Ratio of 2:3:30 in 385​

The value of function k(f(x)) is 12x³ + 32x - 8.

Function composition is a way to combine two or more functions to form a new function. In this case, we are given two functions f(x) and k(x), and we need to find the value of k(f(x)), which means we need to apply the function k(x) to the output of the function f(x).

Here we have

Functions f(x)= 3x³ +8x -2 and k(x) = 4x

To find k(f(x)), we need to substitute the expression for f(x) into k(x) wherever we see x. So, we have:

k(f(x)) = 4(f(x)) = 4(3x³ + 8x - 2)

We can simplify this expression by distributing the 4:

k(f(x)) = 12x³ + 32x - 8

Therefore,

The value of function k(f(x)) is 12x³ + 32x - 8.

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"It can vary - it really depends on the distribution of the variable."

The number of intervals, or bins, to choose when creating a histogram can vary depending on the distribution of the variable.

Most often, about 8-10 intervals are used, but there is no set rule. It is generally recommended to have at least 5 intervals, but if the data is highly skewed or has outliers, more intervals may be needed to accurately represent the distribution.

Ultimately, the goal is to choose a number of intervals that provides a clear visual representation of the data without oversimplifying or overcomplicating the histogram.

The number of intervals or bins to be chosen when creating a histogram can vary and it really depends on the distribution of the variable.

While most often, about 8-10 bins are used, there is no hard and fast rule for the number of bins to be used in a histogram.

In general, the number of bins should be large enough to display the shape of the distribution clearly, but not so large that it obscures important features of the distribution or leads to overfitting.

A minimum of 5 bins is recommended to display the basic shape of the distribution, but more bins may be necessary for complex or multi-modal distributions.

Depending on the distribution of the variable, a histogram's number of intervals or bins can be altered.

There is no established guideline, however 8–10 intervals are typically utilized.

A minimum of five intervals are often advised, however if the data is extremely skewed or contains outliers, more intervals could be required to correctly depict the distribution.

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The height of the pyramid whose volume is already given would be = 1,440,000 ft

To calculate the height of the pyramid, the formula of the Volume of the pyramid should be used.

Volume = 1/3lwh

where l = base length = 8h-30 ft= 3.75 ft

w = base width= 8h+20 ft = -2.5 ft

h = h ft

The volume of the pyramid = 4,500,000 cubic feet

4,500,000 = 1/3 × (3.75)(-2.5)h

Make h the subject of formula;

h = 4500000×3/3.75×(-2.5)

h = 13500000/9.375

h = 1,440,000 ft.

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Answer:

$481

Step-by-step explanation:

37×$17=$481

he made $481

The measure of angle I in the triangle HIJ using given measurements is equal to 46.05 degrees.

In the triangle HIJ,

The measure of angle J is equal to 90 degrees.

This implies ,

HI is the hypotenuse.

JH is the opposite side to angle I.

In triangle HIJ,

Using trigonometric ratio we get,

sin ∠I = Opposite side / Hypotenuse

Substitute the values we have,

⇒ sin ∠I = 4.8 / 6.7

⇒ sin ∠I = 0.72

Now , take sin⁻¹ both the side of the equation we get,

⇒sin⁻¹(sin ∠I) = sin⁻¹( 0.72 )

Here sin⁻¹(sin ∠I) = ∠I

⇒∠I = sin⁻¹( 0.72 )

⇒∠I = 46.05 degrees

Therefore, the measure of angle I is equal to 46.05 degrees.

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The compound interest investment earns more interest than the simple interest investment, and the difference becomes more significant over time.

After 10 years, the difference is relatively small, but after 20 years, the compound interest investment has earned over $3,700 more than the simple interest investment.

To calculate the amount after 10 and 20 years, we can use the following formulas:

Simple Interest: A = P * (1 + r * t)

Compound Interest: A = P * (1 + r/n)^(n*t)

Where:

Using these formulas and the information given in the table, we can calculate the amount after 10 years and 20 years for each type of investment.

For simple interest, the interest is not compounded, so we just add the interest to the principal:

Amount after 10 years: A = $50,000 * (1 + 0.0275 * 10) = $68,750

Amount after 20 years: A = $50,000 * (1 + 0.0275 * 20) = $87,500

For compound interest, we need to use the formula above with n=12 (since the interest is compounded monthly):

Amount after 10 years: A = $50,000 * (1 + 0.0275/12)^(12*10) = $68,704.23

Amount after 20 years: A = $50,000 * (1 + 0.0275/12)^(12*20) = $91,262.47

To compare the two investments, we can look at the difference between the amounts after 10 and 20 years:

Difference after 10 years: $68,750 - $68,704.23 = $45.77

Difference after 20 years: $87,500 - $91,262.47 = $3,762.47

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The measure of the angle m∠FGH is 83°.

Since the measure of an angle formed by a two tangents drawn from a point outside the circle is one-half the the difference of the intercepted arcs.

Thus, we can say:

m∠FGH = 1/2 * (∠FIH - 97°)

∠FIH = 360 - 97 = 263° (sum of angle in a circle)

m∠FGH = 1/2 * (263 - 97°)

m∠FGH =  1/2 * 166

m∠FGH = 83°

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Point A = (5,4). If you rotated A 90 degrees about the point (2,-1), the coordinates of A' is (-1,2).

Rotation is the process of rotating an object or a point around a fixed point or axis. In mathematics, rotation refers to a transformation that preserves the size and shape of an object while changing its orientation. It is a basic geometric transformation that is used in various fields, including mathematics, physics, engineering, and computer graphics.

In a two-dimensional space, a rotation is typically described by an angle of rotation and a fixed point, which is known as the center of rotation. The angle of rotation represents the amount by which the object is rotated, while the center of rotation is the point around which the object is rotated. In a three-dimensional space, a rotation is described by an axis of rotation and an angle of rotation.

To rotate point A 90 degrees counterclockwise about the point (2,-1), we can use the following formula:

A' = (x', y') = (a + (x - a) cosθ - (y - b) sinθ, b + (x - a) sinθ + (y - b) cosθ)

where (a,b) is the center of rotation and θ is the angle of rotation (90 degrees in this case).

Substituting the given values, we get:

a = 2, b = -1, x = 5, y = 4, θ = 90 degrees

x' = 2 + (5 - 2) cos(90) - (4 + 1) sin(90) = 2 - 3 = -1

y' = -1 + (5 - 2) sin(90) + (4 + 1) cos(90) = -1 + 3 = 2

Therefore, the coordinates of A' are (-1, 2).

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Answer:

To find the values of f(g(x)) for the given values of x, we need to first evaluate g(x) for each value of x, and then plug the result into f(x).

Using the given functions:

g(x) = 2x - 5

f(x) = √(x+1)

Therefore, we have:

f(g(x)) = √(g(x) + 1) = √(2x - 5 + 1) = √(2x - 4) = 2√(x - 2)

So, we can complete the table as follows:

x f(g(x))

4 2

10 4

20 6

34 8

52 10

Therefore, the completed table is:

x f(g(x))

4 2

10 4

20 6

34 8

52 10

The correct answer is option B. Translate 1 to the left, scale vertically by 1/2, then reflect over the y-axis.

The process of modifying the shape, location, or features of a graph is often referred to as graph transformation. Graphs are visual representations of mathematical functions or data point connections, often represented on a coordinate plane.

Translations, reflections, rotations, dilations, and other changes to the look of a graph are examples of graph transformations.

For the given problem, Transformation to get the desired result can be carried out as:

Hence, to convert the graph of "y = k(x)" to the graph of "y = -k(x + 1)," the correct sequence of transformations is to translate 1 unit to the left, scale vertically by 1/2, and then reflect across the y-axis, which is option B.

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The output of the LTI system with frequency response function [tex]h(w) = 1/(jw^3)[/tex], given an input[tex]x(t)[/tex], is:

[tex]y(t)[/tex]= inverse Fourier transform of [tex][1/(jw^3) X(w)][/tex]

To compute the output of an LTI system with frequency response function [tex]h(w) = 1/(jw^3)[/tex], given an input x(t), we can use the Fourier transform:

[tex]H(w)[/tex] = Fourier transform of [tex]h(t)[/tex]

[tex]X(w)[/tex] = