The data set shown has a mean of 34 and a standard deviation of 9. How many of these data points have a z-score less than 0.7

The theoretical probability of spinning green on the spinner, divided into 4 equal-size sections colored red, green, orange, and blue, is ¼ or 25%.

In this scenario, the spinner has four equal-size sections. Since each section is of equal size, the probability of landing on any specific section is the same. Therefore, the probability of spinning green, which is one out of the four possible outcomes, is 1/4 or 25%.

To calculate the theoretical probability, we divide the favorable outcomes (spinning green) by the total possible outcomes. In this case, there is one favorable outcome (green) out of four possible outcomes (red, green, orange, and blue), resulting in a probability of 1/4 or 25%.

It's important to note that theoretical probability is based on the assumption of equally likely outcomes and assumes a large number of trials. In practice, actual outcomes may deviate from theoretical probabilities due to factors like imbalances in the spinner or inherent randomness.

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The area of the given shape is 47 yard².

Given a shape.

The shape consists of a rectangle and a triangle.

The area of the shape can be found by adding the individual area of the rectangle and the triangle.

Area of rectangle = length × width

                              = 4 × 5

                              = 20 yard²

Area of the triangle = 1/2 × base × height

Base length = 2 + 2 + 5 = 9 yd

Height = 6 yd

Area of triangle = 1/2 × 9 × 6

                          = 27 yard²

Total area of the shape = 20 yard² + 27 yard² = 47 yard²

Hence the area is 47 yard².

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To find C∇f·dr, where C is a constant and f has parametric equations[tex]x = t^2 + 1[/tex] and [tex]y = t^3 + t[/tex] for 0 ≤ t ≤ 1, we need to evaluate the line integral. The line integral ∇f·dr represents the work done along the curve defined by the parametric equations.

To calculate C∇f·dr, we first need to find the gradient of the function f. The gradient of f is given by ∇f = (∂f/∂x, ∂f/∂y), where ∂f/∂x and ∂f/∂y are the partial derivatives of f with respect to x and y, respectively.

Taking the partial derivatives of f = (x, y) with respect to x and y, we get ∂f/∂x = 2t and ∂f/∂y = [tex]3t^2[/tex] + 1.

Next, we need to parameterize the curve defined by the given parametric equations. The curve is defined for 0 ≤ t ≤ 1.

To evaluate the line integral C∇f·dr, we substitute the gradient components (∂f/∂x, ∂f/∂y) and the differential elements (dx, dy) with their corresponding expressions in terms of t.

Finally, we integrate the dot product C(∂f/∂x dx + ∂f/∂y dy) along the curve from t = 0 to t = 1. The result will depend on the constant C and can be computed using the given table of values for x and y.

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The complete question is:

A Table Of Values Of A Functionfwith Continuous Gradient Is Given. Find

A table of values of a functionfwith continuous gradient is given. FindCnablaf�dr, whereChas parametric equationsx=t2+ 1,y=t3+t, 0t1.

x\y 0 1 2

0 2 7 5

1 4 6 8

2 9 3 10

The age of the guy is 29.72 years, the age Gerald is 59.44 years and the age of gill is 9.8 years.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given data in the question,

The equation according to the given statement will be,

The age of Gerald is 2x,

The age of the guy is x and the age of the gill is 0.33x.

So, the equation will be,

[tex]\sf x + 2x + 0.33x = 99[/tex]

[tex]\sf 3.33x = 99[/tex]

[tex]\sf x = \dfrac{99}{3.33}[/tex]

[tex]\sf \bold{x = 29.72}[/tex]

Age of Gerald, 2x = 2(29.72) = 59.44 years.

Age of guy, x = 29.72 years and,

Age of gill, 0.33x = 0.33(29.72) = 9.8 years.  

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The perimeter of the shape is 28.65 cm.

We have,

Circumference of a circle = Angle/360 x 2πr

Now,

r = 7 cm

Angle = 120

Substitute the values.

Arc length intercepted by 120.

= Angle/360 x 2πr

= 120/360 x 2 x 3.14 x 7

= 14.65 cm

Now,

The perimeter of the shape.

= 7 + 7 + 14.65

= 28.65 cm

Thus,

The perimeter of the shape is 28.65 cm.

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The average stopping distance when driving at 55 mph on dry, level pavement can vary depending on several factors such as vehicle condition, road conditions, and driver reaction time.

Therefore, it is not possible to provide an exact average stopping distance without more specific information.

However, as a general guideline, it is commonly recommended to use the "3-second rule" for following distance. This means that you should maintain a distance from the vehicle in front of you that would allow you to come to a complete stop within three seconds. At higher speeds like 55 mph, the stopping distance will be longer compared to lower speeds.

To estimate the average stopping distance, you can consider the total stopping distance, which is the sum of the perception distance, reaction distance, and braking distance. The perception distance is the distance your vehicle travels while you recognize a need to stop, the reaction distance is the distance traveled during your reaction time, and the braking distance is the distance covered while your vehicle comes to a stop after applying the brakes.

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To calculate the probabilities of the given events when randomly selecting a permutation of {1, 2, 3}, we need to consider the total number of possible permutations and the number of permutations that satisfy each event.

Total number of permutations:

There are 3 elements in the set {1, 2, 3}, so the total number of permutations is 3! = 3 × 2 × 1 = 6.

(a) 1 precedes 3:

In this case, we want to find the number of permutations where 1 appears before 3. The valid permutations are {1, 2, 3} and {2, 1, 3}, which means there are 2 permutations that satisfy this event.

Probability of 1 precedes 3: P(1 precedes 3) = Number of permutations satisfying the event / Total number of permutations = 2 / 6 = 1/3.

(b) 3 precedes 1:

Here, we want to find the number of permutations where 3 appears before 1. The valid permutations are {3, 1, 2} and {3, 2, 1}, so there are 2 permutations that satisfy this event.

Probability of 3 precedes 1: P(3 precedes 1) = Number of permutations satisfying the event / Total number of permutations = 2 / 6 = 1/3.

(c) 3 precedes 1 and 3 precedes 2:

To find the number of permutations where 3 appears before 1 and 3 appears before 2, we can examine the valid permutations: {3, 1, 2} and {3, 2, 1}. Only these two permutations satisfy both conditions.

Probability of both events: P(3 precedes 1 and 3 precedes 2) = Number of permutations satisfying the events / Total number of permutations = 2 / 6 = 1/3.

Therefore, the probabilities are:

(a) P(1 precedes 3) = 1/3

(b) P(3 precedes 1) = 1/3

(c) P(3 precedes 1 and 3 precedes 2) = 1/3

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The complex number z = 2 - 8i in Trigonometric form ,the correct option is: 8.246(cos 75.964° + isin 75.964°).

The complex number z = 2 - 8i in trigonometric form, The trigonometric form is typically written as z = r(cos θ + isin θ), where r represents the magnitude and θ represents the argument.

The magnitude of z, we use the formula: |z| = sqrt(Re(z)^2 + Im(z)^2), where Re(z) is the real part and Im(z) is the imaginary part of z.

In this case, Re(z) = 2 and Im(z) = -8, so we have:

|z| = sqrt(2^2 + (-8)^2) = sqrt(4 + 64) = sqrt(68) ≈ 8.246

The argument (angle) of z, we use the formula: θ = atan(Im(z)/Re(z)), where atan is the arctangent function.

In this case, θ = atan((-8)/2) = atan(-4) ≈ -75.964° or 284.036° (adding or subtracting multiples of 360° does not change the angle).

Putting it all together, the complex number z = 2 - 8i can be expressed in trigonometric form as:

8.246(cos 75.964° + isin 75.964°) or 8.246(cos 284.036° + isin 284.036°).

Therefore, the correct option is: 8.246(cos 75.964° + isin 75.964°).

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[tex]-(5\cdot(-4))=-(-20)=20[/tex]

Distributive property works only for addition.

[tex]a(b+c)=ab+ac[/tex] but [tex]a(bc)=abc[/tex], not [tex]ab+ac[/tex] or something like that.

Answer:

[tex]-(-5\times(-4))=-(-20)=20[/tex]

Step-by-step explanation:

Notice that the product within the brackets is:

[tex]5\times(-4)=-20[/tex]

Then, by first evaluating the product within the brackets, we get the following:

[tex]-(5\times(-4))=-(-20)[/tex]

Finally, note that the negative of negative twenty is twenty as follows:

[tex]-(-20)=20[/tex]

*Note on your mistake:

You cannot distribute the negative sign to each component of a product.

This can only happen if the expression within the bracket is a sum, for instance:

[tex]-(5+(-4))=-5+4[/tex]

The graph of the function f(t) for −3π ≤ t ≤ 3π can be sketched as follows:

For −π ≤ t < 0, f(t) = −2t − π, which forms a linear segment with a negative slope in the range from −π to 0.

For 0 ≤ t < π, f(t) = 2t − π, which forms a linear segment with a positive slope in the range from 0 to π.

The function repeats periodically with a fundamental interval of 2π, so the graph will continue to alternate between these two linear segments as t increases or decreases beyond the given range.

Based on the graph, we can observe that the function f(t) is an odd function because it exhibits symmetry about the origin. It satisfies the property f(-t) = -f(t) for all values of t.

(b) To calculate the Fourier series for f(t), we need to find the coefficients a0, an, and bn. The Fourier series for a periodic function f(t) is given by:

f(t) = a0/2 + Σ[ancos(nωt) + bnsin(nωt)]

In this case, the fundamental frequency ω = 2π/2π = 1, and the coefficients can be calculated as follows:

a0 = (1/π) * ∫[-π, π] f(t) dt = 0 (since f(t) is odd and the integral of an odd function over a symmetric interval is zero)

an = (1/π) * ∫[-π, π] f(t) * cos(nωt) dt = 0 (since the integrand is odd, the integral of the product with an even function is zero)

bn = (1/π) * ∫[-π, π] f(t) * sin(nωt) dt

For n = 1, we have:

bn = (1/π) * ∫[-π, π] f(t) * sin(t) dt

= (1/π) * [∫[-π, 0] (-2t - π) * sin(t) dt + ∫[0, π] (2t - π) * sin(t) dt]

Evaluating the integrals, we find:

bn = (1/π) * [-2∫[-π, 0] t * sin(t) dt - ∫[-π, 0] π * sin(t) dt + 2∫[0, π] t * sin(t) dt - ∫[0, π] π * sin(t) dt]

By integrating term by term, we can find the values of bn for n = 1 and higher.

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The number of bags of maize loaded is A = 50 bags

Given data ,

A lorry weighs 3.2 tonnes when empty. It weighed 7.7 tonnes when loaded with 90 kg bags of maize.

To find the number of bags of maize loaded onto the lorry, we need to calculate the difference in weight between the loaded and empty states, and then convert that difference into the weight of the bags.

The weight of the lorry when loaded with bags of maize is 7.7 tonnes, and when empty, it weighs 3.2 tonnes. Therefore, the weight of the bags of maize is:

7.7 tonnes - 3.2 tonnes = 4.5 tonnes

On simplifying the equation , we get

Number of bags = (Weight of maize) / (Weight per bag)

= 4.5 tonnes / 0.09 tonnes

= 50 bags

Hence , there were 50 bags of maize loaded onto the lorry

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To find the general expressions for the autocorrelation function rzz() of z(t) in terms of the autocorrelation functions of x(t) and y(t), we need to consider the relationship between z(t), x(t), and y(t).

If z(t) is a linear combination of x(t) and y(t), we can express it as:

z(t) = a * x(t) + b * y(t)

where a and b are constants.

The autocorrelation function of z(t), denoted as rzz(), can be calculated as:

rzz() = E[z(t) * z(t + )]

Substituting the expression for z(t), we have:

rzz() = E[(a * x(t) + b * y(t)) * (a * x(t + ) + b * y(t + ))]

Expanding this expression and applying the linearity property of expectation, we get:

rzz() = a^2 * Exx() + b^2 * Eyy() + 2ab * Exy()

where Exx(), Eyy(), and Exy() are the autocorrelation functions of x(t), y(t), and the cross-correlation function between x(t) and y(t), respectively.

Therefore, the general expression for the autocorrelation function rzz() of z(t) in terms of the autocorrelation functions of x(t) and y(t) is given by:

rzz() = a^2 * Exx() + b^2 * Eyy() + 2ab * Exy()

This expression demonstrates how the autocorrelation of z(t) can be determined based on the autocorrelation functions of x(t) and y(t) along with their cross-correlation.

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Answer:Using two of the points on the line, you can find the slope of the line by finding the rise and the run. The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run: Slope =riserun Slope = rise run .

Step-by-step explanation:

Answer:

I don't understand your question

Step-by-step explanation:

writing it clearly

Answer:

x=77°

Step-by-step explanation:

angles in triangle add to 180°

180°-43°-60°=x°

77°=x°

The equation of the tangent plane to f(x, y) = x^2 - 2xy + 3y^2, with slopes 2 in the positive x direction and 2 in the positive y direction, is 2x + 4y - 8 = 0.

To locate the equation of the tangent airplane to the floor described with the aid of the feature f(x, y) = [tex]x^2 - 2xy + 3y^2[/tex], we need to decide the gradient vector and consider it at a given point.

The gradient vector will grant the ordinary vector to the tangent plane, and by way of the use of the slope information, we can discover the equation of the plane.

Calculate the partial derivatives of the feature with recognize to x and y:

f_x = 2x - 2y

f_y = -2x + 6y

Set up a device of equations the use of the given slope information:

f_x = 2

f_y = 2

Solve the machine of equations to discover the factor where the slopes are satisfied:

2x - 2y = 2 --> x - y = 1 --> x = y + 1

-2x + 6y = 2 --> -x + 3y = 1 --> -x = 1 - 3y --> x = 3y - 1

Setting the two expressions for x equal to every other:

y + 1 = 3y - 1

2 = 2y

y = 1

Substitute y = 1 into both expression for x:

x = 1 + 1

x = 2

Therefore, the factor the place the slopes are comfy is (2, 1).

Evaluate the gradient vector at the factor (2, 1):

grad(f) = (f_x, f_y) = (2x - 2y, -2x + 6y)

= (2(2) - 2(1), -2(2) + 6(1))

= (2, 4)

The ordinary vector to the tangent airplane is the gradient vector (2, 4).

Using the point-normal structure of the equation for a plane, the equation of the tangent airplane is:

2(x - 2) + 4(y - 1) + d = 0

To decide the price of d, alternative the coordinates of the factor (2, 1):

2(2 - 2) + 4(1 - 1) + d = 0

0 + 0 + d = 0

d = 0

The equation of the tangent airplane is:

2(x - 2) + 4(y - 1) = 0

Simplifying the equation, we have:

2x - 4 + 4y - 4 = 0

2x + 4y - 8 = 8

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The 95% confidence interval for the true difference between the average mass of eggs in small and large nests can be represented by a range of values with a lower and upper bound.

A confidence interval is a statistical range that provides a level of certainty about the true value of a population parameter. In this case, we are interested in the true difference between the average mass of eggs in small and large nests. The 95% confidence interval indicates that if we were to repeat the sampling process multiple times, we would expect the true difference to fall within this range 95% of the time.

To calculate the 95% confidence interval for the true difference between the average mass of eggs in small and large nests, we need to use statistical methods to estimate the population parameters based on sample data. This involves calculating the mean and standard deviation of the sample data, as well as the sample size. Once we have these values, we can use a formula to calculate the margin of error, which is the amount of uncertainty in our estimate due to the random sampling process. The margin of error is typically expressed as a percentage or a range of values. To calculate the confidence interval, we add and subtract the margin of error from the sample estimate. The resulting range of values represents the 95% confidence interval for the true population parameter.

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The total area of all the Circles used by Princess is 4710 square centimeters.

The total area of all the circles used by Princess, The formula for the area of a circle is given by:

A = πr²

where A represents the area and r is the radius of the circle. Since we are given the diameter of each circle (20 cm), we can calculate the radius by dividing the diameter by 2:

r = 20 cm / 2 = 10 cm

Substituting this value into the area formula, we have:

A = π(10 cm)²

Now, let's calculate the area of one circle:

A = 3.14 * (10 cm)² ≈ 314 cm²

Therefore, the area of one circle is approximately 314 square centimeters.

