Which of the following measures can be precisely located on the graph of a skewed distribution without doing any calculations? Variance Standard deviation Mode Mean Median

The SOS company has the lower initial cost with $10 as initial amount.

Given that are two companies with their different plans for homework help,

The SOS company's graph is given, and the Lifeline company says you can pay $25 as a registration fee and then can continue with $0.40 for each minute.

We are asked to compare the plans for each company to check which company has a lower initial cost.

So,

In SOS, there is $10 for 0 minutes, and the in lifeline company there is a $25 as a registration fee.

Since, $25 > $10, so people will prefer the SOS more.

Hence the SOS company has the lower initial cost with $10 as initial amount.

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Answer:

25) $6.15

26) 300

Step-by-step explanation:

25)

p(k) = 1600/(k + 20)

p(240) = 1600/(240 + 20)

p(240) = 1600/260

p(240) = 6.15

Answer: $6.15

26)

p(k) = 5

p(k) = 1600/(k + 20)

5 = 1600(k + 20)

5(k + 20) = 1600

5k + 100 = 1600

5k = 1500

k = 300

Answer: 300

Answer:

Difference = Surface Area_small - Surface Area_large ≈ 63.72 cm^2 - 85.39 cm^2 ≈ -21.67 cm^2

Step-by-step explanation:

Radius of the larger hollow ball (r_outer) = 3 cm

For the smaller hollow balls, since they are identical, we assume that the outer and inner radii are the same:

Radius of the smaller hollow balls (r_inner) = r_outer/2 = 3 cm / 2 = 1.5 cm

Now, let's calculate the surface area for both cases:

Surface area of the larger hollow ball:

Surface Area_large = 4π(r_outer^2 - r_inner^2)

Surface Area_large = 4π(3^2 - 1.5^2)

Surface Area_large = 4π(9 - 2.25)

Surface Area_large = 4π(6.75)

Surface Area_large ≈ 85.39 cm^2

Surface area of the smaller hollow balls (each):

Surface Area_small = 4π(r_outer^2 - r_inner^2)

Surface Area_small = 4π(1.5^2 - 0.75^2)

Surface Area_small = 4π(2.25 - 0.5625)

Surface Area_small = 4π(1.6875)

Surface Area_small ≈ 21.24 cm^2

Now, let's compare the surface areas:

The total surface area of the three smaller hollow balls = 3 * Surface Area_small ≈ 3 * 21.24 cm^2 ≈ 63.72 cm^2

Therefore, it takes more paint to paint the three smaller hollow balls compared to the larger hollow ball. The difference in surface area is given by:

Difference = Surface Area_small - Surface Area_large ≈ 63.72 cm^2 - 85.39 cm^2 ≈ -21.67 cm^2

The difference is negative because the surface area of the larger hollow ball is greater than the combined surface area of the three smaller hollow balls.

Angle A( angle WXY) must be an Blunt angle, the cosine of an blunt angle is negative.          

The angles of triangle WXY must be true, we can  dissect the given side lengths using the Law of Cosines. The Law of Cosines states that in a triangle, the forecourt of one side is equal to the sum of the places of the other two sides minus twice their product, multiplied by the cosine of the included angle.  Let's denote angle WXY as angle A, angle WYX as angle B, and angle XYW as angle C. According to the Law of Cosines, we have  WX2 =  WY2 XY2- 2 * WY * XY * cos( A)  132 =  152 102- 2 * 15 * 10 * cos( A)  169 =  225 100- 300 * cos( A)  69 = -300 * cos( A)  cos( A) = -69/ 300  the cosine of an angle is a value between-1 and 1, we can conclude that-69/ 300 is within this range. thus, angle A( angle WXY) must be an blunt angle. This is because the cosine of an blunt angle is negative.

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The equation to calculate the length is 4x²/2 = 90 and the diagonals are 3√5 and 12√5

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

One diagonal is 4 times the length of the other

The area of the rhombus is 90 square feett

This means that

y = 4x

Where

x = short diagonal

The area of the rhombus is then calculated as

A = xy/2

So, we have

A = 4x²/2

The area is 90

So, we have

4x²/2 = 90

So, we have

x² = 90 * 2/4

Evaluate

x² = 45

Take the square roots

x = 3√5

Next, we have

y = 4 * 3√5

Evaluate

y = 12√5

Hence, the equation to calculate the length is 4x²/2 = 90

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a) The formula to calculate the sample size required to estimate a population proportion for unknown values of the population proportion and margin of error at a certain level of confidence is given by:

$$n = \frac{z^2pq}{E^2}$$

Where, z is the z-score associated with the level of confidence, p is the estimated population proportion, q is 1-p, and E is the margin of error. According to the given problem, the margin of error E = 0.09 and the confidence level is 95%. Thus, the value of z corresponding to this level of confidence is 1.96 (approx.). We don't have any prior information about the population proportion, therefore, we can take the maximum possible value for p, which is 0.5, because it makes the sample size maximum (due to maximum variance) and the margin of error maximum (due to minimum standard error).

Therefore,

p = 0.5 and q = 1 - p = 0.5.

Substituting these values in the formula for sample size, we get:

$$n = \frac{1.96^2 \times 0.5 \times 0.5}{0.09^2} \approx. \boxed{96}$$

Therefore, approximately 96 elementary school children need to be selected to estimate the proportion p who have received a medical examination during the past year with a margin of error of 0.09 and 95% confidence.

b) If prior information about the population proportion is available, the sample size can be determined using the formula:

$$n = \frac{z^2p'q'}{E^2}$$

Where,

p' is the estimated value of the population proportion obtained from prior information. In this case, p' = 0.9, and q' = 1 - p' = 0.1. All other values are the same as in part

(a).Substituting these values in the formula, we get:$$n = \frac{1.96^2 \times 0.9 \times 0.1}{0.09^2} \approx. \boxed{59}$$

Therefore, approximately 59 elementary school children need to be selected to estimate the proportion p who have received a medical examination during the past year with a margin of error of 0.09 and 95% confidence, assuming prior information about the population proportion is available.

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Answer: d O(-6,4)

Step-by-step explanation:

The amount of candy that costs $1. 80 per pound that she will be able to use would be = 107 candies.

The mass of candy that Miss Ann has selected = 80 pounds

The cost of each pound of the candy = $2.40 per pound

The cost of the selected candy by its mass = 80×2.4 = $192

But the amount of candy that cost $1.80 per pound she will be able to make = 192/1.8 = 107 (approximately)

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We can use the properties mentioned above  : Geometry Unit 10: Circles Homework 7. :1. AP = AQ , 2. ∠APO = ∠AQO = 90°

To find the value or measure of the given problem, we must consider the properties of tangent segments and circles.

Recall that tangent segments to a circle from an external point are congruent, meaning they have equal lengths. Additionally, a tangent line forms a right angle (90°) with the radius at the point of tangency.

Now, let's assume we are given a circle with center O and two tangent segments, AP and AQ, from an external point A. Since both segments are tangent to the circle,

Using these properties, we can find the value or measure of the unknown quantities in the problem. Please provide the specific problem details for a more accurate and precise answer.

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In mathematics, the point below which a specified percentage of the observations fall is commonly referred to as the percentile.

A percentile is a measure that indicates the relative position of a particular value within a dataset.

For example, if a value is at the 80th percentile, it means that 80% of the observations in the dataset are below that value, and only 20% of the observations are above it.

Percentiles are often used to analyze and understand the distribution of data, especially in fields such as statistics, probability, and data analysis. They provide insights into how individual data points compare to the overall dataset and help identify outliers or extreme values.

A percentile is a statistical measure that indicates the relative standing of a particular value within a dataset. It represents the point below which a specified percentage of the observations or data points fall. Percentiles are primarily used to understand the distribution of data and analyze how individual values compare to the overall dataset.

To calculate a percentile, the dataset is arranged in ascending order, from the smallest value to the largest value. The position of a specific percentile is then determined based on the percentage of data points below it. For example, the 75th percentile represents the value below which 75% of the data points fall.

Percentiles are commonly used in various fields, including statistics, probability, and data analysis. They provide valuable insights into the spread, variability, and distribution of data. Here are a few key points to consider:

1. Median: The median is the 50th percentile, representing the value that divides the dataset into two equal halves. It is a measure of central tendency and provides information about the middle point of the distribution.

2. Quartiles: Quartiles divide the dataset into four equal parts. The first quartile, or the 25th percentile (Q1), represents the value below which 25% of the data points fall. The third quartile, or the 75th percentile (Q3), represents the value below which 75% of the data points fall. The difference between Q3 and Q1 is known as the interquartile range (IQR) and provides insights into the spread of the middle 50% of the data.

