)

= 8√5 square centimeters.

Now, we need to get an approximate value for the area using a calculator or by estimating √5 as 2.24:

8(2.24) ≈ 17.92 square centimeters, which is closest to 18.

Therefore, the answer is: 18 square centimeters or 18 cm².

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The domain and the range of the function in this problem are given as follows:

The function is defined for all real values except x = 3, which is the vertical asymptote, and assumes negative values, hence:

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To dilate the points H(-1, -1), A(1, 0), and T(-1, 2) by a scale factor of 2 from the point (-1, 2), So the answer is: the dilated points are H(-3, 3), A(-1, 4), and T(-3, 6) when dilated by a scale factor of 2 from the point (-1, 2).

The following steps are:

1. Calculate the translation vector from (-1, 2) to the origin (0, 0). Subtract the coordinates of the origin from the coordinates of the point (-1, 2):

Translation vector = (-1 - 0, 2 - 0) = (-1, 2).

2. Apply the dilation to each point using the scale factor of 2. Multiply the translation vector by the scale factor:

Dilation vector = Scale factor * Translation vector

= 2 * (-1, 2)

= (-2, 4).

3. Translate the points back to their original position by adding the dilation vector to each point:

Dilated point H: (-1, -1) + (-2, 4) = (-3, 3)

Dilated point A: (1, 0) + (-2, 4) = (-1, 4)

Dilated point T: (-1, 2) + (-2, 4) = (-3, 6)

So, the dilated points are H(-3, 3), A(-1, 4), and T(-3, 6) when dilated by a scale factor of 2 from the point (-1, 2).

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According to the Bible, Nehemiah left Hanani, along with Hananiah the commander of the citadel, in charge of Jerusalem while he traveled. This is mentioned in Nehemiah 7:2, which states:

"Then I put Hanani my brother and Hananiah the commander of the citadel in charge of Jerusalem, for he was a faithful man and feared God more than many."

Nehemiah, a cupbearer to the Persian king Jerusalem, was granted permission to return to Jerusalem to rebuild its walls. During his absence, he entrusted the responsibility of overseeing Jerusalem to Hanani and Hananiah. Hanani is described as Nehemiah's brother and Hananiah as the commander of the citadel, indicating their positions of authority and trustworthiness.

Nehemiah's decision to leave Hanani and Hananiah in charge highlights his confidence in their faithfulness and fear of God, indicating that he believed they would fulfill their duties responsibly during his absence.

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The cost of the apples is 4 euros per kilo and the cost of the bananas is 6 euros per kilo.

We know that Juan has apples that cost 4 euros per kilo, and Fran has banans that cost 2 more euros than tha apples.

Then if the cost of the apples is A, and the cost of the bananas is B, we can write the linear equation:

B = A + 2

We know that A = 4, replacing that we will get:

B = 4 + 2

B = 6

The bananas cost 6 euros per kilo.

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In "Highest Duty: My Search for What Really Matters," Captain Sully's childhood is described as characterized by curiosity, discipline, and a sense of responsibility.

Evidence from the text reveals that he displayed a keen interest in aviation from a young age, built model airplanes, and read aviation books. Moreover, his father's military background instilled discipline and taught him the importance of responsibility. These traits shaped his character and laid the foundation for his future career as a pilot.

The book "Highest Duty: My Search for What Really Matters" provides insights into Captain Sully's childhood and highlights certain aspects of his character. One key inference is his curiosity and passion for aviation. The text mentions that as a child, Sully built model airplanes, spent time at the library studying aviation books, and even constructed a small airfield in his backyard. These activities indicate his early fascination with flying and his drive to learn more about the subject.

Additionally, the influence of Sully's father is evident in his upbringing. His father, a military officer, instilled discipline in his son, emphasizing the importance of adhering to rules and regulations. This upbringing likely contributed to Sully's disciplined approach to his work as a pilot and his commitment to following procedures meticulously.

Furthermore, Sully's sense of responsibility is evident throughout the book. As a child, he took on responsibilities such as taking care of his younger siblings and helping his mother. This early sense of responsibility laid the groundwork for his future career, where he would be entrusted with the lives of passengers and crew members.

In conclusion, Captain Sully's childhood can be described as marked by curiosity, discipline, and a strong sense of responsibility. His passion for aviation, disciplined upbringing, and early sense of responsibility shaped his character and played a significant role in his successful career as a pilot.

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The sum of (x - 8x^2 - 15) and (2 + 12x - 3x^2) is represented by the expression -11x^2 + 13x - 13.

To find the sum of the two given expressions, we add the corresponding terms together.