Since Princess used 15 circles, we can find the total area by multiplying the area of one circle by the number of circles:

Total area = 314 cm² * 15 = 4710 cm²

Hence, the total area of all the circles used by Princess is 4710 square centimeters.

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We have shown that for any connected graph G with at least one cycle, we can remove some edges such that the resulting subgraph is bipartite and connected.

A graph is a graphic or visual representation of facts or values. The points on a graph are frequently used to depict the relationships between two or more objects.

To prove the statement, let's consider a connected graph G with at least one cycle.

Case 1: G is already bipartite.

If G is already bipartite, then the statement is trivially true. We don't need to remove any edges because G is already bipartite and connected.

Case 2: G is not bipartite.

If G is not bipartite, it means that there exists at least one odd cycle in G. In order to make G bipartite, we can remove any one of the edges from the odd cycle. Removing a single edge will break the cycle and create two separate connected components.

Let's denote the original graph with the odd cycle as G', and the resulting subgraph after removing one edge as G''. By removing a single edge, G'' will consist of two connected components, each of which is bipartite. This is because removing one edge from the odd cycle creates two separate paths, and each path can be assigned a different color to form a bipartite graph.

Since G'' is the result of removing one edge from G', it is still connected because all the vertices in G' are still connected through the remaining edges. Thus, G'' is a connected subgraph of G and is also bipartite.

Therefore, we have shown that for any connected graph G with at least one cycle, we can remove some edges such that the resulting subgraph is bipartite and connected.

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Answer:21.9

Step-by-step explanation:

A value which 25% of the data lie below include the following: (A) the lower quartile (Q1) and it is 75.

Based on the information provided about the box-and-whisker plot of this data set, we would determine the five-number summary for the given data set as follows:

Generally speaking, the Lower or first quartile (Q₁) represents the 25% of the data in a box-and-whisker plot and it is equal to 75.

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The corresponding angle to angle 9, according to the figure  is

angle 11

Corresponding angles are a pair of angles that are formed on the same side of a transversal line and in the same relative position with respect to the parallel lines being intersected by the transversal.

In simpler terms corresponding angles are formed when a line crosses two parallel lines  and the angles are in corresponding positions on each of the parallel lines.

Using the figure, the parallel lines are l and m and angle 9 and angle 11  are at the vertex of he triangles formed.

The two triangles formed are congruent (parallel lines l and line m ensures equal length of sides), According  to CPCTC theorem

angle 9 ≅ angle 11

angle 20 ≅ angle 6

angle 16 ≅ angle 7

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complete question

What is/are two corresponding angles to angle 9?

To perform the hypothesis test to determine whether the mean GPA for business students differs from the mean GPA at the whole university, we will use the critical value method.

Given:

Sample size (n) = 18

Sample mean (x(bar)) = calculated using the provided GPAs

Population mean (μ) = 2.88

Population standard deviation (σ) = 0.5

Significance level (α) = 0.05

Step 1: Define the null and alternative hypotheses:

Null hypothesis (H0): The mean GPA for business students is equal to the mean GPA at the whole university (μ = 2.88).

Alternative hypothesis (Ha): The mean GPA for business students differs from the mean GPA at the whole university (μ ≠ 2.88).

Step 2: Determine the critical value(s):

Since we are using the critical value method and have a two-tailed test, we need to find the critical values for the given significance level (α = 0.05) and degrees of freedom (df = n - 1 = 18 - 1 = 17). We can consult the t-distribution table or use statistical software. For α = 0.05 and df = 17, the critical values are approximately ±2.110.

Step 3: Calculate the test statistic:

The test statistic for this scenario is the t-statistic, which measures how far the sample mean deviates from the population mean, taking into account the sample size and standard deviation. The formula for the t-statistic is:

t = (x(bar) - μ) / (σ / sqrt(n))

Using the given values, we can calculate the t-statistic:

t = (x(bar) - μ) / (σ / sqrt(n))

t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Step 4: Evaluate the test statistic:

Calculate the t-statistic using the provided values:

t = (x(bar) - μ) / (σ / sqrt(n))

Calculate the sample mean (x(bar)) using the provided GPAs.

