The circle below is centered at (4,-1) and has a radius of 3. What is it’s equation?

The perimeter and the area of each composite figure are, respectively:

Case 10: Perimeter: p = 16 + 8√2, Area: A = 24

Case 12: Perimeter: p = 28, Area: A = 32

Case 14: Perimeter: p = 6√2 + 64 + 3π , Area: A = 13 + 9π

In this question we find three composite figures, whose perimeter and area must be found. The perimeter is the sum of all side lengths, while the area is the sum of the areas of simple figures. The length of each line is found by Pythagorean theorem:

r = √[(Δx)² + (Δy)²]

The perimeter of the semicircle is given by following formula:

s = π · r

And the area formulas needed are:

Rectangle

A = w · l

Triangle

A = 0.5 · w · l

Semicircle

A = 0.5π · r²

Where:

Now we proceed to determine the perimeter and the area of each figure:

Case 10

Perimeter: p = 2 · 8 + 4 · √(2² + 2²) = 16 + 8√2

Area: A = 4 · 0.5 · 2² + 4² = 8 + 16 = 24

Case 12

Perimeter: p = 2 · 4 + 4 · 2 + 4 · 2 + 2 · 2 = 8 + 8 + 8 + 4 = 28

Area: A = 4 · 6 + 2 · 2² = 24 + 8 = 32

Case 14

Perimeter: p = 2√(3² + 3²) + 2 · 2 + 2 · 2 + 2 · 2 + π · 3 = 6√2 + 64 + 3π

Area: A = 2 · 0.5 · 3² + 2² + π · 3² = 9 + 4 + 9π = 13 + 9π

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Answer:

The answer is 1.25 km = 1,250

                       1.7 cm =17 mm

                       345 m = 0.345 km K12 test.

Step-by-step explanation:

The answer is 1.25 km = 1,250

                      1.7 cm =17 mm

                      345 m = 0.345 km K12 test.

Answer:

about +–1%; between 46.5% and 47.5%

Step-by-step explanation:

The shooting method is a numerical technique used to solve differential equations with specified boundary conditions. In this case, we will apply the shooting method to solve the second-order differential equation \(7d^2y/dx^2 - 2dy/dx - yx = 0\) with the boundary conditions y(0) = 5 and y(20) = 8.

To solve the given differential equation using the shooting method, we will convert the second-order equation into a system of first-order equations. Let's introduce a new variable, u, such that u = dy/dx. Now we have two first-order equations:

dy/dx = u

du/dx = (2u + yx)/7

We will solve these equations numerically using an initial value solver. We start by assuming a value for u(0) and integrate the equations from x = 0 to x = 20. To satisfy the boundary condition y(0) = 5, we need to choose an appropriate initial condition for u(0).

We can use a root-finding method, such as the bisection method or Newton's method, to adjust the initial condition for u(0) until we obtain y(20) = 8. By iteratively refining the initial guess for u(0), we can find the correct value that satisfies the second boundary condition.

Once the correct value for u(0) is found, we can integrate the equations from x = 0 to x = 20 again to obtain the solution y(x) that satisfies both boundary conditions y(0) = 5 and y(20) = 8.

The shooting method involves converting the given second-order differential equation into a system of first-order equations, assuming an initial condition for the derivative, and iteratively adjusting it until the desired boundary condition is satisfied.

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Answer: 320 meters cubed

Step-by-step explanation: Take half of the base for the triangle(being 4 m), multiply 4 and 8 (32 m squared), and multiply 32 by 10, which results in 320 meters cubed.

Answer:

No, it will be less than 15.1

Step-by-step explanation:

It will be less than 15.1 because you are multiplying 15.1 by a number that is less than 1, so the product will be less than 15.1.

The phrases "how does it take over a complete being in a single, momentary look" are used to describe who feels for the other more in the relationship, they say. As a result, choice D is right.

I experience momentary emotions at any particular time. It's essential for me to acknowledge that bad emotions exist when they do. and to pay close attention to them. That helps me better manage these emotions.

When a switch is activated and the button removed, the switch performs a brief action and then returns to its original state.

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The correct question is:

How do the phrases "how does it take over an entire being in a single, momentary glance", "not only beloved by the gods but also beloved by me, Ariadne", and "together as one being for all eternity" impact the meaning of the story?