3. Percentile Ranks: Percentile ranks indicate the percentage of data points that are below a specific value. For example, if a student scores in the 80th percentile on a standardized test, it means they performed better than 80% of the test-takers.

4. Outliers: Percentiles can be useful in identifying outliers, which are data points that significantly deviate from the rest of the dataset. Extremely high or low percentiles may indicate unusual or extreme values that warrant further investigation.

5. Normal Distribution: In a normal distribution, the 50th percentile (median) coincides with the mean and mode, and specific percentiles have known standard deviations from the mean (e.g., the 68-95-99.7 rule).

Percentiles are versatile tools for summarizing and analyzing data, providing valuable insights into the distribution and relative positions of individual values. They enable comparisons and help make informed decisions based on the characteristics of a dataset.

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The length of AB is approximately 8.602 units, and the length of A'B' is approximately 7.211 units.

To find the coordinates of A' when the line segment is dilated from the origin by a factor of 2, we can multiply the coordinates of A by 2.

Coordinates of A: (x₁, y₁) = (-2, 3)

Coordinates of A' = (2 * x₁, 2 * y₁) = (2 * (-2), 2 * 3) = (-4, 6)

Therefore, the coordinates of A' are (-4, 6).

To find the coordinates of B, we can observe the graph and read the coordinates directly.

Coordinates of B: (x₂, y₂) = (3, -4)

Therefore, the coordinates of B are (3, -4).

Next, we need to find the length of AB using the distance formula:

Length of AB = √((x₂ - x₁)² + (y₂ - y₁)²)

            = √((3 - (-2))² + (-4 - 3)²)

            = √((3 + 2)² + (-4 - 3)²)

            = √(5² + (-7)²)

            = √(25 + 49)

            = √74

            ≈ 8.602 (rounded to the nearest three decimal places)

Finally, we need to find the length of A'B' using the distance formula:

Length of A'B' = √((x₂' - x₁')² + (y₂' - y₁')²)

              = √((-4 - 0)² + (6 - 0)²)

              = √((-4)² + 6²)

              = √(16 + 36)

              = √52

              ≈ 7.211 (rounded to the nearest three decimal places)

Therefore, the length of AB is approximately 8.602 units, and the length of A'B' is approximately 7.211 units.

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The greatest Integer that belongs to the interval (-∞, 8) is 7, as it is the largest whole number that is less than 8 within the given interval.

1. The greatest integer that belongs to the interval [-1, 17), we need to determine the largest whole number that is less than or equal to 17. In this case, the interval includes -1 but does not include 17.

The greatest integer in the interval [-1, 17) is 16.

To clarify, the greatest integer that belongs to the interval [-1, 17) is 16 because it is the largest whole number that is less than 17 and also within the specified interval.

2. For the interval (-∞, 8), the range extends from negative infinity to 8, where negative infinity is not an actual number but rather represents the concept of going infinitely in the negative direction. In this interval, we are looking for the largest integer that is less than 8.

The greatest integer in the interval (-∞, 8) is 7.

Since the interval does not include 8 and extends infinitely in the negative direction, the largest integer within this interval is 7.

the greatest integer that belongs to the interval (-∞, 8) is 7, as it is the largest whole number that is less than 8 within the given interval.

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In the given problem, we have u = (4, 0, -4) and v = (4, 7, 8). The inner product u, v is defined as 2u1v1 + 3u2v2 + u3v3. To find the values of u, v, u, v, and d(u, v), let's calculate them step by step.

First, let's calculate u, v:

The inner product u, v = 2u1v1 + 3u2v2 + u3v3

      = 2(4)(4) + 3(0)(7) + (-4)(8)

      = 32 + 0 + (-32)

      = 0

Next, let's calculate u:

u = ||u|| = sqrt(u, u)

     =[tex]\sqrt{2u1^2 + 3u2^2 + u3^2}[/tex]

     = [tex]\sqrt{(2(4)^2 + 3(0)^2 + (-4)^2)}[/tex]

     = 4√3

Similarly, let's calculate v:

v = ||v|| = sqrt(v, v)

     = [tex]\sqrt{2v1^2 + 3v2^2 + v3^2}[/tex]

     = [tex]\sqrt{2(4)^2 + 3(7)^2 + (8)^2)}[/tex]

     = 9√3

Finally, let's calculate d(u, v):

d(u, v) = ||u - v|| = sqrt((u - v), (u - v))

               = [tex]\sqrt{(u1 - v1)^2 + (u2 - v2)^2 + (u3 - v3)^2}[/tex]

               = ([tex]\sqrt{(4 - 4)^2 + (0 - 7)^2 + (-4 - 8)^2}[/tex])

               = [tex]\sqrt{193}[/tex]

In summary, u, v = 0, u = 4√3, v = 9√3, and d(u, v) = square root of(193).

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The Riemann sum with n = 6 and midpoints as sample points for f(x) = 2x^2 - 7 represents an approximation of the definite integral of f(x) over the interval [0, 3].

The value of the Riemann sum (10.875) represents an estimation of the area between the curve of f(x) and the x-axis within the given interval.

Calculate the width of each subinterval: Δx = (3 - 0) / n = 3/6 = 0.5.

Determine the midpoint of each subinterval: xᵢ = 0 + (i - 0.5)Δx, where i ranges from 1 to n.

For i = 1, x₁ = 0 + (1 - 0.5)(0.5) = 0.25

For i = 2, x₂ = 0 + (2 - 0.5)(0.5) = 0.75

For i = 3, x₃ = 0 + (3 - 0.5)(0.5) = 1.25

For i = 4, x₄ = 0 + (4 - 0.5)(0.5) = 1.75

For i = 5, x₅ = 0 + (5 - 0.5)(0.5) = 2.25

For i = 6, x₆ = 0 + (6 - 0.5)(0.5) = 2.75

Evaluate f(x) at each midpoint: f(xᵢ) = 2(xᵢ)^2 - 7.

f(x₁) = 2(0.25)^2 - 7 = -6.875

f(x₂) = 2(0.75)^2 - 7 = -5.625

f(x₃) = 2(1.25)^2 - 7 = -3.125

f(x₄) = 2(1.75)^2 - 7 = 0.375

f(x₅) = 2(2.25)^2 - 7 = 4.875

f(x₆) = 2(2.75)^2 - 7 = 11.375

Calculate the Riemann sum: R_n = Δx * [f(x₁) + f(x₂) + f(x₃) + f(x₄) + f(x₅) + f(x₆)].

R₆ = 0.5 * [-6.875 + (-5.625) + (-3.125) + 0.375 + 4.875 + 11.375] = 10.875.

The Riemann sum with n = 6 and midpoints as sample points, in this case, gives an approximation of the definite integral of f(x) = 2x^2 - 7 over the interval [0, 3]. The value of the Riemann sum (10.875) represents an estimation of the area between the curve of f(x) and the x-axis within the given interval.

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To find the length of the vector x = -4e1 + 5e2 - 4e3 - 5e4 + 4e5 + 2e6, denoted as ||x||, we can use the formula:

||x|| = sqrt((x1)^2 + (x2)^2 + (x3)^2 + (x4)^2 + (x5)^2 + (x6)^2),

where x1, x2, x3, x4, x5, and x6 are the coefficients of the vector x in terms of the standard basis vectors e1, e2, e3, e4, e5, and e6.

Plugging in the values, we have:

||x|| = sqrt((-4)^2 + (5)^2 + (-4)^2 + (-5)^2 + (4)^2 + (2)^2)

Simplifying the equation:

||x|| = sqrt(16 + 25 + 16 + 25 + 16 + 4)

||x|| = sqrt(102)

Therefore, the length of the vector x is sqrt(102).

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Answer: The amount of plastic wrap used to wrap the container is approximately 3.06π square inches.

Step-by-step explanation: To calculate the total surface area of the cylindrical candy container, we need to consider the area of the two circular ends (top and bottom) and the area of the curved surface (lateral area).

The area of each circular end is given by the formula: A = πr^2, where r is the radius. Since the diameter is given as 1.8 inches, the radius is half of that, which is 0.9 inches.

Area of each circular end = π(0.9)^2 = 0.81π square inches.

The area of the curved surface (lateral area) is given by the formula: A = 2πrh, where r is the radius and h is the height of the rectangle. The height is given as 0.8 inches.

Curved surface area = 2π(0.9)(0.8) = 1.44π square inches.

To find the total surface area, we add the areas of the two circular ends and the curved surface area:

Total surface area = 2(Area of circular ends) + Curved surface area

= 2(0.81π) + 1.44π

= 1.62π + 1.44π

= 3.06π square inches.

Therefore, the amount of plastic wrap used to wrap the container is approximately 3.06π square inches.