Step 5: Determine whether to reject the null hypothesis:

Compare the absolute value of the calculated t-statistic with the critical value(s) from Step 2. If the absolute value of the t-statistic is greater than the critical value(s), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

If there is enough evidence to conclude that the mean GPA for business students differs from the mean GPA at the whole university, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

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The perimeter of a triangle with sides are,

⇒ P = 38 inches

Since, We know that;

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

Sides of triangle are,

⇒ 14 inches, 8 inches, and 16 inches

We know that;

Sum of all sides of a triangle are called Perimeter of triangle.

Hence, We get;

the perimeter of a triangle with sides are,

P = 14 inches + 8 inches + 16 inches

P = 38 inches

Thus, by definition of perimeter, the perimeter of a triangle with sides are,

⇒ P = 38 inches

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The value of arc RS is 105⁰.

The value of angle GHJ is 73⁰.

The value of angle GIJ is 73⁰.

The value of angle ABC is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

m∠ABC = ¹/₂ (arc AC ) (interior angle of intersecting secants)

m∠ABC = ¹/₂ ( 34⁰ )

m∠ABC = 17⁰

The value of arc RS is calculated as follows;

arc RT = 2 x ( 42⁰) (interior angles of intersecting secants)

arc RT = 84⁰

arc RS = 360 - (RT + TS) (sum of angles in a circle)

arc RS = 360 - ( 84 + 171)

arc RS = 360 - 255

arc RS = 105⁰

The value of angle GHJ is calculated as follows;

arc GJ = 360 - (68 + 31 + 115)

arc GJ = 146⁰

angle GHJ = ¹/₂ x 146⁰ = 73⁰

angle GIJ = angle GHJ = 73⁰ (vertical opposite angles are equal).

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The value of SS (Sum of Squares) for this population is 30. The answer is c.

To calculate SS, we use the formula:

SS = ΣX² - ((ΣX)² / N)

Given that ΣX = 12, ΣX² = 54, and N = 6, we can substitute these values into the formula:

SS = 54 - ((12)² / 6)

  = 54 - (144 / 6)

  = 54 - 24

  = 30

The value of SS represents the sum of the squared deviations of each score from the mean. It quantifies the variability or dispersion within the data set. In this case, the given values of ΣX and ΣX² allow us to calculate SS by substituting them into the formula.

By performing the necessary calculations, we find that SS for this population is 30. It is important to note that SS is commonly used in various statistical analyses, such as calculating variance and standard deviation, to assess the spread of data points from the mean.

Hence, the correct option is: c. 30

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The equation Y=-3x-1 represents a linear relationship between x and y, and can be used to model real-world situations such as distance vs. time or cost vs. quantity.

The equation Y=-3x-1 represents a straight line on a coordinate plane. The "slope-intercept" form of the equation is y=mx+b, where m is the slope and b is the y-intercept.

In this case, the slope is -3 and the y-intercept is -1. This means that the line goes downwards at a rate of 3 units for every 1 unit to the right, and intersects the y-axis at -1.

To find the solution to this equation, you would need to have a specific value for either x or y.

If you were given a value for x, you could plug it into the equation to find the corresponding value for y. If you were given a value for y, you could solve for x by rearranging the equation.

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The measure of the arc angles which subtends angles at the center are: TP = 132°, WTQ = 228°, SP = 222° and RT = 135°.

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.

So;

arc angle TP = 132° {vertical angles}

arc angle WTQ = 132 + (TW + PQ)

TW and PW are vertical angles and are equal so; TW = [360 - 2(132)]/2

TW = PQ = 48

arc angle WTQ = 132° + (48 + 48) = 228

arc angle SP = 180° + SW

SW = 90 - TW

SW = 90 - 48 = 42

arc angle SP = 180° + 42 = 222°

arc angle RT = 180 - QR

QR = 90/2 = 45°

arc angle RT = 180 - 45 = 135°

Therefore, the following are measures of the arc angles which subtends angles at the center: TP = 132°, WTQ = 228°, SP = 222° and RT = 135°.

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hello

the answer to the question is:

for the length of DF, divide the DEF triangle into two identical right angled triangles. hence;

Cos 68° = 9/DF ----> DF = EF = 24

hence, you should look for all the triangles with these three angles (20°, 35° and 125°);

A) similar, B) different, C) similar, D) similar, E) different