The given expressions are:

(x - 8x^2 - 15) and (2 + 12x - 3x^2)

When we combine like terms, we get:

x + 2 - 8x^2 + 12x - 3x^2 - 15

Simplifying further, we combine the terms with the same power of x:

(-8x^2 - 3x^2) + (x + 12x) + (2 - 15)

This simplifies to:

-11x^2 + 13x - 13

Therefore, the sum of the two expressions is represented by the expression -11x^2 + 13x - 13.

Understanding how to combine like terms and simplify expressions allows us to find the sum of given expressions. By adding the corresponding terms and simplifying, we arrive at the final expression that represents the sum.

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The function f(z) = (z + 10)^2 is differentiable everywhere because it satisfies the Cauchy-Riemann equations, which are necessary conditions for complex differentiability. The partial derivatives of f with respect to x and y exist and are continuous, ensuring differentiability.

The function f(z) = (z + 10)^2 is differentiable everywhere, we need to verify that it satisfies the Cauchy-Riemann equations. The Cauchy-Riemann equations state that for a complex function f(z) = u(x, y) + iv(x, y), where u and v are real-valued functions of two real variables x and y, the following conditions must hold:

1. ∂u/∂x = ∂v/∂y (the partial derivative of u with respect to x is equal to the partial derivative of v with respect to y).

2. ∂u/∂y = -∂v/∂x (the partial derivative of u with respect to y is equal to the negative partial derivative of v with respect to x).

Let's evaluate these partial derivatives for the given function f(z) = (z + 10)^2:

First, we express z as z = x + iy, where x and y are real numbers. Then, we have:

f(z) = (x + iy + 10)^2 = (x + 10 + iy)^2 = (x + 10)^2 + 2i(x + 10)y - y^2.

Now, we can identify u(x, y) and v(x, y) as:

u(x, y) = (x + 10)^2 - y^2,

v(x, y) = 2(x + 10)y.

Taking the partial derivatives, we have:

∂u/∂x = 2(x + 10),

∂u/∂y = -2y,

∂v/∂x = 2y,

∂v/∂y = 2(x + 10).

We can observe that ∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x, which satisfy the Cauchy-Riemann equations. Since the partial derivatives exist and are continuous for all x and y, we can conclude that f(z) = (z + 10)^2 is differentiable everywhere.

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The magnitude of an earthquake with an energy release of 7.079 × 10^26 is approximately 8.

To find the magnitude (M) of an earthquake with an energy release of 7.079 × 10^26, we can substitute this value into the given equation:

M = (2/3)log(E) - 9.9

where E is the amount of energy released.

Substituting E = 7.079 × 10^26 into the equation:

M = (2/3)log(7.079 × 10^26) - 9.9

Now, let's calculate the magnitude:

M = (2/3)log(7.079) + (2/3)log(10^26) - 9.9

Using the properties of logarithms:

M = (2/3)log(7.079) + (2/3)(26) - 9.9

M = (2/3)log(7.079) + 17.33 - 9.9

M = (2/3)log(7.079) + 7.43

Now, we can evaluate the logarithm:

M = (2/3)(0.850) + 7.43

M = 0.567 + 7.43

M ≈ 7.997

Rounding to the nearest whole number, the magnitude of the earthquake is 8.

Therefore, the magnitude of an earthquake with an energy release of 7.079 × 10^26 is approximately 8.

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The area of the polygon JKLMNP, representing the bus route, is 6400 square miles based on the given scale of 16 square miles per grid square.

In the given information, the polygon JKLMNP represents a bus route with specific vertices, and each grid square represents 16 square miles.

The vertices of the polygon are given as:

J (2, 4)

K (2, 7)

L (7, 7)

M (7, 2)

N (5, 2)

P (5, 4)

To determine the area of the polygon in terms of square miles, we need to calculate the area of the shape enclosed by the given vertices.

The distance between the vertices on the x-axis represents the width of the polygon, and the distance between the vertices on the y-axis represents the height.

Calculating the width:

KJ = 7 - 2 = 5 units

Calculating the height:

ML = 7 - 2 = 5 units

To convert these units to miles, we multiply by the given scale of 16 square miles per grid square:

Width = 5 * 16 = 80 square miles

Height = 5 * 16 = 80 square miles

Finally, to find the area of the polygon, we multiply the width by the height:

Area = Width * Height = 80 * 80 = 6400 square miles

Therefore, the area of the polygon JKLMNP, representing the bus route, is 6400 square miles based on the given scale of 16 square miles per grid square.

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The net (total) change to the money supply is $40 million for money supply.

