3. Pi is defined as the ratio of the circumference of a circle to the diameter of that circle. Which of the following correctly explains why the formula for the circumference of a circle is 2 mr 7 (1 point)

Two times equals the distance from one side of the circle to the other. When you multiply that by r, you get the distance around the circle, or the circumference.

Pi times requals the diameter of the circle. The diameter is half the circle, so when you multiply it by 2, you get the distance around the entire circle, or the circumference.

Two times requals the diameter of the circle. Pi is needed for all circle formulas, so you multiply by since you are finding the circumference.

Two times requals the diameter of the circle. Pi equals the circumference divided by the diameter. When you multiply, the diameter is in both the numerator and the denominator, which cancels out, leaving the circumference.​

Answer:

7

Step-by-step explanation:

In an 30-60-90 right triangle, the longer leg is the shorter leg multiplied by [tex]\sqrt{3}[/tex]

So [tex]7\sqrt{3} =x*\sqrt{3[/tex]

[tex]7=x[/tex]

x=7

Answer:

A. 21

Step-by-step explanation:

This is a 30-60-90 triangle, where you have one 30° angle, one 60°, and one 90° (aka right) angle.  

The sides of a 30-60-90 triangle adhere to the following rules:

Since 7√3 is the length of the side opposite the 30° angle, the entire expression represents x.

Since the length of the side opposite the 60° angle is given by x * √3, the length of this side is (7√3)(√3).

Simplifying gives us 7*3, which is 21.

Thus, the value of x in the triangle is 21 (answer choice A.)

Answer:

[tex]\frac{3}{7}[/tex] <  [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

[tex]\frac{3}{7}[/tex] ? [tex]\frac{3}{5}[/tex]

We have to get both fractions with the same denominator to compare them.

[tex]\frac{3}{7}[/tex] = [tex]\frac{15}{35}[/tex]

[tex]\frac{3}{5}[/tex] = [tex]\frac{21}{35}[/tex]

[tex]\frac{15}{35} < \frac{21}{35}[/tex]

So, [tex]\frac{3}{7}[/tex] <  [tex]\frac{3}{5}[/tex]

Answer:

21 - 12p

Step-by-step explanation:

I hope this helps and I'm super sorry if I'm wrong!

Answer:

None of the given options (A, B, C, D) match the correct investment amount.

Explaination:

A = P * e^(rt),

where:

A = the future amount (in this case, $34,000),

P = the principal amount (the initial investment),

e = Euler's number (approximately 2.71828),

r = the interest rate (2.9% expressed as a decimal, so 0.029),

t = the time period (18 years).

We can rearrange the formula to solve for P:

P = A / e^(rt).

Now we can plug in the given values and calculate the investment amount:

P = $34,000 / e^(0.029 * 18).

Using a calculator, we can evaluate e^(0.029 * 18) and divide $34,000 by the result to find the investment amount.

Calculating e^(0.029 * 18) gives us approximately 1.604.

P = $34,000 / 1.604 ≈ $21,179.55

The correct answer is Screw option needs to be set to something greater than 0.

To get the vertical movement and create a helix-like shape using the screw modifier, Caroline needs to change the screw option to something greater than 0.

The screw option determines the amount of vertical displacement or height of the helix shape.

By setting the screw option to a value greater than 0, Caroline can control the vertical movement of the model as it spirals along the axis, resulting in a helix-like shape.

Therefore, the correct answer is:

Screw option needs to be set to something greater than 0.

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The mass of the sea glass in the box is 1265 grams.

To find the mass of the sea glass in grams, we need to subtract the mass of the empty box from the total mass of the box with the sea glass. Let's convert all the units to grams for consistency.

Mass of the empty box = 235 grams

Total mass of the box with sea glass = 1 1/2 kilograms = 1.5 kilograms = 1500 grams

To determine the mass of the sea glass, we subtract the mass of the empty box from the total mass:

Mass of the sea glass = Total mass of the box with sea glass - Mass of the empty box

Mass of the sea glass = 1500 grams - 235 grams

Performing the subtraction:

Mass of the sea glass = 1265 grams

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The percentile of 6.2 in the given data set is 40%.

