Find an equation of a circle centred

[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{p})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{p}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{7}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ -5 }\implies \cfrac{4-p}{1}=-5 \\\\\\ 4-p=-5\implies 4=-5+p\implies 9=p[/tex]

As a result, the difference is 837 grammes between the cones' respective masses.

Describe density.

Mass per unit volume is measured using density. It is described as a substance's mass per unit volume. The following is the density formula:

Mass / Volume equals density.

So, The formula m = V, where m is the mass, is the density, and V is the volume, can be used to determine each cone's mass.

The formula below can be used to determine each cone's mass:

- The mass of a steel cone weighs 1298.21 grams or 7.75 grams per cubic centimeter.

- The granite cone weighs 460.76 grams, or 2.75 grams per cubic centimeter.

- Mass of steel cone = 7.75 g/cm³ × 167.55 cm³ = 1298.21 grams

- Mass of granite cone = 2.75 g/cm³ × 167.55 cm³ = 460.76 grams

for difference of masses = 1298.2 grams - 460.76  grams = 837 grams

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By using the cosines law we can say that, Velma and Fred are approximately 17.39 meters apart.

What is law of cosine?

The Law of Cosines is a formula used in trigonometry to relate the sides and angles of a triangle. It states that for any triangle with sides a, b, and c and angles A, B, and C opposite those sides, the following equation holds:

[tex]$c^2 = a^2 + b^2 - 2ab \cos(C)$[/tex]

where c is the side opposite angle C.

We can solve this problem using the law of cosines. Let's call the distance between Velma and Fred "[tex]$d$[/tex]". Then, we have:

[tex]$c^2 = a^2 + b^2 - 2ab \cos(C)$[/tex]

where [tex]$c$[/tex] is the distance between Velma and Fred (which we want to find), [tex]$a$[/tex] is the distance between Shaggy and Velma (which is 20 meters), [tex]$b$[/tex] is the distance between Shaggy and Fred, and [tex]$C$[/tex] is the angle formed at Shaggy (which is 30 degrees).

We can rearrange this equation to solve for [tex]$d$[/tex]:

[tex]$d^2 = a^2 + b^2 - 2ab \cos(C)$[/tex]

[tex]$d^2 = 20^2 + b^2 - 2(20)(b) \cos(30)$[/tex]

[tex]$d^2 = 400 + b^2 - 20b \sqrt{3}$[/tex]

We also know that the angle formed at Fred is 105 degrees, which means that the angle formed at Velma is 45 degrees (since the angles in a triangle sum to 180 degrees). This means that we can use the law of sines to find the value of [tex]$b$[/tex]:

[tex]$\dfrac{b}{\sin(B)} = \dfrac{a}{\sin(A)}$[/tex]

[tex]$\dfrac{b}{\sin(105)} = \dfrac{20}{\sin(45)}$[/tex]

[tex]$b = 20 \dfrac{\sin(105)}{\sin(45)}$[/tex]

[tex]$b \approx 27.68$[/tex]

Now we can substitute this value of [tex]$b$[/tex] into the equation we derived earlier to find [tex]$d$[/tex]:

[tex]$d^2 = 400 + (27.68)^2 - 20(27.68)\sqrt{3}$[/tex]

[tex]$d \approx 17.39$[/tex]

Therefore, Velma and Fred are approximately 17.39 meters apart.

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The slope and y-intercept of the following equation are:

Slope = 4.

y-intercept = 1.

In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

Based on the information provided above, an equation that models the line is represented by this mathematical equation;

y = mx + c

y = 11x + 41

By comparison, we have the following:

mx = 4x

Slope, m = 4.

Initial number or y-intercept, c = 1.

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a) The time that Rodrigo spent practicing during the third week is 5.42 hours.

b) The equation that represents the problem is 15¹/₃ = 5¹/₄ + 4²/₃ + x.

An equation is a mathematical statement showing that two or more mathematical or algebraic expressions are equal or equivalent.

Equations are represented using the equal symbol (=), unlike algebraic expressions that contain variables, constants, numbers, and values.

The time spent during the first week = 5¹/₄ hours

The time spent during the second week = 4²/₃ hours

The total time spent during the three weeks period = 15¹/₃ hours

Let the time spent during the third week = x

15¹/₃ = 5¹/₄ + 4²/₃ + x

x = 15¹/₃ - (5¹/₄ + 4²/₃)

x = 5.41663

Thus, solving the equation, Rodrigo spent 5.42 hours practicing the guitar during the third week.

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The ratio of ribbon to bouquets is 2:5, meaning for every 2 meters of ribbon, 5 bouquets can be made. For every 7 bouquets, 3 meters of ribbon are needed, meaning the ratio is 3:7.

A ratio is a comparison of two numbers or quantities that are related to each other in some way. It is the relationship between the sizes of two or more things, expressed as the quotient of one divided by the other.

Ratios can be used to compare different aspects of a set of data, such as the ratio of boys to girls in a classroom, or the ratio of red cars to blue cars on a street. They are also used in many real-world applications, such as finance, engineering, and science.

Ribbon to bouquets ratio is 2:5, which means that for every 2 units of ribbon, there are 5 bouquets.

With a ribbon to bouquet ratio of 1:3, the number of bouquets is three times the amount of ribbon.

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By answering the presented question, we may conclude that height of the cone is approximately 2.9 centimeters.

A cone is a three-dimensional geometric shape having a flat base and a smooth tapering apex, also known as a vertex. A cone is formed on a plane with no vertices by joining a sequence of line segments, half-lines, or lines that are common to all points on the base. A cone is a three-dimensional structure with a smooth transition from a flat, usually circular, base to the vertex or apex, which acts as the axis to the centre of the base. A cone is a three-dimensional geometric form having an upwardly flattened curving surface.

volume of a cone:

[tex]V = 1/3 * \pi * r^2 * h\\r = 4 cm\\V = 143.6 cm^3\\143.6 = 1/3 * \pi * 4^2 * h\\143.6 = 16/3 * \pi * h\\h = 143.6 / (16/3 * \pi)\\h = 2.9 cm\\[/tex]

height of the cone is approximately 2.9 centimeters.

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Answer:

Glad we helped

Step-by-step explanation:

Answer:

8.

Step-by-step explanation:

That would be by a factor of 2^3 = 8.

The value of x is equal to 21 units when scale is 1:7 and a given side on figure A is 3 units.

We know that Figure A is a scaled image of Figure B, with a scale of 1:7. This means that every length in Figure A is one-seventh the length of the corresponding length in Figure B. For example, if a side in Figure B is 14 units long, the corresponding side in Figure A would be 2 units long (14 divided by 7).

In question a side on figure A is 3 units:

Side on Figure B = 7 * Side on Figure A

x = 7 * 3

x = 21 units

Therefore, x is equal to 21 units when scale is 1:7 and a given side on figure A is 3 units.

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The complete question is :

Figure A is a scale image of Figure B, as shown.

The scale that maps Figure A onto Figure B is 1:7

Enter the value of x.

From the figure, the value of x is given as 17 units

In mathematics, a ratio shows how many times one number contains another.

The ratio of the sides of the figure is as follows

3x-7/x+5 = 2/1

cross and multiply to have 3x - 7 = 2(x+5)

opening the brackets to have

3x -7 = 2x +10

collecting like terms to have

3x-2x = 10+7

x = 17 units

In conclusion, the value of x is 17 units

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To find the approximate population of China, we need to multiply the population of Vatican City by 1.75 × 106:

Population of China = Population of Vatican City × 1.75 × 106

Population of China = 800 × 1.75 × 106

Population of China = 1.4 × 109

Therefore, the approximate population of China is 1.4 × 109, which is option D.

The average rate of change of the function f(x) over the interval [-2, -9] is -6.

To determine the average rate of change of the function f(x) over the interval [-2, -9], we need to find the slope of the secant line that connects the points (-2, f(-2)) and (-9, f(-9)).

We first find the values of f(-2) and f(-9):

f(-2) = (-2)² + 5(-2) + 14 = 4 - 10 + 14 = 8

f(-9) = (-9)² + 5(-9) + 14 = 81 - 45 + 14 = 50

So, the two points are (-2, 8) and (-9, 50).

The slope of the secant line between these two points is:

slope = (f(-9) - f(-2)) / (-9 - (-2)) = (50 - 8) / (-9 + 2) = 42 / -7 = -6

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[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 20\%\to \frac{20}{100}\dotfill &0.2\\ t=\textit{elapsed time} \end{cases} \\\\\\ A = 50(1 + 0.2)^{t} \implies \boxed{A =50(1.2)^t}[/tex]

Answer: 2sw or 2ab

Step-by-step explanation:

The cone and cylinder above have the same radius and height and the volume of the cone is 171 cubic inches.

Volume of a three-dimensional shape is the space occupied by the shape.

Given that,

Radius and height of the cylinder and the cone are same.

Let r and h be the radius and height of each of the cylinder and the cone.

Volume of the Cone = 1/3 π r² h

Volume of the cone = We have, volume of the cylinder is 57 cubic inches.

1/3 π r² h = 57

Multiplying both sides by 3,

π r² h = 57 × 3

π r² h = 171 cubic inches π r² h

Hence the volume of the cone is 171 cubic inches

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Answer:

77

Step-by-step explanation:

We Know

30% of r = 33

Find 1% by taking

33 / 30 = 1.1

What is 70% of R?

We take

1.1 x 70 = 77

So, 70% of R is 77

The question requires to first find the value of R by solving the equation (0.30*R = 33). Then, calculate 70% of R by multiplying the found R value with 0.70.

The question tells us that 30% of R equals 33. To find the value of R, we can set up an equation where 0.30 (which is 30% in decimal form) times R equals 33. Dividing both sides of the equation by 0.30 will give us the value for R. Once we have found R, we can then find 70% of R by multiplying R by 0.70 (70% in decimal form).

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Answer:

linear

Step-by-step explanation:

yw

Therefore, the value of x in each triangle is approximately 5.4 and 11.1, respectively.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It involves the study of trigonometric functions such as sine, cosine, and tangent, which are used to relate the angles of a triangle to the lengths of its sides. Trigonometry has a wide range of applications in fields such as physics, engineering, navigation, surveying, and astronomy. For example, trigonometry is used in navigation to calculate the angles between a ship and a lighthouse, or between two ships, in order to determine their relative positions. In engineering, trigonometry is used to calculate the forces acting on structures such as bridges and buildings, and to design and build machines that rely on the principles of motion and energy.

Here,

For the first triangle, we have:

Using the sine ratio,

sin(36) = x / 9

Solving for x, we get:

x = 9 sin(36)

≈ 5.4

Rounding to the nearest tenth, we get:

x ≈ 5.4

For the second triangle, we have:

Using the tangent ratio,

tan(27) = x / 21

Solving for x, we get:

x = 21 tan(27)

≈ 11.1

Rounding to the nearest tenth, we get:

x ≈ 11.1

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Answer:

yes

Step-by-step explanation:

Option D, which has 92° and 66° curves, is the correct choice. The total of these angles is 158°, which is needed for the final two angles.

The triangle with edges in the ratio $3:4:5 is therefore "yes" a right-angled triangle. Note: We can only apply Pythagoras' Theorem to right-angled triangles; it cannot be applied to any other triangles.

Let's add the given angle measures: 52° + 70° + 44° + 36° = 202°. This means that the sum of the measures of the remaining two angles in the two triangles is:

360° - 202° = 158°

As a result, since both options A and B have one angle that is higher than 90 degrees, we can rule them out.

Option C has angles of 88° and 68°, which add up to 156°.

Since the highest sum of two acute angles is 180°, the other two angles would have to have a sum of 204°, which is not feasible.