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The expression 6⁻³ is equivalent to 1/216

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

The laws of indices are used in the simplification of mathematical operations. For example:

[tex]x^{-n}=\frac{1}{x^n}[/tex]

Given the expression 6⁻³

Applying the laws of indices:

6⁻³ = 1/6³ = 1/216

The expression 6⁻³ is equivalent to 1/216

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To find the area of a region under the standard normal curve, the following information would typically be provided in the question:

1. The specific boundaries or limits of the region: The question should provide the z-scores or values that determine the starting and ending points of the region of interest. For example, it could specify "Find the area under the standard normal curve between z = -1.5 and z = 2.0."

2. The type of region: The question might specify whether the desired area is for a specific tail (e.g., "Find the area to the left of z = 1.8") or for a specific interval (e.g., "Find the area between z = -0.5 and z = 1.2").

3. Clear instructions or context: The question should provide sufficient context or instructions to ensure a clear understanding of what area needs to be found. It could specify a particular percentage or probability associated with the region, or it could relate to a specific problem or scenario where finding the area under the standard normal curve is necessary.

By providing these details, the question enables you to determine the appropriate steps to calculate the area using methods such as z-tables, statistical software, or mathematical formulas.

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2467 rolls of Angel Soft MEGA toilet paper can fit into the Closet space.

The volume of the closet space, we multiply the length, width, and height of the closet. Given that the dimensions of the closet are:

Length = 48 inches

Width = 48 inches

Height = 84 inches

Volume of the closet = Length * Width * Height

Volume = 48 * 48 * 84 = 193,536 cubic inches

The volume of the closet space is 193,536 cubic inches.

To calculate the volume of one roll of toilet paper, we use the formula for the volume of a cylinder. Given that the diameter of the roll is 5 inches and the height is 4 inches, the formula for the volume of a cylinder is:

Volume = π * (radius)^2 * height

The radius of the roll is half the diameter, so the radius is 5/2 = 2.5 inches.

Volume of one roll = 3.14 * (2.5)^2 * 4 = 78.5 cubic inches

The volume of one roll of Angel Soft MEGA toilet paper is 78.5 cubic inches.

the number of rolls that can fit into the closet space, we divide the volume of the closet space by the volume of one roll.

Number of rolls = Volume of closet space / Volume of one roll

Number of rolls = 193,536 / 78.5

Number of rolls ≈ 2467

2467 rolls of Angel Soft MEGA toilet paper can fit into the given closet space.

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To sketch the resultant force (r), we need to add two or more forces vectorially. We can then calculate the magnitude and angle of the resultant force (r) using trigonometry and the Pythagorean theorem.

Let's assume that we have two forces F1 and F2 acting on the object at different angles.To sketch the resultant force (r), we need to have two or more forces acting on an object.

To determine the resultant force (r), we need to add the two forces vectorially. This means that we need to draw the two forces as vectors, with their tails meeting at the same point. The resultant force (r) will then be the vector that connects the tail of the first force to the head of the second force.Once we have sketched the resultant force (r), we can calculate its magnitude and angle. The magnitude of the resultant force can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

In this case, the two sides are the x and y components of the resultant force (r). The x and y components can be calculated using trigonometry, where the angle between the resultant force and the x-axis is known. Once we have calculated the x and y components, we can use the Pythagorean theorem to find the magnitude of the resultant force (r). The angle of the resultant force can be calculated using inverse trigonometric functions, such as the arctan function.

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The series ∑(n=2)^∞ (1/n²) is convergent.

To determine the convergence or divergence of the series, we can use the p-series test. The p-series test states that if we have a series of the form ∑(n=1)^∞ (1/[tex]n^p[/tex]), then the series converges if p > 1 and diverges if p ≤ 1.

In the given series, we have ∑(n=2)^∞ (1/n²), which can be written as ∑(n=1)^∞ (1/n²) with the first term (1/1²) removed. This series is a specific case of the p-series where p = 2. Since 2 is greater than 1, according to the p-series test, the series converges.

The convergence of the series ∑(n=2)^∞ (1/n²) can also be verified using the integral test. The integral test states that if a function f(x) is continuous, positive, and decreasing on the interval [1, ∞), and if f(n) = a(n), then the series ∑(n=1)^∞ a(n) converges if and only if the improper integral ∫(1 to ∞) f(x) dx converges.