To determine the percentile of 6.2 in the given data set, we can use the following steps:

Arrange the data set in ascending order:

4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2

Count the number of data points that are less than or equal to 6.2. In this case, there are 4 data points that satisfy this condition: 4.2, 4.6, 5.1, and 6.2.

Calculate the percentile using the formula:

Percentile = (Number of data points less than or equal to the given value / Total number of data points) × 100

In this case, the percentile of 6.2 can be calculated as:

Percentile = (4 / 10) × 100 = 40%

The percentile of 6.2 in the sample data set is therefore 40%.

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The difference quotient of the function f(x) = 12x + 1 is 12.

The difference quotient of a function measures the average rate of change of the function between two points. To find the difference quotient of the function f(x) = 12x + 1, we can follow these steps:

Select two points on the function, let's call them x and x + h, where h is a small positive value.

Evaluate the function at those two points to get the corresponding y-values. For f(x) = 12x + 1, we have:

f(x) = 12x + 1

f(x + h) = 12(x + h) + 1

Calculate the difference quotient by subtracting the values and dividing by h:

[f(x + h) - f(x)] / h

= [(12(x + h) + 1) - (12x + 1)] / h

= [12x + 12h + 1 - 12x - 1] / h

= (12h) / h

= 12

In this case, since the function is linear with a slope of 12, the difference quotient is constant and equal to the slope of the function. This means that for every unit increase in x, the function f(x) increases by 12.

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Jacob bought 0.7 yards of ribbon.

To find out how many yards of ribbon Jacob bought, we need to determine 4/5 of the length of ribbon that Cindy bought.

Cindy bought 7/8 yard of ribbon. To find 4/5 of this length, we multiply 7/8 by 4/5:

(7/8) * (4/5) = (7 * 4) / (8 * 5) = 28/40

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 4:

(28/4) / (40/4) = 7/10

Therefore, Jacob bought 7/10 yard of ribbon.

However, we can convert this fraction to a mixed number or decimal to express it in yards.

To convert 7/10 to a mixed number, we divide the numerator (7) by the denominator (10):

7 ÷ 10 = 0 with a remainder of 7

So, 7/10 is equivalent to 0 7/10 or 0.7 yards.

Therefore, Jacob bought 0.7 yards of ribbon.

In summary, Jacob bought 7/10 yard or 0.7 yards of ribbon.

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The correct solutions to the quadratic equation are:

c. -8

e. 2

To determine the solutions to the quadratic equation 2x^2 + 6x - 10 = x^2 + 6, we need to solve for x.

First, let's simplify the equation by combining like terms:

2x^2 + 6x - 10 - x^2 - 6 = 0

x^2 + 6x - 16 = 0

Now, we can solve this quadratic equation by factoring or by using the quadratic formula.

By factoring:

(x + 8)(x - 2) = 0

Setting each factor equal to zero, we get:

x + 8 = 0 --> x = -8

x - 2 = 0 --> x = 2

So, the solutions to the quadratic equation are x = -8 and x = 2.

Now, let's check the given options:

a. -2: This value is not a solution to the equation.

b. 1/3: This value is not a solution to the equation.

c. -8: This value is a solution to the equation.

d. -1/2: This value is not a solution to the equation.

e. 2: This value is a solution to the equation.

f. 8: This value is not a solution to the equation.

The following are the proper answers to the quadratic equation: c. -8 e.2

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There are no zero pairs in the expression.

To calculate the number of zero pairs in statement 9 + (-16), we need to clarify the expression and determine any matching positive and negative numbers.

In this respect, 9 and -16 have unlike signs. To simplify, we can rewrite the expression as 9 - 16, which is similar to adding the opposite of 16.

Here, let's look for zero pairs. A zero pair incorporate a positive and negative number that cancel each other out and occur in a sum of zero.

In the expression 9 - 16, there are no identical positive and negative numbers.