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Answer: 37

Step-by-step explanation: so first you have to realize that i what I’m doing and you not listen to me

Answer:

Step-by-step explanation:

The distance of the fire from the road is d ≈ 6.15 miles + 2.94 miles ≈ 9.09 miles.

The two expressions for d give slightly different values. This is due to the fact that we rounded the values of x and y in our calculations.

In problem 9, we can use trigonometry to find the distance, d, of the fire from the road. Let x be the distance from Star Point Ranger Station to the fire, and let y be the distance from Twin Pines Ranger Station to the fire. Then, we have:

tan(34°) = d/x

tan(14°) = d/y

Multiplying both sides of each equation by the respective denominator and simplifying, we get:

d = x tan(34°)

d = y tan(14°)

Since the two expressions for d are both equal, we can set them equal to each other and solve for x and y:

x tan(34°) = y tan(14°)

x = (y tan(14°))/tan(34°)

Substituting the value we found for y in problem 7, which was y = 6.15 miles, we get:

x = (6.15 miles) * tan(14°) / tan(34°) ≈ 2.94 miles

Therefore, the distance of the fire from the road is d ≈ 6.15 miles + 2.94 miles ≈ 9.09 miles.

Now, let's check our answers using both expressions for d:

d = x tan(34°) ≈ 2.94 miles * tan(34°) ≈ 2.94 miles * 0.704 = 2.07 miles

d = y tan(14°) ≈ 6.15 miles * tan(14°) ≈ 6.15 miles * 0.249 = 1.53 miles

As we can see, the two expressions for d give slightly different values. This is due to the fact that we rounded the values of x and y in our calculations. If we use the exact values, we would get slightly different values for d, but they would still be very close.

In real life, it is important to be as accurate as possible when dealing with emergencies such as fires. However, in this case, the difference between the two values of d is relatively small, so it may not have a significant impact on the response to the fire. Nevertheless, it is important to use the most accurate values possible to ensure the safety of those involved.

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The magnitude of the electric field between the plates is 3.86 × [tex]10^7[/tex]N/C. The sign indicates the direction of the electric field, which depends on the sign of the charge on the plates.

The strength of the electric field between the plates can be calculated using the formula:

E = σ/ε0

where σ is the surface charge density, ε0 is the permittivity of free space, and E is the electric field strength.

The surface charge density is given by:

σ = Q/A

where Q is the charge on each plate and A is the area of each plate.

Substituting the given values, we get:

σ = ±0.0000470 C / 0.138 [tex]m^2[/tex] = ±0.000341 C/[tex]m^2[/tex]

The permittivity of free space is:

ε0 = 8.85 × [tex]10^{-12[/tex] F/m

Substituting the values, we get:

E = σ/ε0 = ±0.000341 C/[tex]m^2[/tex] / 8.85 × [tex]10^{-12[/tex] F/m = ±3.86 × [tex]10^7[/tex] N/C

The magnitude of the electric field between the plates is 3.86 × [tex]10^7[/tex]N/C. The sign indicates the direction of the electric field, which depends on the sign of the charge on the plates.

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The probability that at most 13 of the residers in the sample entered a jury process in the once 12 months is 0.000158.

A normal distribution, also known as a Gaussian distribution or bell wind, is a probability distribution that's symmetric and bell- shaped. It's characterized by its mean( μ) and standard divagation( σ).

Given

Sample size( n) = 500

Probability of an individual entering a jury process( p) = 15 = 0.15

We want to calculate the probability that at most 13 of the residers in the sample entered a jury process.

Let X be the arbitrary variable representing the number of residers who entered a jury process in the sample.

Using the binomial accretive distribution function( CDF), we can calculate the probability as follows

P( X ≤ 13 of n) = Σ( k = 0 to k = 0.13 n)( n C k)

Here, n = 500

p = 0.15

k = int(0.13 n)

So, binom.cdf( int(0.13 500), 500,0.15) ≈0.000158

Thus, The likelihood that 13% of the sample's residents received a jury summons in the previous year is 0.000158.