In this case, the function f(x) = 1/x² satisfies the conditions of the integral test. Integrating f(x) over the interval [1, ∞) gives us ∫(1 to ∞) 1/x²dx = [-1/x] from 1 to ∞, which equals 0 - (-1) = 1. Since the integral is finite and positive, the series converges.

Therefore, both the p-series test and the integral test confirm that the series ∑(n=2)^∞ (1/n²) is convergent.

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Answer:

x = 9

Step-by-step explanation:

5(x - 7) = 10

5x - 35 = 10

5x = 45

x = 9

Answer

x = 9

Step-by-step explanation

For now, I will focus on the left hand side of the equation and simplify it as much as I can.

[tex]\sf{5(x-7)=10}[/tex]

[tex]\sf{5x-35=10}[/tex]

Now we move on to the right hand side too. Subtract 35 from each side:

[tex]\sf{5x=10+35}[/tex]

[tex]\sf{5x=45}[/tex]

Divide each side by 5

[tex]\sf{x=9}[/tex]

Therefore x = 9

the Pearson bivariate correlation coefficient (r) for the given data is approximately 0.257.

To calculate the Pearson bivariate correlation coefficient, we need to determine the correlation between the number of drinks consumed and the memory scores. Let's label the number of drinks as variable X and the memory scores as variable Y.

Given the following data:

X = [1, 1, 0, 1, 0, 9, 1, 0, 9, 3, 7]

Y = [10, 19, 21, 04, 86, 50, 91, 93, 7]

First, we need to calculate the means (average) of X and Y.

Mean of X ([tex]\bar{X}[/tex]):

[tex]\bar{X}[/tex] = (1 + 1 + 0 + 1 + 0 + 9 + 1 + 0 + 9 + 3 + 7) / 11 = 32 / 11 ≈ 2.909

Mean of Y ([tex]\bar{Y}[/tex]):

[tex]\bar{Y}[/tex]= (10 + 19 + 21 + 04 + 86 + 50 + 91 + 93 + 7) / 9 = 381 / 9 ≈ 42.333

Next, we need to calculate the standard deviations of X and Y.

Standard deviation of X (sX):

sX = √[((1 - [tex]\bar{X}[/tex])² + (1 - [tex]\bar{X}[/tex])² + (0 - [tex]\bar{X}[/tex])² + (1 - )² + (0 - [tex]\bar{X}[/tex])² + (9 - [tex]\bar{X}[/tex])² + (1 - [tex]\bar{X}[/tex])² + (0 - [tex]\bar{X}[/tex])² + (9 - [tex]\bar{X}[/tex])² + (3 - [tex]\bar{X}[/tex])² + (7 - [tex]\bar{X}[/tex])²) / (n - 1)]

where n is the number of data points, which is 11 in this case.

sX = √[((1 - 2.909)² + (1 - 2.909)² + (0 - 2.909)² + (1 - 2.909)² + (0 - 2.909)² + (9 - 2.909)² + (1 - 2.909)² + (0 - 2.909)² + (9 - 2.909)² + (3 - 2.909)² + (7 - 2.909)²) / (11 - 1)]

sX = √[((-1.909)² + (-1.909)² + (-2.909)² + (-1.909)² + (-2.909)² + (6.091)² + (-1.909)² + (-2.909)² + (6.091)² + (0.091)² + (4.091)²) / 10]

sX = √[(3.641 + 3.641 + 8.433 + 3.641 + 8.433 + 37.296 + 3.641 + 8.433 + 37.296 + 0.008 + 16.749) / 10]

sX = √[128.621 / 10]

sX = √12.8621

sX ≈ 3.589

Standard deviation of Y (sY):

sY = √[((10 - 42.333)² + (19 - 42.333)² + (21 - 42.333)² + (04 - 42.333)² + (86 - 42.333)² + (50 - 42.333)² + (91 - 42.333)² + (93 - 42.333)² + (7 - 42.333)²) / (9 - 1)]

sY = √[((-32.333)² + (-23.333)² + (-21.333)² + (-38.333)² + (43.667)² + (7.667)² + (48.667)² + (50.667)² + (-35.333)²) / 8]

sY = √[(1051.444 + 545.778 + 453.111 + 1473.778 + 1901.444 + 58.778 + 2366.444 + 2566.444 + 1250.778) / 8]

sY = √[12116.209 / 8]

sY = √1514.526

sY ≈ 38.922

Finally, we can calculate the Pearson bivariate correlation coefficient (r):