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The solutions of the system of equations are (2, -1) and (-4, 17)

The given system of equations is:

y = x² - x - 3

y = -3x + 5

To find the solutions, we need to solve these equations simultaneously.

Set the equations equal to each other:

x² - x - 3 = -3x + 5

Simplify and rewrite the equation in standard form:

x² - x + 3x - 3 - 5 = 0

x² + 2x - 8 = 0

Factor the quadratic equation:

(x - 2)(x + 4) = 0

Now we can solve for x by setting each factor equal to zero:

x - 2 = 0 or x + 4 = 0

Solving for x, we get:

x = 2 or x = -4

To find the corresponding y-values, we substitute these x-values into either of the original equations. Let's use equation 1):

For x = 2:

y = (2)² - 2 - 3 = 4 - 2 - 3 = -1

For x = -4:

y = (-4)² - (-4) - 3 = 16 + 4 - 3 = 17

As a result, the system of equations has two solutions: (2, -1) and (-4, 17).

The right responses are therefore (2, -1) and (-4, 17).

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The approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

To solve the equation 1/x-1 = |x-2| using three iterations of successive approximation, we will start with an initial guess and refine it using an iterative process.

Given that the equation involves absolute value, we will consider two cases:

Case 1: x - 2 ≥ 0

In this case, |x-2| simplifies to x-2, and the equation becomes 1/(x-1) = x-2.

Case 2: x - 2 < 0

In this case, |x-2| simplifies to -(x-2), and the equation becomes 1/(x-1) = -(x-2).

Now, let's perform the successive approximation:

Iteration 1:

Let's start with an initial guess, x = 2.

Case 1: When x - 2 ≥ 0,

1/(2-1) = 2-2,

1/1 = 0,

which is not true.

Case 2: When x - 2 < 0,

1/(2-1) = -(2-2),

1/1 = 0,

which is not true.

Since our initial guess did not satisfy the equation in either case, we need to choose a different initial guess.

Iteration 2:

Let's try x = 3.

Case 1: When x - 2 ≥ 0,

1/(3-1) = 3-2,

1/2 = 1,

which is not true.

Case 2: When x - 2 < 0,

1/(3-1) = -(3-2),

1/2 = -1,

which is not true.

Again, our guess did not satisfy the equation in either case.

Iteration 3:

Let's try x = 2.5.

Case 1: When x - 2 ≥ 0,

1/(2.5-1) = 2.5-2,

1/1.5 = 0.5,

which is true.

Case 2: When x - 2 < 0,

1/(2.5-1) = -(2.5-2),

1/1.5 = -0.5,

which is not true.

Our guess of x = 2.5 satisfies the equation in Case 1.

Therefore, the approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

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The surface area of the given triangle is approximately 33.74 square centimeters.

To calculate the surface area of a triangle, we need the lengths of two sides and the included angle between them. However, in this case, you provided the lengths of all three sides (6 cm, 7 cm, and 12 cm).

To determine the surface area, we can use Heron's formula, which is applicable to triangles with all three side lengths known.

Heron's formula states that the surface area (A) of a triangle with side lengths a, b, and c is given by:

[tex]A = \sqrt(s \times (s - a) \times (s - b) \times (s - c))[/tex]

where s is the semi perimeter of the triangle, calculated as:

s = (a + b + c) / 2

Plugging in the given side lengths, we have:

s = (6 cm + 7 cm + 12 cm) / 2 = 25 / 2 = 12.5 cm

Now we can substitute the values into Heron's formula:

[tex]A = \sqrt(12.5 cm \times (12.5 cm - 6 cm) \times (12.5 cm - 7 cm) \times (12.5 cm - 12 cm))[/tex]

[tex]= \sqrt(12.5 cm \times 6.5 cm \times 5.5 cm \times 0.5 cm)[/tex]

= √(1137.5 cm^4)

≈ 33.74 cm^2

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Answer: seconds

Step-by-step explanation:

The elliptical ceiling is approximately 30 ft high at the center.