(A) They describe how quickly Ariadne and Theseus fell in love.

(B) They explain how Ariadne was the one who initiated the relationship.

(C) They emphasize how Ariadne is easily overcome by feelings of love.

(D) They explain who cares more for the other in the relationship.

The person has walked a total of 28 miles. To calculate total distance walked by the person, we add up the distances in each direction

5 miles East + 6 miles Southeast + 6 miles South + 7 miles Southwest + 4 miles East

When we add these distances together, we get:

5 + 6 + 6 + 7 + 4 = 28

Therefore, the person has walked a total of 28 miles.

In more detail, let's break down the distances walked in each direction:

- 5 miles East: This means the person walked 5 miles in the East direction.

- 6 miles Southeast: This means the person walked 6 miles in the direction that is both South and East.

- 6 miles South: This means the person walked 6 miles in the South direction.

- 7 miles Southwest: This means the person walked 7 miles in the direction that is both South and West.

- 4 miles East: This means the person walked 4 miles in the East direction.

By adding up these distances, we find that the person has walked a total of 28 miles.

#A person starts walking from home and walks: 5 miles East 6 miles Southeast 6 miles South 7 miles Southwest 4 miles East This person has walked a total of ---miles

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Answer:

-4

Step-by-step explanation:

12/-3=-4

The given matrix A is a 2x2 matrix.

First, we find the characteristic polynomial by taking the determinant of the matrix A minus λ times the identity matrix I:

|A - λI| =

|1-λ 2 |

| 3 2-λ| = (1-λ)(2-λ) - 2(3) = λ^2 - 3λ - 4

Thus, the characteristic polynomial of A is λ^2 - 3λ - 4.

Next, we find the eigenvalues of A by solving the characteristic polynomial:

λ^2 - 3λ - 4 = 0

(λ - 4)(λ + 1) = 0

Thus, the eigenvalues of A are λ1 = 4 and λ2 = -1.

To find the eigenvectors, we solve the system of linear equations (A - λI)x = 0 for each eigenvalue.

For λ1 = 4, we have:

(1-4)x1 + 2x2 = 0

3x1 - 2x2 = 0

Solving this system, we get the eigenvector x1 = [2, 3] (or any non-zero scalar multiple of it).

For λ2 = -1, we have:

(1+1)x1 + 2x2 = 0

3x1 + 2+1x2 = 0

Solving this system, we get the eigenvector x2 = [-1, 3] (or any non-zero scalar multiple of it).

To find an invertible matrix P such that P^-1 AP is diagonal, we construct the matrix P using the eigenvectors x1 and x2 as its columns. That is,

P = [2 -1; 3 3]

We can verify that P is invertible by calculating its determinant:

|P| = (2)(3) - (-1)(3) = 9

Since |P| is non-zero, P is invertible.

Then, we calculate P^-1:

P^-1 = (1/9)[3 1; -3 2]

Finally, we can check that P^-1 AP is diagonal:

P^-1 AP = (1/9)[3 1; -3 2][1 2; 3 2][2 -1; 3 3]

= (1/9)[12 0; 0 -1][2 -1; 3 3]

= [8/3 -4/3; -3 1]

Thus, we have found the characteristic polynomial, eigenvalues, eigenvectors, and invertible matrix P such that P^-1 AP is diagonal.

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There is no significant difference in the proportion of college enrollees between females and males who have completed high school within the past 12 months.

To determine if the difference in proportions is statistically significant or if it could be due to chance.

We will conduct a hypothesis test. Our null hypothesis (H₀) is that there is no difference in the proportion of college enrollees between females and males. Our alternative hypothesis (H₁) is that there is a difference in the proportion of college enrollees between females and males.

We can use a two-sample z-test to test this hypothesis. The formula for the test statistic is:

z = (p₁ - p₂) / √(p'* (1 - p') * ((1 / n₁) + (1 / n₂)))

where p₁ and p₂ are the sample proportions, p' is the pooled proportion, n₁ and n₂ are the sample sizes.