r = Σ[(X - [tex]\bar{X}[/tex])(Y - [tex]\bar{Y}[/tex])] / √[Σ(X - [tex]\bar{X}[/tex])² * Σ(Y - [tex]\bar{Y}[/tex])²]

r = [(1 - 2.909)(10 - 42.333) + (1 - 2.909)(19 - 42.333) + (0 - 2.909)(21 - 42.333) + (1 - 2.909)(04 - 42.333) + (0 - 2.909)(86 - 42.333) + (9 - 2.909)(50 - 42.333) + (1 - 2.909)(91 - 42.333) + (0 - 2.909)(93 - 42.333) + (9 - 2.909)(7 - 42.333) + (3 - 2.909)(7 - 42.333)] / [√[(1 - 2.909)² + (1 - 2.909)² + (0 - 2.909)² + (1 - 2.909)² + (0 - 2.909)² + (9 - 2.909)² + (1 - 2.909)² + (0 - 2.909² + (9 - 2.909)² + (3 - 2.909)² + (7 - 2.909)²) * √[(10 - 42.333)² + (19 - 42.333)² + (21 - 42.333)² + (04 - 42.333)² + (86 - 42.333)² + (50 - 42.333)² + (91 - 42.333)² + (93 - 42.333)² + (7 - 42.333)²)]

r = [(-1.909)(-32.333) + (-1.909)(-23.333) + (-2.909)(-21.333) + (-1.909)(-38.333) + (-2.909)(43.667) + (6.091)(7.667) + (-1.909)(48.667) + (-2.909)(50.667) + (6.091)(-35.333) + (0.091)(-35.333)] / [√[3.641 + 3.641 + 8.433 + 3.641 + 8.433 + 37.296 + 3.641 + 8.433 + 37.296 + 0.008 + 16.749) * √[1051.444 + 545.778 + 453.111 + 1473.778 + 1901.444 + 58.778 + 2366.444 + 2566.444 + 1250.778]

r = [61.743 + 44.645 + 63.367 + 73.315 + 100.245 + 46.661 + 47.046 + 88.464 - 214.025 - 2.503] / [√130.888 * 1514.526]

r = 346.958 / [37.414 * 38.922]

r ≈ 0.257

Therefore, the Pearson bivariate correlation coefficient (r) for the given data is approximately 0.257.

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The circumference of the circle to the nearest tenth is 18.2 cm.

The circumference is the distance around a circle. We can calculate the circumference using either the diameter or radius of a circle.

Given,

Circumference of the circle:

[tex]=\sf2\pi r[/tex]

[tex]=2\times3.14\times2.9[/tex]

[tex]=6.28\times2.9[/tex]

[tex]\sf = 18.212\thickapprox\bold{18.2 \ cm}[/tex]

Hence, 18.2 cm is the required circumference of the circle rounded to nearest tenth.

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The formula for the circumference of a circle is:

C = 2πr

where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Given a radius of 2.9 inches, we can substitute this value into the formula and calculate the circumference:

C = 2πr

C = 2 × 3.14 × 2.9

C ≈ 18.18

Rounding to the nearest tenth, we get:

C ≈ 18.2

Therefore, the circumference of the circle with a radius of 2.9 inches is approximately 18.2 inches.

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Answer:

terms - 4

variables - x,y

coefficients - 5,2,3

constants - 1/2

In the context of the table provided, the term "tariff" refers to the price or rate per kilowatt-hour (kWh) of electricity consumption.

The table shows the Ingquza local municipality's domestic electricity tariffs at the low season.

In the context of the table provided, the term "tariff" refers to the price or rate per kilowatt-hour (kWh) of electricity consumption.

It represents the amount of money charged by the Ingquza Local Municipality for each unit of electricity used within specific usage blocks. The tariff is stated in South African Rand (ZAR) per kWh and is exclusive of the Value Added Tax (VAT) of 15%.

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i) (6, 4) and (6, -2)

j) (-5, 2) and (7.-7) This two distance and midpoint are not pairs of points.