To find the height of the elliptical ceiling at the center, we can use the properties of an ellipse.

In this case, the two foci of the ellipse represent the positions where Juan and his friend are standing.

The distance between the two foci is 80 ft, and Juan is 20 ft away from the nearest wall.

This means that the sum of the distances from any point on the ellipse to the two foci is constant and equal to 80 + 20 = 100 ft.

Since Juan is standing at one focus and the distance to the nearest wall is given, we can determine the distance from Juan to the farthest wall by subtracting the distance to the nearest wall from the sum of the distances.

Distance from Juan to the farthest wall = 100 ft - 20 ft = 80 ft.

The height of the elliptical ceiling at the center is equal to half of the distance between the nearest and farthest walls.

Height of elliptical ceiling = (80 ft - 20 ft) / 2 = 60 ft / 2 = 30 ft.

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Hello!

[tex]32 = 25x^2 - 4\\\\32 + 4 = 25x^2\\\\36 = 25x^2\\\\25x^2 - 36 = 0\\\\x = \dfrac{-b \±\sqrt{b^2 - 4ac} }{2a} \\\\\\x = \dfrac{-0 \±\sqrt{0^2 - 4 \times 25 \times (-36) } }{2 \times 25} \\\\\\x = \dfrac{\±60}{50} \\\\\boxed{x = \±\frac{6}{5} }[/tex]

The speed of Jake's initial trip is x = 24 kilometers per hour, and the speed of the return trip is x + 6 = 30 kilometers per hour.

Let's assume that Jake's speed during the initial trip is represented by "x" kilometers per hour.

On the return trip, he drives 6 kilometers per hour faster, so his speed can be represented as "x + 6" kilometers per hour.

To find the time taken for each trip, we can use the formula Time = Distance / Speed.

For the initial trip, the time taken is 120 kilometers divided by x kilometers per hour, which gives us 120/x hours.

On the return trip, the time taken is 120 kilometers divided by (x + 6) kilometers per hour, which gives us 120/(x + 6) hours.

According to the problem, the return trip takes 1 hour less than the initial trip. So we can set up the equation:

120/x - 1 = 120/(x + 6)

To solve this equation, we can multiply both sides by x(x + 6) to eliminate the denominators:

120(x + 6) - x(x + 6) = 120x

Simplifying this equation:

120x + 720 - x² - 6x = 120x

Combining like terms:

x² + 6x - 720 = 0

Now we can solve this quadratic equation by factoring or using the quadratic formula. By factoring, we find:

(x + 30)(x - 24) = 0

This gives us two potential solutions: x = -30 or x = 24.

Since speed cannot be negative, we discard the solution x = -30.

Therefore, the speed of Jake's initial trip is x = 24 kilometers per hour, and the speed of the return trip is x + 6 = 30 kilometers per hour.

So, Jake drives at a speed of 24 kilometers per hour on the initial trip and 30 kilometers per hour on the return trip.

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Answer:

The total amount with annual compounding is 23,304.79 .

The interest with annual compounding is $18,304.79.

The total amount with semi annual compounding is 24,005.10.

The interest with semi annual compounding is $19,005.10.

The total amount with quarterly compounding is 24,377.20.

The interest with quarterly compounding is $19,377.20.

What are the total amount and interest?

The formula for determining the total amount is:

FV = PV(1 + r/m)^nm

Where:

FV =total amount

PV = amount deposited

r  = interest rate

n  = number of years

m = number of compounding

Interest = FV - amount deposited

FV = 5000 x (1.08)^20 = 23,304.79

Interest = 23,304.79 - 5000 = $18,304.79

FV =5000 x (1.08/2)^(2 x 20) =24,005.10

Interest = 24,005.10 - 5000 = $19,005.10

FV =5000 x (1.08/4)^(20 x 4) =24,377.20

Interest = 24,377.20 - 5000 = $19,377.20

Step-by-step explanation:

Answer:

Step-by-step explanation:

To calculate the amount Aditi needs to pay, we need to apply the discounts step by step based on the given offer.

