A spring's natural length is 10 m. If it requires 7 J to stretch the spring from 11 m to 18 m, find the amount of work required to stretch the spring from 18 m to 21 m. Round your answer to 4 decimal places. Note your answers must be in joules. If you need a calculator use the following link: Desmos c^7

The constant of proportionality of 5 tells us that the volume of the cylinder is five times greater than it would be if the radius were 1 cm.

The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height. If h = 5 and V is directly proportional to r² with a constant of proportionality of 5, then we can write the following equation:

V = 5r²

This equation tells us that the volume of the cylinder is 5 times the square of the radius. For example, if the radius is 1 cm, then the volume of the cylinder is 5 cm³. If the radius is 2 cm, then the volume of the cylinder is 20 cm³.

The fact that the volume of the cylinder is directly proportional to the square of the radius means that the volume increases more rapidly as the radius increases. For example, when the radius is doubled from 1 cm to 2 cm, the volume increases from 5 cm³ to 20 cm³, which is a fourfold increase.

For example, if the radius is 2 cm, then the volume of the cylinder is 20 cm³, which is five times greater than the volume of a cylinder with a radius of 1 cm and a height of 5 cm.

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Derek can watch a maximum of (M/7.25) number of movies, where $M represents his budget for movie.

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. There are two types of inequalities namely strict and slack inequalities.

Given is Derek who enjoys going to the movies. He budgets a month for movies and admissions for one movie cost $7.25.

Assume that the budget for movies is $M.

The cost of admission in one movie = $7.25

Suppose that Derek can watch [x] number of movies. Then, the given inequality will represent the number of movies Derek can watch -

7.25x ≤ M

x ≤ (M/7.25)

Therefore, Derek can watch a maximum of (M/7.25) number of movies, where $M represents his budget for movie.

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Answer:

∠ C = 100°

Step-by-step explanation:

since 2 sides of the triangle are congruent then the triangle is isosceles with base angles congruent.

consider the angle inside the triangle to the left of 140°

this angle and 140° are a linear pair and sum to 180°

angle + 140° = 180° ( subtract 140° from both sides )

angle = 40°

then the angle on the left of the triangle = 40° ( base angles congruent )

the sum of the angles in a triangle = 180° , so

∠ C + 40° + 40° = 180°

∠ C + 80° = 180° ( subtract 80° from both sides )

∠ C = 100°

The chemicals under considerationm an important quantity is the total proportion Y1 +Y2 found in any sample.V(Y1 + Y2) = Var(Y1) + Var(Y2) + 2Cov(Y1, Y2) = 1/18 + 1/18 + 2(1/144) = 5/72.

To find E(Y1 + Y2), we first find the marginal distribution of Y1 and Y2 by integrating the joint density function over the other variable as follows:

f1(y1) = ∫f(y1,y2)dy2 = ∫2dy2 from 0 to 1-y1 = 2(1-y1) for 0 ≤ y1 ≤ 1

f2(y2) = ∫f(y1,y2)dy1 = ∫2dy1 from 0 to 1-y2 = 2(1-y2) for 0 ≤ y2 ≤ 1

Now we can find E(Y1 + Y2) as follows:

E(Y1 + Y2) = ∫∫(y1 + y2)f(y1,y2)dy1dy2

= ∫∫(y1 + y2)2dy1dy2 over the region 0 ≤ y1 ≤ 1-y2, 0 ≤ y2 ≤ 1

E(Y1 + Y2) = ∫0^1∫0^(1-y1) (y1 + y2)2dy2dy1

= ∫0^1[y1(y1/2 + 2/3) + 1/3]dy1

= 7/12

To find V(Y1 + Y2), we can use the fact that V(Y1 + Y2) = V(Y1) + V(Y2) + 2Cov(Y1, Y2), where Cov(Y1, Y2) is the covariance of Y1 and Y2. First, we need to find the variances of Y1 and Y2:

Var(Y1) = E(Y1^2) - [E(Y1)]^2 = ∫∫y1^22dy1dy2 - [∫∫y1f(y1,y2)dy1dy2]^2

= ∫0^1∫0^(1-y1) y1^22dy2dy1 - [∫0^1(2y1-2y1^2)dy1]^2

= 1/18

Var(Y2) = E(Y2^2) - [E(Y2)]^2 = ∫∫y2^22dy1dy2 - [∫∫y2f(y1,y2)dy1dy2]^2

= ∫0^1∫0^(1-y2) y2^22dy1dy2 - [∫0^1(2y2-2y2^2)dy2]^2

= 1/18

Now we need to find the covariance of Y1 and Y2:

Cov(Y1, Y2) = E(Y1Y2) - E(Y1)E(Y2) = ∫∫y1y2f(y1,y2)dy1dy2 - (∫∫y1f(y1,y2)dy1dy2)(∫∫y2f(y1,y2)dy1dy2)

= ∫0^1∫0^(1-y1) 2y1y2dy2dy1 - (7/12)(7/12)

= 1/144

Therefore, V(Y1 + Y2) = Var(Y1) + Var(Y2) + 2Cov(Y1, Y2) = 1/18 + 1/18 + 2(1/144) = 5/72.

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Answer:

daddys_angel_yt

Step-by-step explanation:

Answer:

Step-by-step explanation:

Ricardoconsort14 and RicardoOrtVill

Answer:

p

=

2

(

4

x

+

3

)

+

2

(

2

x

−

6

)

or simplified  

p

=

12

x

−

9

Explanation:

By definition the perimeter of an object is the length of all its sides.

Also by definition, for a rectangle the 2 sides of the width are equal and the 2 sides of the length are equal.

Therefore the equation for the perimeter of a rectangle can be written as:

p

=

2

⋅

l

+

2

⋅

w

where  

p

is the perimeter,  

l

is the length and  

w

is the width.

Substituting what was given about the length and width gives the equation:

p

=

2

(

4

x

+

3

)

+

2

(

2

x

−

6

)

Simplifying this equation gives:

p

=

8

x

+

3

+

4

x

−

12

p

=

8

x

+

4

x

+

3

−

12

p

=

12

x

−

9

Step-by-step explanation:

Answer:

Step-by-step explanation:

As per picture we have:

This gives us:

Two sides and included angle congruent - ASA postulate

As per above congruency we have:

Finding CD:

Answer:

\(6.8\ cm\)

Step-by-step explanation:

\(We\ are\ given:\\OM\ is\ altitude\ of\ \triangle AOB\\ON\ is\ altitude\ of\ \triangle DOC\\Now,\\Lets\ only\ focus\ on\ the\ interior\ triangles\ inside\ the\ two\ above\ triangles.\\They\ are:\\\triangle OMA\ and\ \triangle ONC.\\\\We\ observe\ that:\\\angle AMO=90[As\ it\ is\ the\ altitude\ of\ \triangle AMO]\\\angle ONC=90[As\ it\ is\ the\ altitude\ of\ \triangle ONC]\\Hence,\\\angle AMO= \angle ONC=90\\\\\)

\(We\ also\ observe\ that,\\\angle MOA\ and\ \angle CON\ are\ vertically\ opposite\ as\ they\ are\ one\ pair\\ of\ opposite\ angles\ formed\ by\ the\ intersection\ of\ Lines\ AC\ and\ MN.\\We\ know\ that,\\"When\ two\ straight\ lines\ intersect,\ the\ pairs\ of\ vertically\ opposite\\ angles\ formed\ are\ equal".\\Hence,\\\angle MOA= \angle CON\)

\(Lastly,\\We\ are\ given\ that,\\MO=ON\)

\(Now,\\The\ ASA\ Congruence\ Criterion\ states\ that' If\ two\ angles\ and\ the\ includ\\ side\ of\ one\ triangle\ is\ equal\ to\ the\ corresponding\ angles\ and\ the\ includ\\ side\ of\ the\ second\ triangle,\ both\ triangles\ are\ congruent'.\\Hence,\\\triangle AMO \cong \triangle CNO.\)

\(Hence,\\AM=NC [Corresponding\ Parts\ of\ Congruent\ Triangles]\\We\ can\ observe\ that,\\CD=DN+NC\\Hence,\\DN=2.6\ cm [Given]\\NC=AM=4.2\ cm [Proven]\\Hence,\\DC=2.6+4.2=6.8\ cm\)

Answer:

1.6

Step-by-step explanation:

12.8/8 = 1.6

15.2/9.5 = 1.6

Scale factor = 1.6

Answer:

207

Step-by-step explanation:

It automatically can not be -207 and -21 because you can't have a negative distance. To find the correct answer between 21 and 207, first you have to add 93 and 114. You do this because -93 is below the number line, so you have to add it to 114. 114 + 93 = 207

207

I hope this helps

Respuesta:

Juan = 12

Carlos = 24

Explicación paso a paso:

Dejar :

Cantidad que tiene Juan = x

Cantidad que Carlos tiene = 2x

Restando 6 de la cantidad de Carlos y sumando 6 la cantidad de Juan, ambos tendrán la misma cantidad

x + 6 = 2x - 6

Recopilar términos semejantes

x - 2x = - 6 - 6

-x = - 12

Dividir ambos lados por - 1

-x / - 1 = - 12 / - 1

x = 12

Por tanto, Juan tiene 12

Y Carlos tiene 2x = 12 * 2 = 24

Answer:

if it's not on a test, just guess

Step-by-step explanation:

A solution to −34x+2=(14)x+1 is x = 1/48

In this question, we have been given functions f(x) = -34x + 2 and g(x) =(14)x + 1

We need to find the solutions to −34x + 2 = (14)x + 1

i.e., we need to find the solution to f(x) = g(x)

Consider, f(x) = g(x)

-34x + 2 = (14)x + 1

-34x + 2 - 14x = 14x + 1 - 14x

-48x + 2 = 1

-48x = -1

x = 1/48

Therefore, a solution to −34x+2=(14)x+1 is x = 1/48

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Answer:

AED 1000

Step-by-step explanation:

The  price is 600 after 40% discount

if original price is ,

100% : x = 60% : 600

1 : x = 0.6 : 600

600 = 0.6x

 x = 1000

Answer:

∠ T = 126°

Step-by-step explanation:

in an isosceles trapezoid

• lower base angles are congruent

• any lower base angle is supplementary to any upper base angle

then

∠ U = ∠ W = 54° , so

∠ T + ∠ U = 180°

∠ T + 54° = 180° ( subtract 54° from both sides )

∠ T = 126°

Step-by-step explanation:

let the number be x

so,

25% of x = 16

→ 25/100 × x = 16

→ x = 16 × 100/25

→ x = 1600/25 → 64

therefore,

25% of 64 is 16.

Hope this answer helps you dear!

16 is 25% of 64.

Percentage is the fraction of an amount that is usually expressed as a number out of hundred. Percentages are a measure of frequency.

In order to determine the number, divide 16 by 25%

16 / 25%

16 / 0.25 = 64

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Answer: 9π/2

Step-by-step explanation:

A semicircle is half of a circle. Therefore, you must divide the area by 2.

\(A=\frac{\pi r^2 }{2}\)

Since we know the radius, we can directly plug it into the formula.

\(A=\frac{\pi (3)^2}{2} =\frac{9\pi }{2}\)

Since the problem stated to give the answer in terms of π, 9π/2 is our answer.

Answer:

\(\frac{9\pi }{2}\) cm²

Step-by-step explanation:

The area of a semicircle can be expressed by the formula \(\frac{\pi r^{2} }{2} = A\).

When you plug in the radius, you get \(\frac{\pi 3^{2} }{2} = \frac{\pi 9}{2} = \frac{9\pi }{2}\).

Answer:

7

Step-by-step explanation:

The square root of 49 is 7

Caroline's bill before tax and tip was $16.15. A sales tax of 6.5% was added, and Caroline tipped 18% on the amount after the sales tax.

To calculate the total cost of the meal, we need to add the sales tax and the tip to the bill amount. The sales tax is calculated by multiplying the bill amount by the tax rate of 6.5% (or 0.065). Therefore, the sales tax amount is $16.15 * 0.065 = $1.05.

After adding the sales tax, the subtotal of the bill becomes $16.15 + $1.05 = $17.20. Caroline then calculates the tip on the subtotal. The tip amount is found by multiplying the subtotal by the tip rate of 18% (or 0.18). The tip amount is $17.20 * 0.18 = $3.10.

The total cost of the meal, including the bill, tax, and tip, is $16.15 + $1.05 + $3.10 = $20.30.

To determine the percent by which the total cost exceeds the bill, we calculate the difference between the total cost and the bill, which is $20.30 - $16.15 = $4.15. Then we divide this difference by the bill amount and multiply by 100 to get the percentage: ($4.15 / $16.15) * 100 ≈ 25.68%.

Rounding to the nearest whole number, the total cost of the meal exceeds the bill by approximately 27%.

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Answer: They can be arranged 720 different ways

K-Means uses Euclidean distance. The output includes average and maximum distances, separation, and convergence after iterations related to the number of starting seeds.

In the output of a K-Means cluster analysis, "Ave Distance" refers to the average distance between the data points and their assigned cluster centroids.

"Max Distance" represents the maximum distance between any data point and its assigned centroid. "Separation" indicates the distance between the centroids of different clusters, reflecting how well-separated the clusters are.

Convergence in K-Means clustering refers to the point when the algorithm reaches stability and the cluster assignments no longer change significantly.

When the video mentions convergence after 4 iterations, it means that after four rounds of updating cluster assignments and re-computing centroids, the algorithm has achieved a stable result.

The "Number of starting seeds" option determines how many initial random seeds are used for the algorithm, and it can affect the number of iterations needed for convergence. Increasing the number of starting seeds may result in faster convergence as it explores different initial configurations.

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The answer is either A. IQR, because Sunny Town is symmetric or B. IQR, because Beach Town is skewed.

A distribution refers to the pattern of how data is spread out or distributed across different values or intervals. It is a way to describe and analyze the shape, center, and spread of a set of data.

To determine the location with the most consistent temperature, we need to measure the variability of the temperature data in both locations. The measure of variability that is appropriate for this purpose is the interquartile range (IQR), which measures the spread of the middle 50% of the data.

Therefore, the answer is either A. IQR, because Sunny Town is symmetric or B. IQR, because Beach Town is skewed, depending on the shape of the distributions. If the temperature data in Sunny Town is symmetric, then the IQR would be appropriate to measure the spread of the data. If the temperature data in Beach Town is skewed, then the IQR would also be appropriate to measure the spread of the data. However, if the temperature data in either location is not skewed, then the range would not be an appropriate measure of variability.

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For a basic loan application, the information which is not expect to see usually on it, is the doctor’s name and address. Option b is correct.

A loan application is the application, which is written for the bank manger to apply for a loan from a particular bank.

The basic loan application include,

The format of loan application include,

Thus, For a basic loan application, the information which is not expect to see usually on it, is the doctor’s name and address. Option b is correct.

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Answer:

To put it in simple terms, the answer is b., which is doctor's name and address

Step-by-step explanation:

you're welcome

The answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.

In this scenario, P(Z ≤ b) represents the cumulative probability of a standard normal distribution up to the value of b. To find the corresponding value of b, we need to find the z-score that corresponds to a cumulative probability of 0.0311.

By looking up the z-table or using a statistical calculator, we can find that the z-score corresponding to a cumulative probability of 0.0311 is approximately -1.865.

Therefore, the answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.

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Answer: 20 and 11

Step-by-step explanation: Let x = the larger number

Let y = the smaller number

x + y = -9

x - y = 31

2x = 22

x = 11

x + y = -9

11 + y = -9

y = -20

Answer:

Nonproportional

Step-by-step explanation:

Hope This Helps