Given, p₁ = 0.72, p₂ = 0.65, n₁ = 175, n₂ = 160

p' = (x₁ + x₂) / (n₁ + n₂)

x₁ = 126 (0.72 * 175) and x₂ = 104 (0.65 * 160).

p' = (126 + 104) / (175 + 160) = 0.684

By applying the above values we get,

z = (0.72 - 0.65) / √(0.684 * (1 - 0.684) * ((1 / 175) + (1 / 160))) ≈ 2.11

The critical value for a two-tailed test with alpha = 0.01 is approximately ±2.58. Since our calculated z-value (2.11) is less than the critical value, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that there is a significant difference in the proportion of college enrollees between females and males.

Therefore, there is no significant difference in the proportion of college enrollees between females and males who have completed high school within the past 12 months.

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Answer: \(2\sqrt{22}\)

Step-by-step explanation:

Pythagorean theorem: \(a^{2} +b^{2} = c^{2}\), where a and b are the legs and c is the hypotenuse.

We can solve for x by only using the left side of the triangle. Since we're only using the left side of the triangle, we can reduce 18 by 2 to get 9. Now we plug in our information to the equation.

\(9^{2} +b^{2} = 13^{2}\)

\(81 +b^{2} = 169\)

Since we don't know what \(b^{2}\) is, we're going to isolate it by subtracting 81 on both sides

\(b^{2} = 88\)

We have to square root both sides in order to find out b (or x in the problem).

\(\sqrt{b^{2}} = \sqrt{88}\)

When you put this on a calculator it would result in \(2\sqrt{22}\) which is the answer d in the problem.

Answer:

Obtuse Triangle.

Step-by-step explanation:

If you search it up, you will see, and I hope that this helps! <3

Answer:

An obtuse triangle.

Step-by-step explanation:

An obtuse triangle has one obtuse angle. It must also have two acute angles because of the triangle sum theorem.

Hope this helps.

The probability of selecting randomly household having less than two cars is given by option b. 0.553.

To find the probability of randomly selecting a household that has less than two cars,

Calculate the probability for the values of the random variable x that are 0 or 1.

The total number of households in the town is given as 1000.

The number of households with 0 or 1 car is the sum of the frequencies for x = 0 and x = 1,

Number of households with 0 or 1 car

= 125 + 428

= 553

To find the probability, we divide the number of households with 0 or 1 car by the total number of households,

Probability of randomly selecting a household with less than two cars

= Number of households with 0 or 1 car / Total number of households

= 553 / 1000

= 0.553

Therefore, the probability of household having less than two cars is option b. 0.553.

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Answer: don't no

Step-by-step explanation:

To draw the horizontal alignment for the curve on that shape on 12D, follow these steps:

Step 1: First of all, we have to determine the horizontal alignment for the curve. The horizontal alignment consists of a series of tangents, curves, and spirals.

Step 2: After that, we have to select the appropriate curve radius for the design speed, the superelevation, and the allowable sight distance.

Step 3: Next, plot the vertical curves with the curve layout. A design speed of 50 mph and a curve radius of 1200 ft will be used in this example.

Step 4: Next, we have to calculate the curve length using the formula Lc = Rθ. Here, Lc is the curve length, R is the radius, and θ is the curve angle. In this case, the curve angle is 4 degrees, so the curve length will be 83.775 ft.

Step 5: Then, we will plot the curve using a tangent-tangent-radius (TTR) method. The TTR method involves drawing a tangent to the curve's point of intersection, then drawing another tangent to the next point of intersection, and finally drawing the curve's arc with the given radius. This process is repeated until the curve's entire length is completed.

Step 6: Finally, label the horizontal and vertical curves, including the stationing and curve radius.

That's how we draw the horizontal alignment for the curve on that shape on 12D.

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To solve this problem both units must have the same units.

So, let's convert quarts to gallons

1 quart ----------------------- 0.25 gallon

34 quarts -------------------- x

x = (34 x 0.25) / 1

x = 8.5 gallons

8.5 gallons or 34 quarts > 8 gallons

The changes in weights (b) did not affect the decision as Worldwide Delivery remained the most suitable provider. However, the increase in ratings for Overnight Shipping (c) resulted in it becoming the most suitable outsourcing provider according to the given criteria.

1) Factor rating
2) Outsourcing provider
3) Logistics services
4) Weights
5) Ratings

a) Factor rating is a method used to evaluate and select an outsourcing provider based on predetermined criteria. In this case, Fernando Garza's firm wants to select a logistics services provider using factor rating. The table provided includes the weights assigned to different criteria (quality, delivery, and cost) and the ratings of three potential providers (Overnight Shipping, Worldwide Delivery, and United Freight).