Step 1: 20% discount on all products

The marked price of the goods is Rs 2400. Applying a 20% discount means she will get a reduction of 20% of the marked price.

20% of Rs 2400 = (20/100) * Rs 2400 = Rs 480

After the first discount, the new bill amount is Rs 2400 - Rs 480 = Rs 1920.

Step 2: Additional 20% discount on the bill amount if it exceeds Rs 1000

The new bill amount after the first discount is Rs 1920. If this amount exceeds Rs 1000, Aditi will get a further discount of 20% on this bill amount.

Since Rs 1920 is greater than Rs 1000, we can apply a 20% discount to it.

20% of Rs 1920 = (20/100) * Rs 1920 = Rs 384

The final amount Aditi needs to pay after both discounts is Rs 1920 - Rs 384 = Rs 1536.

Therefore, Aditi needs to pay Rs 1536.

Answer:

11? I'm so sorry if it's incorrect. I apologize.

Based on the average scores and standard deviations, it appears that Millman's group still has room for improvement before they can reach the level of professional golfers.

To determine whether Millman's golfing group is ready to turn pro, we can compare their performance to that of professional golfers. Based on the provided data, Millman's group consists of 9 amateurs with an average score of 82 and a standard deviation of 2.6.

On the other hand, the professional golfers consist of 500 individuals with an average score of 71 and a standard deviation of 3.1.

To make a meaningful comparison, we can look at the average scores of the two groups. The average score is an indicator of the overall performance, with lower scores being better in golf.

In this case, the professional golfers have an average score of 71, while Millman's group has an average score of 82. This suggests that the professional golfers perform better, on average, than Millman's group.

However, it is also essential to consider the standard deviation, which measures the variability of scores within each group. A smaller standard deviation indicates less variation and greater consistency in performance.

The professional golfers have a standard deviation of 3.1, while Millman's group has a standard deviation of 2.6. This suggests that Millman's group has slightly less variation in scores compared to the professional golfers.

Overall, based on the average scores and standard deviations, it appears that Millman's group still has room for improvement before they can reach the level of professional golfers.

The professional golfers demonstrate better performance, on average, and a slightly higher variability in scores compared to Millman's group. Therefore, it would be advisable for Millman's group to continue refining their skills and striving to improve their scores before considering turning pro.

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When [tex]sin(\theta) = -0.42[/tex] and [tex]\pi < \theta < 3\pi/2[/tex], the value of [tex]cos(\theta)[/tex] is approximately 0.9071.

To find the value of cos([tex]\theta[/tex]) given[tex]sin(\theta) = -0.42[/tex] and [tex]\pi < \theta < 3\pi/2[/tex], we can use the trigonometric identity:

[tex]sin^2(\theta) + cos^2(\theta) = 1[/tex]

Since we are given sin(theta) = -0.42, we can substitute this value into the equation:

[tex](-0.42)^2 + cos^2(\theta) = 1[/tex]

Simplifying:

[tex]0.1764 + cos^2(\theta) = 1[/tex]

Subtracting 0.1764 from both sides:

[tex]cos^2(\theta) = 0.8236[/tex]

Taking the square root of both sides (since cos(theta) is positive):

[tex]cos(\theta) = \sqrt{(0.8236)} \\cos(\theta) = 0.9071[/tex]

Therefore, when [tex]sin(\theta) = -0.42[/tex] and [tex]\pi < \theta < 3\pi/2[/tex], the value of [tex]cos(\theta)[/tex]is approximately 0.9071.

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Answer:

x = 11.62

Step-by-step explanation:

opp / adj would be tangent, so the equation would be 4*tan(71) giving us 11.616, and rounding to the nearest hundredth gives you 11.62

Hope this helps :)

Answer:

--------------------------------

Angles ABD and DBC form a linear pair, hence their sum is 180°.