In this case, the net change in the money supply can be found by using the formula:[tex]M = (1/MPC) * ∆Y[/tex]where:M is the money supply

The total amount of money in an economy at any particular time is referred to as the money supply. It includes many different types of money, including tangible forms like coins and banknotes and wider concepts like demand deposits in banks. Due to its impact on inflation, interest rates, and general economic activity, the money supply is a key economic statistic.

Through monetary policy instruments including open market operations and reserve requirements, central banks play a significant role in controlling the money supply. Policymakers seek to maintain price stability and advance sustainable economic growth by regulating the money supply. Understanding and predicting economic developments requires constant monitoring and analysis of the money supply

MPC is the marginal propensity to consume (given as 0.8)∆Y is the change in income, which can be calculated as follows:∆Y = ∆G - ∆TT

Where:∆G is the change in government spending, given as $20 million- ∆TT is the change in taxes, given as -$12 million

Substituting the values given in the formula, we get:M = (1/0.8) * [20 - (-12)]M = 1.25 * 32M = 40

The net (total) change to the money supply is $40 million.

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To find the probability of selecting Monopoly as the first gift and Scrabble as the second gift without replacement, we need to consider the total number of board games and the number of favorable outcomes. Hence, the probability that the first gift chosen is Monopoly and the second gift is Scrabble is 1/90.

Let's assume there are 10 different board games in the pile. The first person chooses a gift, and since they want to select Monopoly, there is 1 favorable outcome out of the 10 board games. After the first gift is chosen, there are now 9 board games remaining, with 1 of them being Scrabble, which is the desired outcome for the second gift.

The probability of the first gift being Monopoly and the second gift being Scrabble without replacement can be calculated as the product of the probabilities of each event. The probability of choosing Monopoly as the first gift is 1/10, and the probability of choosing Scrabble as the second gift is 1/9.

Therefore, the overall probability can be calculated as (1/10) * (1/9) = 1/90.

Hence, the probability that the first gift chosen is Monopoly and the second gift is Scrabble is 1/90.

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The answer is option A: $8.To find the cost of one 5-inch-by-7-inch picture, we need to solve the system of equations:

Equation 1: 3x + 2y = 52

Equation 2: 2x + 2y = 40

We can solve this system of equations using various methods, such as substitution or elimination. Let's use the elimination method:

Multiply Equation 2 by -1 to create opposite coefficients for y:

-1(2x + 2y) = -1(40)

-2x - 2y = -40

Now, we can add Equation 1 and Equation 2 together:

(3x + 2y) + (-2x - 2y) = 52 + (-40)

x + 0y = 12

x = 12

Substitute the value of x into Equation 1:

3(12) + 2y = 52

36 + 2y = 52

2y = 52 - 36

2y = 16

y = 8

Therefore, the cost of one 5-inch-by-7-inch picture is $8.

So, the answer is option A: $8.

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A parallelogram is a quadrilateral where both pairs of opposite sides are parallel. Therefore, we will consider if the opposite sides are parallel or not.In order to determine if A(-2,3) B(2,2), C(10,5), D(6,7) is a parallelogram or not, we can follow the given steps:

Step 1: First, we will calculate the slope of AB and CD to check if they are equal or not.Slope of AB = (y2-y1)/(x2-x1)= (2-3)/(2-(-2))= -1/4Slope of CD= (y2-y1)/(x2-x1)= (7-5)/(6-10)= 2/-4= -1/2

Therefore, AB and CD have different slopes. They are not parallel.Step 2: Now, we will calculate the slope of BC and AD to check if they are equal or not.Slope of BC= (y2-y1)/(x2-x1)= (5-2)/(10-2)= 3/4Slope of AD= (y2-y1)/(x2-x1)= (7-3)/(6-(-2))= 4/2= 2As AD and BC have different slopes.

They are not parallel.Therefore, the given coordinates of A(-2,3) B(2,2), C(10,5), D(6,7) do not form a parallelogram. We can conclude that A(-2,3) B(2,2), C(10,5), D(6,7) is not a parallelogram.Hopefully, this answer helps you.

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The acceleration due to gravity is typically denoted as -32.2 ft/sec^2, as it acts in the opposite direction of the rocket's upward motion.

The given function "14001" seems to be incomplete or incorrect, as it does not properly represent the height of the rocket in feet, 2 seconds after the rocket is launched. However, I can provide you with a general explanation of how the rocket's height can be modeled using the given information.

To model the height of the rocket in feet, 2 seconds after launch, we need to consider its initial velocity and starting height.

