The volume of a sphere, V , is calculated

Answer:

.12500

Step-by-step explanation:

You gotta divide 12.5 by 100 since it would be 12.5 out of 100.

Answer:

  C. Dilation by 1/2, rotation 180°

Step-by-step explanation:

You want the sequence of transformations that moves ∆ABC to ∆DEF.

We note that the coordinates of corresponding points are ...

Comparing these, we find that D = (-1/2)·A.

The scale factor of -1/2 is equivalent to a dilation by a factor of 1/2 and reflection across the origin. Reflection across the origin is equivalent to a rotation of 180°.

The sequence of transformations that moves ∆ABC to ∆DEF is ...

  C.  A dilation by a factor of 1/2 centered at the origin, followed by a 180° clockwise rotation about the origin.

__

Additional comment

The direction of rotation is irrelevant when the rotation angle is 180°. When the center of dilation is unspecified, it is assumed to be the origin.

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Answer:

y=-7x-3

Step-by-step explanation:

1. Parallel lines have the same slope, so the number that goes in front of x is -7.

2. To find the second number, you need to get the y-intercept by putting the equation into point-slope form and then converting that to y=mx+b format.

Point-slope form:

y-y1=m(x-x1).

m represents the slope, y1 represents the y-value in the ordered pair, and x1 represents the x-value of the ordered pair. Plug these numbers into the equation.

y-32=-7(x+5)

Convert to y=mx+b:

Distribute -7 to x + 5

y-32=-7x-35

Add 32 to both sides

y=-7x-3

3. -3 is the y-intercept because in the equation y=mx+b is b.

The equation of the line in point-slope form and in​ slope-intercept form are both y = 1/2x.

1. Point-Slope Form: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

2. Slope-Intercept Form: y = mx + b, where m is the slope of the line and b is the y-intercept.

3. Standard Form: Ax + By = C, where A and B are coefficients that define the slope and y-intercept of the line.

If a line has a slope of 1/2 and passing through the origin, then:

m = 1/2

(x1, y1) = (0,0)

Plug in the values in the point-slope form and in​ slope-intercept form.

point-slope form

y - y1 = m(x - x1)

y - 0 = 1/2(x - 0)

y = 1/2x

slope-intercept form

y = mx + b

y = 1/2x + b

Substitute the values of x and y and solve for the y-intercept, b.

0 = 1/2(0) + b

b = 0

y = 1/2x + 0

y = 1/2x

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Answer:

A,B, and D!

Step-by-step explanation:

Hope this helps!! :))

we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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The calculated number of police cadets in the group is 25

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

Scouts = 8/13

Police cadets = the rest

This means that

Police cadets = 1 - 8/13

Evaluate

Police cadets = 5/13

Also, we have

Prefects = 3/8 or 15 of scouts

This means that

3/8 * Scouts = 15

Scouts = 40

So, we have

Total = 40/(8/13)

Total = 65

Recall that

Police cadets = 5/13

So, we have

Police cadets = 5/13 * 65

Evaluate

Police cadets = 25

Hence, the number of police cadets in the group is 25

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Combine like terms , we get \(g^3+3g^2+2g\).

In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions so that the result of the expression can be obtained very easily.

For example, 4x + 10x is an algebraic expression with like terms. In order to simplify this algebraic expression, we can add the like terms. Thus, the simplification of the given expression is 14x. In the same way, you can perform all the arithmetic operations on the like terms.

Collect like terms:

\(g^3+g^2+g+2g^2+g\)

Combine like terms:

\(g^3+3g^2+2g\)

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(a) Median is 660.15 (b) Mean is 660.07 (c) Standard Deviation is 1.543 (d) Variance is 2.3801.

To calculate the statistics for the given measurements, let's follow the steps:

(a) The median is the middle value when the measurements are arranged in ascending order.

657.9, 658.2, 659.3, 659.6, 659.8, 660.5, 661.7, 662.1, 662.2, 662.4

There are 10 measurements, so the median is the average of the 5th and 6th values:

Median = (659.8 + 660.5) / 2 = 660.15

(b) The mean is the average of all the measurements.

Mean = (658.2 + 659.8 + 661.7 + 662.1 + 659.3 + 660.5 + 657.9 + 662.4 + 659.6 + 662.2) / 10 = 660.07

(c) The standard deviation is a measure of the dispersion of the measurements around the mean.

First, we calculate the deviations of each measurement from the mean:

Deviation = Measurement - Mean

Then, we square each deviation and find the average:

Variance = [(\((Deviation1)^2\) + \((Deviation2)^2\) + ... + \((Deviation10)^2\)) / 10]

Finally, we take the square root of the variance to obtain the standard deviation:

Standard Deviation = \(\sqrt{Variance\)

Let's calculate it step by step:

Deviation1 = 658.2 - 660.07 = -1.87

Deviation2 = 659.8 - 660.07 = -0.27

Deviation3 = 661.7 - 660.07 = 1.63

Deviation4 = 662.1 - 660.07 = 2.03

Deviation5 = 659.3 - 660.07 = -0.77

Deviation6 = 660.5 - 660.07 = 0.43

Deviation7 = 657.9 - 660.07 = -2.17

Deviation8 = 662.4 - 660.07 = 2.33

Deviation9 = 659.6 - 660.07 = -0.47

Deviation10 = 662.2 - 660.07 = 2.13

Variance = [\((-1.87)^2\) + \((-0.27)^2\) + \(1.63^2\) + \(2.03^2\) + \((-0.77)^2\) + \(0.43^2\) + \((-2.17)^2\) + \(2.33^2\) + \((-0.47)^2\) + \(2.13^2\)) / 10] = 2.3801

Standard Deviation = \(\sqrt{2.3801\) = 1.543

(d) The variance is already calculated in step (c) as 2.3801.

Report:

(a) Median: 660.15

(b) Mean: 660.07

(c) Standard Deviation: 1.543

(d) Variance: 2.3801

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Answer:

Yes.

Step-by-step explanation:

The difference of two rational numbers is always a rational number because the numbers are always complete. There will never be a running number. Think of it as multiplying two positive numbers, you can never receive a negative from two positives.

Answer:

3.625

step by step explanation :

I  just simply searched it up

9514 1404 393

Answer:

Step-by-step explanation:

When Mai receives money, her account balance increases. The amount received can be represented by a positive number.

When Mai spends money, her account balance decreases. The amount spent can be represented by a negative number.

Answer:

Answer is below :)

Step-by-step explanation:

Hope this helps you!

In both cases, the triangle inequality theorem is used to justify the steps, which guarantees the validity of the inequalities.

|a + b| ≤ |a| + |b|

(a) Proving |x| < ε + |c|:

Given: |x - c| < ε

Adding |c| to both sides of the inequality, we have:

|x - c| + |c| < ε + |c|

Applying the triangle inequality to the left side of the inequality, we get:

|x - c + c| < ε + |c|

Simplifying the expression inside the absolute value, we have:

|x| < ε + |c|

Thus, we have proved that |x| < ε + |c|.

(b) Proving |c| - ε < |x|:

Given: |x - c| < ε

Subtracting |c| from both sides of the inequality, we have:

|x - c| - |c| < ε - |c|

Applying the triangle inequality to the left side of the inequality, we get:

|x - c - c| < ε - |c|

Simplifying the expression inside the absolute value, we have:

|x - 2c| < ε - |c|

Adding 2|c| to both sides of the inequality, we get:

|x - 2c| + 2|c| < ε - |c| + 2|c|

Applying the triangle inequality to the left side of the inequality, we have:

|x - 2c + 2c| < ε - |c| + 2|c|

Simplifying the expression inside the absolute value, we have:

|x| < ε + |c|

Rearranging the inequality, we get:

|c| - ε < |x|

Thus, we have proved that |c| - ε < |x|.

In both cases, the triangle inequality theorem is used to justify the steps, which guarantees the validity of the inequalities.

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The stream velocity has no influence on the amount of dissolved load it contains. The amount of dissolved material depends on erosion and deposition carried out in the watercourse. These are affected by factors such as the slope of the land, the resistance of the material to erosion, the size of the sediments transported, etc.

Stream velocity plays an important role in the transport of sediments and dissolved loads in a watercourse. It affects the erosion and deposition processes that occur in the watercourse, which in turn affect the amount of sediment and dissolved load that is carried by the stream. For example, faster stream velocities can cause more erosion of the stream bed, leading to more material being carried in the water.

Sediment is any particulate matter that is transported by a fluid, and it can come in many different forms. The three main types of sediment are:

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Answer:

244 if the difference

Step-by-step explanation:

Answer:

180º Fahrenheit

Answer: 40

Step-by-step explanation

if you look at the number 4 it says it = 10

Then you look at 6 and it = 15

then you look at 8 and it = 20

SO everytime you add 2 it goes up 5.

So if you take the 8 and add 2 that's 10 and 10=25

So when you make your way to 16 it would be 40.

What are the given conditions?

A student's probability of having a sister are 1/2 or 0.5 if they do not have a brother.

Using the above data table, we must determine the likelihood that a student without a brother also has a sister. Analysing the table now

has a sibling: 5

possesses no sisters: 2

has an 18-year-old brother

possesses no brothers: 4

We are looking for the likelihood that a student has a sister and neither a brother (as indicated by the statement "Does not have a brother"). In this instance, there are two children who do not have a brother but do have a sister, making that number the number of positive outcomes.

No matter whether a student has a sister or not, the total number of outcomes is equal to the number of students who do not have a brother. According to the table, there are 4 students without brothers.

As a result, the likelihood that a student who doesn't have a brother will have a sister can be determined as follows:

Probability is calculated as the ratio of the number of favourable outcomes to all possible outcomes.

Probability equals 2/4

Probability equals 0.5 or half.

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Answer:

it would take about 25 hours

The probability that the 3rd patient with heart failure that enters the emergency room is the first one due to outside factors is 0.02712.

Probability of natural occurrences = 0.82Probability of outside factors = 0.18To find the probability that the 3rd patient with heart failure that enters the emergency room is the first one due to outside factors, we have to consider two possibilities:

The first two patients are due to natural occurrences, or the first two patients are due to outside factors.If the first two patients are due to natural occurrences, the probability of the third patient being the first due to outside factors is:0.82 x 0.82 x 0.18 = 0.12272

If the first two patients are due to outside factors, the probability of the third patient being the first due to outside factors is:0.18 x 0.82 x 0.82 = 0.12272

Therefore, the total probability of the third patient being the first due to outside factors is the sum of these two probabilities:0.12272 + 0.12272 = 0.24544But, we have counted the case where all three patients have outside factors twice, so we need to subtract that probability once:0.24544 - 0.01836 = 0.22708

Therefore, the probability that the 3rd patient with heart failure that enters the emergency room is the first one due to outside factors is 0.22708 or approximately 0.02712.

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If a sequence is defined using previous terms, it is known as a recursively defined sequence.

This type of sequence relies on the previous terms to determine the next term in the sequence. The number of terms that are required to define a recursively defined sequence varies depending on the specific sequence. However, if the first few terms of the sequence are given, it can help determine the pattern and the formula used to generate subsequent terms. A good understanding of recursive sequences can be helpful in many areas, including computer programming, mathematics, and finance. A sequence that is defined using its initial terms and a rule relating its subsequent terms to the previous ones is called a recursively defined sequence. In such sequences, each term's value depends on one or more earlier terms. The first few terms serve as the basis, and the recursive formula generates the remaining terms. This approach allows us to find any term in the sequence based on previous ones, ensuring a consistent pattern and progression.

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The series to 10 term is

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512

An equation that represents a sequence based on a rule is called a recurrence relation.

Finding the following term, which is dependent upon the prior phrase, is made easier (previous term). We can readily predict the following term in a series if we know the preceding term.

The term is predicted by multiplying the preceding term by 2

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Answer:

the answer is c okay g;)

Step-by-step explanation:

hope this helps

Answer:c

Step-by-step explanation:the y has to be greater than -1 and x is just a longer negative y