6. The Haley family orders a large pizza for
dinner.
The pizza has a circumference of 25.12 inches.
The radius of the pizza measures 4 inches.
Which of the following ratios relates the
circumference of the pizza to its diameter?

25.12
25.12
©
8
82
B
8
25.12
D
25.12
42

If 0.4 Customers arrives after 1 minute-

0.4*5 = 2.0 cm

From 1947 to 1987, Willowbrook State School served Staten Island's Willowbrook neighborhood as a state-funded facility for youngsters with intellectual disabilities. The school had 6,000 students enrolled by 1965 despite being intended for 4,000.

Aerts entered through the doors of Willowbrook State School in 1971 with former Staten Island Advance writer Jane Kurtin, and took disturbing photos of children and adults with special problems who were confined in cages, hungry, and used as research experiments.

Geraldo Rivera, who was working as an investigative reporter for WABC-TV in New York at the time, began an investigation into Willowbrook soon after and found a number of appalling circumstances there, including overcrowding and subpar sanitary facilities.

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The rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

What is volume?

Volume refers to the amount of three-dimensional space occupied by an object or a substance.

To find the rate of increase in the volume V of a sphere when the surface area S becomes 100π square inches, we need to use the formulas relating the surface area and volume of a sphere to its radius.

The surface area S of a sphere is given by the formula:

\(S = 4\pi r^2,\)

where r is the radius of the sphere.

The volume V of a sphere is given by the formula:

\(V = (4/3)\pi r^3.\)

To find the rate of increase in volume with respect to time, we need to differentiate the volume formula with respect to time.

Given that the radius r is increasing at a uniform rate of 0.3 inches per second, we can write:

dr/dt = 0.3 inches per second.

Now, let's differentiate the volume formula with respect to time:

\(dV/dt = d/dt [(4/3)\pi r^3].\)

Using the power rule of differentiation, we get:

\(dV/dt = (4/3)\pi * 3r^2 * (dr/dt).\)

Simplifying further, we have:

\(dV/dt = 4\pi r^2 * (dr/dt).\)

Since we want to find the rate of increase in cubic inches per second, we need to express the volume in cubic inches.

Substituting the value of the surface area S = 100π square inches into the surface area formula:

\(100\pi = 4\pi r^2.\)

Dividing both sides by 4π, we get:

\(r^2 = 25.\)

Taking the square root of both sides, we find:

r = 5.

Now, we can substitute the value of r into the rate of increase formula:

\(dV/dt = 4\pi(5^2) * (0.3).\)

Simplifying the expression:

dV/dt = 4π(25) * 0.3.

dV/dt = 30π cubic inches per second.

Therefore, the rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

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Answer:

this should be it

Step-by-step explanation:

Therefore , the solution of the given problem of speed comes out to be the average distance travelled is  225 meters.

We can determine how fast that anything is traveling by looking at it from a distance. The amount of distance an object can go in a given length of time depends on its speed. Velocity is calculated using the formula velocity = distance/time. The three most used units of speed are meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) (mph).

Here,

Given :

Time =  40 seconds.

To find the distance:

We use speed and time formula

=> distance = speed * time

=> distance = 15 * 30

=> distance =  225 meters.

Therefore , the solution of the given problem of speed comes out to be the average distance travelled is  225 meters.

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Answer:

C

Step-by-step explanation:

Since GJ bisects ∠ FGH , then ∠ FGJ = ∠ JGH = x + 14

∠ FGH = ∠ FGJ + ∠ JGH , substitute values

4x + 16 = x + 14 + x + 14 = 2x + 28 ( subtract 2x from both sides )

2x + 16 = 28 ( subtract 16 from both sides )

2x = 12 ( divide both sides by 2 )

x = 6

Thus

∠ FGJ = x + 14 = 6 + 14 = 20° → C

The exact behavior and consequences depend on the Operations system's process management mechanisms and the actions taken by process z or the system's process manager.

When process y dies, the Operations system handles the termination of the process and performs certain actions related to its termination. Here are the likely outcomes when process y, with process x as its child and process z as its parent, dies:

1. Process y's termination: When process y dies, the operating system marks it as terminated and frees up any system resources that were allocated to it. This includes releasing memory, closing file descriptors, and removing its entry from the process table.

2. Parent-child relationship: Since process x is the child of process y, the operating system updates the parent-child relationship. Typically, when a parent process dies, the child process is reassigned to another process called the init process or is terminated if no other process adopts it. The exact behavior depends on the operating system's process management policies.