To make his decision, Garza needs to multiply the weight of each criterion by the rating of each logistics provider and sum up the results. The highest sum indicates the most suitable outsourcing provider. Let's calculate the results:

Overnight Shipping:
Quality: 5 (weight) x 90 (rating) = 450
Delivery: 3 (weight) x 70 (rating) = 210
Cost: 2 (weight) x 70 (rating) = 140
Total: 450 + 210 + 140 = 800

Worldwide Delivery:
Quality: 5 (weight) x 80 (rating) = 400
Delivery: 3 (weight) x 85 (rating) = 255
Cost: 2 (weight) x 80 (rating) = 160
Total: 400 + 255 + 160 = 815

United Freight:
Quality: 5 (weight) x 75 (rating) = 375
Delivery: 3 (weight) x 70 (rating) = 210
Cost: 2 (weight) x 95 (rating) = 190
Total: 375 + 210 + 190 = 775

Based on these calculations, Worldwide Delivery has the highest total score of 815, making it the most suitable outsourcing provider according to the given criteria.

b) Garza decides to increase the weights for quality, delivery, and cost to 10, 6, and 4, respectively. This change means that Garza now considers quality to be twice as important as before, delivery to be 1.5 times as important, and cost to be twice as important.

Let's recalculate the results with the updated weights:

Overnight Shipping:
Quality: 10 (weight) x 90 (rating) = 900
Delivery: 6 (weight) x 70 (rating) = 420
Cost: 4 (weight) x 70 (rating) = 280
Total: 900 + 420 + 280 = 1600

Worldwide Delivery:
Quality: 10 (weight) x 80 (rating) = 800
Delivery: 6 (weight) x 85 (rating) = 510
Cost: 4 (weight) x 80 (rating) = 320
Total: 800 + 510 + 320 = 1630

United Freight:
Quality: 10 (weight) x 75 (rating) = 750
Delivery: 6 (weight) x 70 (rating) = 420
Cost: 4 (weight) x 95 (rating) = 380
Total: 750 + 420 + 380 = 1550

With the updated weights, the new results show that Worldwide Delivery still has the highest total score of 1630, making it the most suitable outsourcing provider.

c) If Overnight Shipping's ratings for each of the factors increase by 10%, we need to recalculate the results while considering these changes.

Overnight Shipping:
Quality: 10 (weight) x (90 + 10% of 90) = 990
Delivery: 6 (weight) x (70 + 10% of 70) = 462
Cost: 4 (weight) x (70 + 10% of 70) = 308
Total: 990 + 462 + 308 = 1760

With the increased ratings, Overnight Shipping now has the highest total score of 1760, making it the most suitable outsourcing provider.

In summary, the changes in weights (b) did not affect the decision as Worldwide Delivery remained the most suitable provider. However, the increase in ratings for Overnight Shipping (c) resulted in it becoming the most suitable outsourcing provider according to the given criteria.

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The length of ribbon is still left is 3.35m .

To find out how much ribbon is still left, we need to subtract the length that was shortened from the original length of the ribbon.

First, we need to convert the shortened length from decimeters (dm) to meters (m), since the original length of the ribbon is given in meters. To convert from decimeters to meters, we divide by 10:

=> 23 dm ÷ 10

=> 2.3 m

Now that both lengths are in meters, we can subtract the shortened length from the original length:

=> 5.65 m - 2.3 m

=> 3.35 m

So, 3.35 meters of ribbon is still left.

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Answer:

f(3) = 7

Step-by-step explanation:

Using the recursive formula and f(1) = - 3 , then

f(2) = f(1) + 5 = - 3 + 5 = 2

f(3) = f(2) + 5 = 2 + 5 = 7

The domain of f(x) = x² + 3 and its inverse function g(x) = √(x - 3) are:

The domain of f(x): all real numbers

Range of f(x): all real numbers greater than or equal to 3

The domain of g(x): all real numbers greater than or equal to 3

Range of g(x): all real numbers greater than or equal to 0

The domain of the function f(x) = x² + 3 is all real numbers since any real number can be squared and added to 3. The range of the function is all real numbers greater than or equal to 3 since the square of any real number is non-negative, and adding 3 to a non-negative number gives a result that is greater than or equal to 3.