The rocket's initial velocity is given as 275 ft/sec, which represents the rate at which it is ascending. This velocity will affect the rocket's upward motion.

Additionally, the rocket starts at a height of 3 feet above the ground.

To determine the rocket's height after 2 seconds, we need to take into account the initial velocity, the effect of gravity, and the time elapsed.

Without a specific function or equation, we cannot provide an exact answer. However, in general, we can use the formula for vertical displacement under constant acceleration:

Height = Initial height + (Initial velocity * time) + (0.5 * acceleration * time^2)

Given that the rocket starts at a height of 3 feet and the time is 2 seconds, we can calculate the height of the rocket using the appropriate values of acceleration and initial velocity.

It's important to note that the acceleration due to gravity is typically denoted as -32.2 ft/sec^2, as it acts in the opposite direction of the rocket's upward motion.

Using the formula mentioned above and the provided values, we can determine the height of the rocket 2 seconds after launch. However, without a valid function or additional information, we cannot provide a specific value for the rocket's height.

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To calculate the trimmed mean for each sample by deleting the smallest and largest observation, we remove the extreme values and find the mean of the remaining data. The corresponding trimming percentage is the percentage of observations excluded from the calculation.

The trimmed mean is a way to reduce the influence of outliers or extreme values in a data set by excluding them from the calculation. By deleting the smallest and largest observations, we remove the outliers and focus on the central tendency of the data.

To find the trimming percentage, we need to determine the number of observations excluded relative to the total number of observations in the sample. Suppose the sample has "n" observations.

When we remove the smallest and largest values, we eliminate 2 observations. Therefore, the trimming percentage can be calculated as (2 / n) * 100.

For example, if the sample has 10 observations, the trimming percentage would be (2 / 10) * 100 = 20%. This means that the smallest and largest values are excluded, representing a trimming of 20% of the data.

In summary, the trimmed mean is calculated by removing the smallest and largest observations and finding the mean of the remaining values. The corresponding trimming percentage is determined by dividing the number of observations excluded by the total number of observations in the sample and multiplying by 100.

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The desired revenue for the buffet can be represented by the inequality (P + x) * C ≥ R, where P is the initial price, x represents $1 increases, C is the average number of customers per hour, and R is the desired revenue.



To represent the restaurant owner's desired revenue, we need to create an inequality in standard form based on the given information. Let's assume the initial price of the buffet is $P, and x represents the number of $1 increases. The new price of the buffet would be P + x.The average number of customers per hour is represented by the variable C. The revenue generated per hour can be calculated by multiplying the price paid by each customer (P + x) and the average number of customers per hour (C). Hence, the hourly revenue can be expressed as (P + x) * C.

To create an inequality representing the desired revenue, we need to set a specific target revenue level. Let's assume the owner desires a minimum revenue of R dollars per hour. The inequality representing the desired revenue can be expressed as:

(P + x) * C ≥ R

This inequality states that the product of the new buffet price (P + x) and the average number of customers per hour (C) must be greater than or equal to the desired revenue (R) to meet the owner's expectations.

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Each section of the garden will be 3.4 feet long.

To find the length of each section, we can divide the total length of the garden by the number of sections.

Length of the garden: 40.8 feet

Number of sections: 12

Length of each section = Total length of the garden / Number of sections

Length of each section = 40.8 feet / 12

Length of each section = 3.4 feet

Therefore, each section of the garden will be 3.4 feet long.

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The volume of the cone is approximately 81.249 cm³, rounded to three significant figures. To calculate the volume of a cone, we need to know the slant height and the radius or height of the cone.

However, in this case, we are only given the slant height and the curved surface area of the cone.

Given:

Slant height (l) = 9 cm

Curved surface area (CSA) = 100 cm²

We can start by finding the radius (r) of the cone using the formula for curved surface area:

CSA = π * r * l

Plugging in the given values:

100 = π * r * 9

To solve for r, we can divide both sides of the equation by 9π:

r = 100 / (9π)

Now that we have the radius, we can calculate the volume (V) of the cone using the formula:

V = (1/3) * π * r² * h

Since we don't have the height (h) of the cone, we can express it in terms of the slant height and radius using the Pythagorean theorem:

h = sqrt(l² - r²)

Plugging in the values:

h = sqrt(9² - (100 / (9π))²)

Now we have all the necessary values to calculate the volume:

V = (1/3) * π * r² * h

V = (1/3) * π * (100 / (9π))² * sqrt(9² - (100 / (9π))²)

Calculating the value using a calculator or software, we find:

V ≈ 81.249 cm³

Therefore, the volume of the cone is approximately 81.249 cm³, rounded to three significant figures.