3. Process z's status: Process z, being the parent of process y, may receive a notification or a signal indicating the termination of its child process. The operating system usually sends a SIGCHLD signal to the parent process, allowing it to handle the termination of its child process appropriately. Process z can choose to ignore the signal or perform actions such as cleaning up resources or spawning a new child process to replace the terminated one.

4. Orphaned process: If process z does not handle the termination of process y appropriately or if process z itself terminates before process y, process x becomes an orphaned process. Orphaned processes are typically adopted by the init process or the system's process manager, ensuring that they are handled and terminated properly.

In summary, when process y dies, the operating system marks it as terminated, updates the parent-child relationship, and may notify process z. The exact behavior and consequences depend on the operating system's process management mechanisms and the actions taken by process z or the system's process manager.

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The formula for calculation of circumference of the circle = d π or 2πr where d is diameter of circle and r is the radius of circle

As given in the question the circumference of the circle whose diameter is 2 cm is 6.28cm and we come to know that value of π used here is 3.14 and not 22/7

So, the circumference of the circle whose diameter is 1cm = d π

              = 1 π

            = 1 3.14

                                                                                          = 3.14 cm

Hence the circumference of the circle whose diameter is 1cm using the value of pi as 3.14 comes out to be pi that is 3.14 cm

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Answer:

$12.50

Step-by-step explanation:

100%-20% -> $10

80% -> $10

100% -> \(\frac{100}{80}\) × $10 = $12.50

Answer:

The original price was $12

Answer:

3 minutes

Step-by-step explanation:

The most effective chunking of the digit sequence 14929111776 would depend on the purpose of chunking.

However, a possible effective chunking could be 14-92-91-11-77-6, which groups the digits into pairs or triplets based on their similarity or pattern. Another possible chunking could be 1492-911-1776, which separates the digits based on significant historical events. Ultimately, the effectiveness of chunking would depend on the context and intended use of the sequence. The most effective chunking of the digit sequence 14929111776 would be to group the numbers into smaller, manageable chunks. One possible way to chunk the sequence is: 149-29-11-17-76. This breaks the sequence into five groups, making it easier to remember and process.

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To find the height of a triangle using trigonometry, you can use the sine or cosine ratios. The specific ratio to use depends on the information you have about the triangle.

If you have the length of one side of the triangle and the measure of the angle opposite that side, you can use the sine ratio to find the height. The sine ratio is defined as the length of the side opposite the angle divided by the length of the hypotenuse.

Here are the steps to find the height using the sine ratio:

1. Identify the side of the triangle that represents the height.
2. Determine the angle opposite that side.
3. Measure the length of the side adjacent to the angle or obtain that information from the problem.
4. Use the sine ratio: height = length of adjacent side * sin(angle).

For example, let's say you have a right triangle with an angle of 30 degrees and a side adjacent to that angle measuring 6 units. To find the height, you would use the sine ratio:

height = 6 * sin(30)
height ≈ 3 units

If you have the length of two sides of a right triangle and you need to find the height, you can use the cosine ratio. The cosine ratio is defined as the length of the side adjacent to the angle divided by the length of the hypotenuse.

Here are the steps to find the height using the cosine ratio:

1. Identify the side of the triangle that represents the height.
2. Determine one of the acute angles of the triangle.
3. Measure the lengths of the two sides adjacent to that angle or obtain that information from the problem.
4. Use the cosine ratio: height = length of adjacent side * cos(angle).

For example, let's say you have a right triangle with an angle of 45 degrees and two sides adjacent to that angle measuring 4 units and 4√2 units. To find the height, you would use the cosine ratio:

height = 4 * cos(45)
height ≈ 2.828 units

In summary, to find the height of a triangle using trigonometry, you can use the sine or cosine ratios. The sine ratio applies when you have the length of one side and the angle opposite that side, while the cosine ratio applies when you have the lengths of two sides adjacent to an angle.

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To calculate the derivative of the function f(x) = x + 9x² + 4, we can apply the power rule for differentiation. The power rule states that if we have a term of the form ax^n, then the derivative is given by nx^(n-1).

Let's calculate the derivative f'(x):

f(x) = x + 9x² + 4

To find f'(x), we differentiate each term:

The derivative of x is 1.

The derivative of 9x² is 18x (applying the power rule, where n = 2 and the derivative is 2 * 9x^(2-1) = 18x).

The derivative of 4 is 0 (as it is a constant term).