To find the distance and midpoint between each pair of points, we'll use the distance formula and the midpoint formula. The distance formula is given by:

Distance =[tex]sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]

And the midpoint formula is given by:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Let's calculate the distance and midpoint for each given pair of points:

a) The distance between (0, 5) and (0, -6) is:

Distance =[tex]√((x2 - x1)^2 + (y2 - y1)^2)[/tex]

= [tex]√((0 - 0)^2 + (-6 - 5)^2)[/tex]

= √(0 + 121)

= √121

= 11

The midpoint between (0, 5) and (0, -6) is:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

= ((0 + 0) / 2, (5 + -6) / 2)

= (0, -0.5)

b) The distance between (3, 0) and (-4, 0) is:

Distance =[tex]√((x2 - x1)^2 + (y2 - y1)^2)[/tex]

= [tex]√((-4 - 3)^2 + (0 - 0)^2)[/tex]

= [tex]√((-7)^2 + 0)[/tex]

= √49

= 7

The midpoint between (3, 0) and (-4, 0) is:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

= ((3 + -4) / 2, (0 + 0) / 2)

= (-0.5, 0)

c) The distance between (5, 2) and (7, 6) is:

Distance = [tex]√((x2 - x1)^2 + (y2 - y1)^2)[/tex]

= [tex]√((7 - 5)^2 + (6 - 2)^2)[/tex]

= [tex]√(2^2 + 4^2)[/tex]

= √(4 + 16)

= √20

= 2√5

The midpoint between (5, 2) and (7, 6) is:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

= ((5 + 7) / 2, (2 + 6) / 2)

= (6, 4)

d) The distance between (-3, 4) and (1, -3) is:

Distance = [tex]√((x2 - x1)^2 + (y2 - y1)^2)[/tex]

= [tex]√((1 - (-3))^2 + (-3 - 4)^2)[/tex]

= [tex]√((1 + 3)^2 + (-7)^2)[/tex]

= [tex]√(4^2 + 49)[/tex]

= √(16 + 49)

= √65

The midpoint between (-3, 4) and (1, -3) is:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

= ((-3 + 1) / 2, (4 + (-3)) / 2)

= (-1, 0.5)

e) The distance between (6, 4) and (2, 1) is:

Distance = [tex]√((x2 - x1)^2 + (y2 - y1)^2)[/tex]

= [tex]√((2 - 6)^2 + (1 - 4)^2)[/tex]

=[tex]√((-4)^2 + (-3)^2)[/tex]

= √(16 + 9)

= √25

f) (-2, -4) and (3, 8):

Distance =[tex]sqrt((3 - (-2))^2 + (8 - (-4))^2)[/tex] = [tex]sqrt(5^2 + 12^2[/tex]) = sqrt(25 + 144) = sqrt(169) = 13

Midpoint = ((-2 + 3) / 2, (-4 + 8) / 2) = (0.5, 2)

g) (0, 0) and (5, 10):

Distance =[tex]sqrt((5 - 0)^2 + (10 - 0)^2)[/tex]= [tex]sqrt(5^2 + 10^2)[/tex] = sqrt(25 + 100) = sqrt(125) = 5√5

Midpoint = ((0 + 5) / 2, (0 + 10) / 2) = (2.5, 5)

h) Distance: [tex]√((2 - 4)^2 + (1 - 0)^2[/tex]) = [tex]√((-2)^2 + (1)^2)[/tex] = √(4 + 1) = √5

Midpoint: ((2 + 4)/2, (1 + 0)/2) = (6/2, 1/2) = (3, 1/2)

i) (6, 4) and (6, -2)

j) (-5, 2) and (7.-7) This two distance and midpoint are not pairs of points.

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The point C shows the 13 miles in the given graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given that On Friday, Leo walked 13 miles.

We have to find the points from A-E which shows this to complete the line graph.

According to the given graph, the point C shows the distance which is 13 miles of friday.

Hence, the point C shows the 13 miles in the given graph.

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To find the volume of a frustum of a cone, you can use the formula:

V = (1/3)πh(R^2 + r^2 + Rr)

Where:

V = Volume of the frustum of the cone

h = Height of the frustum of the cone

R = Radius of the bottom base of the frustum of the cone

r = Radius of the top base of the frustum of the cone

π = Pi (approximately 3.14159)

Given:

Height (h) = 5 cm

Radius of bottom base (R) = 7 cm

Radius of top base (r) = 4 cm

Substituting the given values into the formula, we get:

V = (1/3)π(5)(7^2 + 4^2 + 7*4)

V = (1/3)π(5)(49 + 16 + 28)

V = (1/3)π(5)(93)

V = (5/3)π(93)

V ≈ 154.77 cm³

Therefore, the volume of the frustum of the cone is approximately 154.77 cm³.

[tex]\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}[/tex]