To find the domain and range of the inverse function of the given function, we first have to find the inverse function. To do this, we solve the equation y = x² + 3 for x:

x² = y - 3

x = ±√(y - 3)

Since the function f(x) = x² + 3 is not one-to-one (it fails the horizontal line test), we need to restrict its domain to find an inverse function. One way to do this is to restrict the domain to non-negative values of x, which gives us the function g(x) = √(x - 3).

The domain of g(x) is all real numbers greater than or equal to 3 since the square root of a non-negative number is always defined. Since the square root of a non-negative number is always non-negative, the range of g(x) includes all real numbers greater than or equal to 0.

Therefore, the domain of f(x) = x² + 3 and its inverse function g(x) = √(x - 3) are:

The domain of f(x): all real numbers

Range of f(x): all real numbers greater than or equal to 3

The domain of g(x): all real numbers greater than or equal to 3

Range of g(x): all real numbers greater than or equal to 0

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Answer:

I will use the notation:

Cube1 + Cube2 = sum.

Ok, each number cube has 6 options, so the total number of possible combinations is equal to the product of the number of options for each event we have two events (two number cubes).

Then:

C = 6*6 = 36

we have 36 possible combinations.

Now, let's look at the sums that have the same number of combinations (which would mean that have the same number of combinations).

For example, the lower result possible is two ones:

1 + 1 = 2

(only one outcome adds up to 2)

And the maximum result possible is two sixes:

6 + 6 = 12

(only one outcome adds up to 12)

Then 2 and 12 have the same probability, 1/36.

Now we can keep loking at 2 + 1 and 12 - 1.

2 + 1 = 3

The outcomes that add up to 3 are:

1 + 2 = 3

2 + 1 = 3

(two outcomes out of 36)

12 - 1 = 11

The outcomes that add up to 11 are:

6 + 5 = 11

5 + 6 = 11

(Two outcomes out of 36)

Then 3 and 11 have the same probability, 2/36.

And we can notice the pattern here.

4 and 10 will have the same probability 3/36

5 and 9 will have the same probability 4/36

6 and 8 will have the same probability 5/36

7 is the only option that does not have a pair, the probability is 6/36.

Answer:

1

Step-by-step explanation:

Answer:

100-47=53 so 53$ profit

Step-by-step explanation:

Answer:

10.6

Step-by-step explanation:

Pythagorean theorem: a² + b² = c²

Where a and b = the legs and c = hypotenuse

We are given two legs and need to find the hypotenuse

Given:

Short leg (a) = 7

Long leg (b) = 8

Hypotenuse = c

Now to find the value of c we simply plug in the values of the variables into the Pythagorean theorem and solve for c

Pythagorean theorem: a² + b² = c²

a = 7, b = 8, c = c

Plug in values

7² + 8² = c²

Now solve for c

Simplify exponents

49 + 64 = c²

Add

113 = c²

Taking the square root of both sides

c = 10.6 ( rounded to the nearest tenth )

Answer:

c = 10.6

Step-by-step explanation:

\(h {}^{2} = p {}^{2} + b {}^{2} \\ c {}^{2} = (8) {}^{2} + (7) {}^{2} \\ c = \sqrt{64 + 49} \\ c = \sqrt{113} \\c = 10.6\)

Answer:

lol easy its  5

Step-by-step explanation:

150 students scored between 42 and 56 on the district geometry test.

Box whisker plots are used to abstract a collection of data that has been approximated using an interval scale. Just a box plot is another name for it. They are mostly employed while interpreting data. It is one of the graphical approaches that shows how the dataset's data varies from one another. The histogram may be used to display the data as well. Yet a histogram offers a useful presentation. Box and whisker plots are preferable to histograms because they may exhibit numerous sets of data on a single graph, which adds more information.

From the box whisker plot we see that the lower quartile is 42 and the median is 56.

The median represents the 50th percentile whereas lower quartile is 75%.

The difference is:

75 - 50 = 25%.

Now, for 600 scores we have:

25% of 600

= 25/100 (600) = 150

Hence, 150 students scored between 42 and 56 on the district geometry test.

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