Adding up the derivatives of each term, we get:

f'(x) = 1 + 18x + 0

Simplifying the expression, we have:

f'(x) = 1 + 18x

Now, let's calculate the second derivative f''(x). To do this, we differentiate the derivative f'(x) with respect to x:

f'(x) = 1 + 18x

Differentiating each term, we get:

The derivative of 1 is 0 (as it is a constant term).

The derivative of 18x is 18 (as the derivative of a constant times x is the constant).

Therefore, the second derivative f''(x) is:

f''(x) = 0 + 18

Simplifying, we have:

f''(x) = 18

Now let's analyze the intervals where the function f(x) is increasing or decreasing by examining the signs of the first derivative f'(x).

For f'(x) = 1 + 18x, we set it equal to zero to find critical points:

1 + 18x = 0

18x = -1

x = -1/18

Since the first derivative f'(x) = 1 + 18x is a linear function, it is always increasing. Therefore, f(x) is increasing on the entire real number line (-∞, ∞).

Similarly, the second derivative f''(x) = 18 is a positive constant, indicating that the function is concave up on the entire real number line (-∞, ∞).

In conclusion, the function f(x) = x + 9x² + 4 is increasing on the interval (-∞, ∞) and is concave up on the interval (-∞, ∞).

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Answer: g*5 + b*10 ≥ 50.

Step-by-step explanation:

Let's define g = number of rings that land in green boxes.

and b = number of rings that land in blue boxes.

For each ring in the green box you earn 5 points, then if there are g rings in the green box, you have g*5 points.

And for the blue is similar, if there are b rings in the blue box, you will have b*10 points.

Then the total number of points that you will get is:

T = g*5 + b*10.

And the minimum that you need to win is 50 points, the inequality will be:

T ≥ 50

or

g*5 + b*10 ≥ 50.

Answer:

\( \frac{x}{4} + \frac{1}{2} = \frac{1}{8} \)

\( \frac{x}{4} = - \frac{3}{8} \)

\(x = - \frac{3}{2} = - 1 \frac{1}{2} \)

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

Consider the equation, we have only one x term, so taking all the terms without x to the other side and terms with x on one side.

x/4 + 1/2 = 1/8

Take the 1/2 term on the other side,

x/4=1/8 - 1/2

Taking the LCM on the Right side,

x/4 = (1-4) / 8

x/4 = -3/8

Now, we have x/4 so what we can do is, shift the 4 to the other side too, we get,

x = ( -3/8) * 4

x = -3/2

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

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Answer:

1. The value of x is 9.4.

2. The value of y is 17.7.

Step-by-step explanation:

The following data were obtained from the question:

Angle θ = 32°

Hypothenus = y

Opposite = x

Adjacent = 15

1. Determination of the value of x.

The value of x can be obtained as follow:

Angle θ = 32°

Opposite = x

Adjacent = 15

Tan θ = Opposite /Adjacent

Tan 32° = x/15

Cross multiply

x = 15 × Tan 32°

x = 9.4

Therefore, the value of x is 9.4

2. Determination of the value of y.

The value of y can be obtained as follow:

Angle θ = 32°

Hypothenus = y

Adjacent = 15

Cos θ = Adjacent /Hypothenus

Cos 32° = 15/y

Cross multiply

y × Cos 32° = 15

Divide both side by Cos 32°

y = 15/Cos 32°

y = 17.7

Therefore, the value of y is 17.7.

The probability that he gets at least as many heads as tails is half or 50%.

Probability is obtained by dividing the number of chances that it will take to realize a result by the number of total possible chances. To get the right probability for the question asked here, we need to determine:

The number of chances is equal to 4.

The total number of possible chances is given by the equation:

4 × 2 = 8

Two is obtained by recognizing the fact that there are two sides to the coin. So, he could either get a head or a tail when he tosses the nickel.

Therefore;

4/8 = 1/2 or 50%

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Answer:

Option C will be your answer

Step-by-step explanation:

hope it helps

have a great day

Answer:

The answer would be C

Step-by-step explanation

The value of the given trigonometric function cot(π/9) using the cotangent and the unit circle is 2.7475.

For the value of the trigonometric function cot(π/9), we need to understand the properties of the cotangent and the unit circle.

The cotangent function is defined as the ratio of the adjacent side to the opposite side of a right triangle. In terms of sine and cosine, cotangent can be expressed as cot(θ) = cos(θ) / sin(θ).

To find the value of cot(π/9), we can use the unit circle. The unit circle is a circle with a radius of 1, and it helps us visualize the trigonometric functions for angles.