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The area covered by the patch is 63.585 cm²

To find the area covered by the circular patch, we can use the formula for the area of a circle:

Area = πr²

Given that the diameter of the patch is 9 centimeters, we can find the radius (r) by dividing the diameter by 2:

r = 9 cm / 2

r = 4.5 cm

Now, substituting the value of the radius into the area formula:

Area = 3.14 × (4.5 cm)²

Area = 3.14 ×20.25 cm²

Area = 63.585 cm²

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The expression that shows five less than the sum of 12 and a number is `12 + x - 5`, where `x` is the number. The expression can be simplified as `7 + x`.

An expression is a mathematical phrase containing variables, numbers, and mathematical operations. It is a combination of variables, constants, and mathematical operators that express a mathematical relationship. An expression can be evaluated to obtain a number.

An equation is a mathematical statement that equates two expressions. It consists of an equal sign between two expressions. The equal sign represents that the expressions on either side of it have the same value. An equation has an unknown value that can be calculated by solving it.

A sum is the result of adding two or more numbers together. The numbers that are added are called addends. The sum of two numbers is the result of adding them together. For example, the sum of 2 and 3 is 5. The sum of 5 and 7 is 12.A number is a mathematical object used to measure or count something. It represents a quantity or value. Numbers can be whole numbers, fractions, decimals, or negative numbers. Whole numbers are positive integers and zero.

Fractions are numbers that represent a part of a whole. Decimals are numbers that represent fractions in decimal form. Negative numbers are numbers less than zero.

The expression that shows five less than the sum of 12 and a number is `12 + x - 5`, where `x` is the number.

The expression can be simplified as `7 + x`.

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The probability of selecting a red pencil followed by a yellow pencil is 3/182. The probability of choosing a red pencil followed by a yellow pencil is obtained by multiplying the probability of choosing a red pencil and the probability of choosing a yellow pencil without replacing the red pencil.

It is expressed as a fraction, decimal, or percentage. It is computed by dividing the number of possible successful outcomes by the number of total outcomes. The number of pencils in the box is 14.

The probability of choosing a red pencil is 3/14 because there are three red pencils in the box. The likelihood of selecting a red pencil followed by a yellow pencil is the product of these two probabilities:

3/14 × 1/13

= 3/182.

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The correct answer for the formula to describe the sequence is [tex]a_n = a_1.r^{n-1}[/tex].

The general formula of a geometric sequence is:

[tex]a_n = a_1.r^{n-1}[/tex]

[tex]a_n[/tex] is the [tex]n^{th}[/tex] term of the sequence.

[tex]a_1[/tex] is the first term.

[tex]r[/tex] is the common ratio.

[tex]n[/tex] is the term number.

Examine each option:

[tex]1 . f(x_1) = -2f(x)[/tex]

[tex]f(x_n) = a_1(-2)^{n-1}[/tex]

In this case, the common ratio [tex]r[/tex] is [tex]-2[/tex], and the first term is [tex]a_1[/tex] can be any value.

[tex]2.f(x_1) = -\dfrac{1}{2}f(x)[/tex]

[tex]f(x_n) = a_1(-\dfrac{1}{2} )^{n-1}[/tex]

The common ratio [tex]r[/tex] is -1/2.

[tex]3.f(x_1) = \dfrac{1}{2}f(x)[/tex]

[tex]f(x_n) = a_1(\dfrac{1}{2} )^{n-1}[/tex]

The common ratio [tex]r[/tex] is  1/2

[tex]4. f(x_1) = 2f(x)[/tex]

[tex]f(x_n) = a_1(2)^{n-1}[/tex]

The common ratio [tex]r[/tex] is [tex]2[/tex].

The sequence for all the functions is [tex]a_n = a_1.r^{n-1}[/tex].

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The formulas describe geometric sequences where each term is a constant factor of the preceding one. f(x+1) = –2f(x), f(x+1) = 2f(x) are sequences with terms that multiply by -2 and 2 respectively, whereas f(x+1) = -1/2f(x) and f(x+1) = 1/2f(x) describe sequences where each term is half of the previous.

The formula used to describe the sequence depends on the type of sequence that is being studied. In the formulas given, f(x+1) represents the next term in the sequence and f(x) represents the current term. The number being multiplied with f(x) determines the ratio or difference between successive terms which characterizes the type of sequence.

In contrast, f(x+1) = -1/2f(x) and f(x+1) = 1/2f(x) represent sequences where each term is half the previous term, which are exponentially decreasing sequences, the first being negative and the second being positive.

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