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The question attached here is seems to be incomplete, the complete question is

What proportion of US Residents receive a jury summons each year? A polling organization plans to survey a random sample of 500 US Residents to find out. Let be the proportion of residents in the sample who received a jury summons in the previous 12 months. According to the National Center for State Courts, 15 \% of US residents receive a jury summons each year. Suppose that this claim is true.

5. Calculate the probability that at most 13% of the residents in the sample received a jury summons in the past 12 months.

Answer:

Step-by-step explanation:
[tex]168yd^{2}[/tex]

Answer:

168 yd²

Step-by-step explanation:

4 × 7 yd × 12 yd / 2 = 168 yd²

To solve this system of equations using the elimination method, we need to eliminate one of the variables. One way to do this is to add the two equations together in a way that will eliminate one of the variables.

First, we can multiply the second equation by -1 to change the sign of all its terms:

-6x + 5y = 1

-6x - 4y = 10

Now we can add the two equations together to eliminate x:

( -6x + 5y ) + ( -6x - 4y ) = 1 + 10

Simplifying the left side and the right side:

-12x + y = 11

Now we have one equation with one variable, y. We can solve for y by isolating it on one side of the equation:

-12x + y = 11

y = 12x + 11

We can substitute this expression for y into either of the original equations to solve for x. Let's use the first equation:

-6x + 5y = 1

-6x + 5(12x + 11) = 1

Simplifying the left side:

54x + 55 = 1

Subtracting 55 from both sides:

54x = -54

Dividing both sides by 54:

x = -1

So the solution to the system of equations is x = -1 and y = 1. We can check this solution by substituting these values into both original equations and verifying that they are true.

The expression of the function using the specified formats are presented as follows;

Please find attached the required graph of the function f(x) = -2·(x - 4)² + 1 created with MS Excel

The table of values for the function can be presented as follows;

[tex]\begin{tabular}{|c|c|c|} \cline{1-2}x& f(x) \\ \cline{1-2}1 & -17\\ \cline{1-2} 2 & -7 \\ \cline{1-2} 3 & -1 \\ \cline{1-2} 4 & 1 \\ \cline{1-2} 5 & -1\\\cline{1-2} 6 & -7 \\ \cline{1-2} 7 & -17 \\ \cline{1-2}\end{tabular}[/tex]

The mapping diagram can be presented as follows;

x [tex]{}[/tex]  f(x)

1 → -17

2 → -7

3 → -1

4 → 1

5 → -1

6 → -7

7 → -17

The function expressed using set notation can be presented as follows;

f(x) = {-17, -7, -1, 1, -1, -7, -17} where x ∈ {1, 2, 3, 4, 5, 6, 7}

A function is a rule that assigns a unique value for the output for each input value.

The specified function is; f(x) = -2·(x - 4)² + 1

Please find attached the graph of the parabola, created with MS Excel, which is a parabola that opens downwards, with a vertex of (4, 1)

The table of values can be presented as follows;

 x  |  f(x)

-----|------

 1  |  -17

 2  |   -7

 3  |   -1

 4  |    1

 5  |   -1

 6  |   -7

 7  |  -17

Mapping diagram:

A mapping diagram is a diagram that illustrates how an element of a set is paired with elements in another set.

The mapping diagram for the function can be made to show how the x-values are mapped to the f(x) values as follows;

1  →  -17

2  →   -7

3  →   -1

4  →    1

5  →   -1

6  →   -7

7  →  -17

Set notation;

The function, f(x) = -2·(x - 4)² + 1 can be expressed using set notation for the interval 1 ≤ x ≤ 7, which is the set of integers between 1 and 7, inclusive, which is presented as follows;

Set of x-values; {1, 2, 3, 4, 5, 6, 7}

Set of f(x) values is therefore; {-17, -7, -1, 1, -1, -7, -17}

Therefore, we get f(x) = -2·(x - 4)² + 1 expressed using set notation can be presented as follows;

f(x) = {-17, -7, -1, 1, -1, -7, -17}, where, x ∈ {1, 2, 3, 4, 5, 6, 7}

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