In the unit circle, the angle π/9 is a reference angle of 20 degrees. By drawing a right triangle within the unit circle, we can determine the values of sine and cosine for this angle.

For the angle π/9, the cosine (adjacent side) can be found by taking the x-coordinate of the corresponding point on the unit circle, which is cos(π/9) = 0.9397.

Similarly, the sine (opposite side) can be found by taking the y-coordinate of the corresponding point on the unit circle, which is sin(π/9) = 0.3420.

Now, we can substitute the values of cosine and sine into the cotangent formula:

cot(π/9) = cos(π/9) / sin(π/9) = 0.9397 / 0.3420 ≈ 2.7475.

Therefore, the value of cot(π/9) is approximately 2.7475.

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Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Answer:

Vertical angles.

Step-by-step explanation:

Both c. f is continuous on the interval [-2,3], where f(-2)=0 and f(3)=20 and d. f is continuous on the interval [-2,3], where f(-2)=15 and f(3)=30 options are correct. given below is the explanation of the result.

using Intermediate value theorem:(statement: suppose that f∈c[a,b] and f(a)≠f(b) then given a number λ lies between f(a) and f(b) there exist a point c ∈(a,b) such that f(c)=λ)

know according to the Intermediate value theorem both option c and d are correct here because either f(a)<f(b) for a number λ lies between f(a) and f(b) there exist a point c ∈(a,b) such that f(c)=λ) here if we take  interval [-2,3], where f(-2)=0 and f(3)=20 the theorem is applicable. if we have f(a)>f(b) for a number λ lies between f(a) and f(b) there exist a point c ∈(a,b) such that f(c)=λ so if we take the interval [-2,3], where f(-2)=15 and f(3)=30,the above stated theorem is applicable.

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Answer: part(1) = 3:7            part(2) =  part to whole

Step-by-step explanation:

p1 = you just put the three red pints against all of pints added up together

p2 = this ratio would be called part to whole, as it is part of the ratio against the whole ratio.

Answer:

29/12=2.41666667

..................=2.33333333

.......................=2.58

second

Step-by-step explanation:

Answer:

B and D both lead to failure. I have no idea how to pick which one is right. I guess D but don't be surprised if it is B. The question tries to do too much.

D

Step-by-step explanation:

No.

You need one more fact.

You can't pick A. Angles are not noted.

B: there is no mention of parallel sides. This is why the proposition fails to give a parallelogram.

C: you haven't got both sides being parallel. You haven't even got one set of opposite sides being parallel

D: This is probably another alternative. You don't know anything about 1 set of opposite sides.

E: No angles are marked.

Distribute coefficients and simplify, isolate variables and solve for them. The solution is x = 9.

Equations are mathematical statements that assert the equality between two expressions. In other words, equations express that two things are equal. They usually contain one or more variables, which are letters or symbols that represent unknown values. The equations provide a way to relate these unknowns to each other and to known values, making it possible to solve for the unknowns.

To solve the equation 4(x-9)+2(x-3)=12, you need to simplify each side of the equation by distributing the coefficients of the parentheses and combining like terms.

The first step would be to distribute the 4 and 2 coefficients:

4(x-9) + 2(x-3) = 12

4x - 36 + 2x - 6 = 12

Then you can combine like terms on each side of the equation:

6x - 42 = 12

Next, you need to isolate the variable (x) by adding 42 to both sides:

6x = 54

Finally, you can solve for x by dividing both sides by 6:

x = 9

the solution to the equation is x = 9.

Therefore, Distribute coefficients and simplify, isolate variables and solve for them. The solution is x = 9.

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The table that have a constant of proportionality between y and x of 12 is the first table

From the question, we have the following parameters that can be used in our computation:

The table of values

From the first table of values, we have the following readings

(x, y) = (1/2, 6), (2, 24) and (10, 120)

Using the above as a guide, we have the following:

The constant of proportionality between y and x in the graph is

k = y/x

Substitute the known values in the above equation, so, we have the following representation

k = 6/(1/2) = 24/2 = 120/10

Evaluate

k = 12 = 12 = 12

Hence, the constant of proportionality between y and x in the first table is 12

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Complete question

Which table has a constant of proportionality between y and x of 12?

x          1/2               2             10

y           6                24          120

x          1/4               3             12

y           3                60          144

x          1/3               6             9

y           4                78          117

Answer:

(4,3)

Step-by-step explanation:

Solve the equation:

3<2(4)-5

3<8-5

❌3<3 ❌

3 is not less than three, hence this is the phony

i hope this helps!