Set up an equation and solve for x:

Substitute 40.5 for x and find the measure of ∠DBC:

Answer:

Fractions are like pancakes: you can flatten them horizontally or vertically. Horizontal flattening means you shrink the x-value by multiplying it by a huge number before doing anything else. Vertical flattening means you squish the y-value by multiplying the whole function by a tiny number. For example, if f (x) = x^2, then f (2x) is horizontally flattened by 2 and f (0.5x^2) is vertically flattened by 0.5. Don't worry, it's not rocket science, it's just math.

a. The t-value is 1.895.

b. The t-value is 1.734.

c. The t-value is 2.898.

To calculate the t-statistic for a confidence interval, we first need to determine the degrees of freedom (df), which depends on the sample size minus one. We can then use a t-distribution table, software, or calculator to find the t-value at the desired confidence level and degrees of freedom.

a. For a 90% confidence interval with 8 observations, the degrees of freedom is 7. Using the t-distribution table or calculator,

b. For a 90% confidence interval with 18 observations, the degrees of freedom is 17. Using the t-distribution table or calculator,

c. For a 99% confidence interval with 18 observations, the degrees of freedom is 17. Using the t-distribution table, software, or calculator,

Note that as the sample size increases, the degrees of freedom increase and the t-value approaches the value of the standard normal distribution for large sample sizes. This means that for large sample sizes, we can use the z-value instead of the t-value in confidence interval calculations.

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Using row operations to write the augmented matrix, the value of x, y and z are 2, -12 and 11

To solve the system using row operations, we'll write the augmented matrix and perform row operations to transform it into row-echelon form. Here are the steps:

1. Write the augmented matrix for the system of equations:

  [1  1  -1  |  1]

  [4  -1  1  |  9]

  [1  -3  2  |  -14]

2. Perform row operations to transform the matrix into row-echelon form:

  R2 = R2 - 4R1

  R3 = R3 - R1

  [1  1   -1  |  1]

  [0  -5  5   |  5]

  [0  -4  3   |  -15]

3. Perform row operations to further transform the matrix into row-echelon form:

  R2 = -R2/5

  R3 = -4R2 + R3

  [1  1   -1  |  1]

  [0  1   -1  |  -1]

  [0  0   -1  |  -11]

4. Perform row operations to obtain a diagonal of 1s from left to right:

  R1 = R1 + R3

  R2 = R2 + R3

  [1  1   0  |  -10]

  [0  1   0  |  -12]

  [0  0   -1 |  -11]

5. Perform row operations to transform the matrix into reduced row-echelon form:

  R3 = -R3

  [1  1   0  |  -10]

  [0  1   0  |  -12]

  [0  0   1  |  11]

The resulting matrix corresponds to the system of equations:

x + y = -10

y = -12

z = 11

Therefore, the solution to the given system of equations is x = -10 - y, y = -12, and z = 11.

So, the solution is x = -10 - (-12) = 2, y = -12, and z = 11.

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In a Production Possibility Curve (PPC) with product output Y on the vertical axis and product output X on the horizontal axis the following points are described as follows.

- Point Q represents an unemployment rate of 100 percent. It is located at the origin, where both axes intersect, indicating no product output due to complete unemployment.

- Point R signifies full employment and is located at the maximum product output on the X-axis, showing the economy's capacity when all resources are fully utilized.

- Point S indicates where the US economy typically operates, within the usual range of product output levels on the X-axis, reflecting a balanced unemployment rate that includes frictional and structural unemployment.

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The statement that is correct option d: The spread of the number of activities for Class N is less than for Class M.

The term 'spread' in mathematics refers to the difference between the largest and smallest values in a dataset or the range of the data. It's the extent to which the dataset is spread out.The median is the center of a dataset. It's the number that lies in the middle of the sorted values. Half the values are greater than the median, while the other half are lesser than the median.

An outlier is a value that is very different from the other values in the dataset.In class M, there are no outliers. The distribution is skewed to the right since most students have only a few activities, and some have many. The median is between 2 and 3.

In class N, there are no outliers. Most students have a moderate number of activities, and the spread is less than in Class M. The median is between 5 and 6.Hence, the correct statement is The spread of the number of activities for Class N is less than for Class M.The correct answer is d

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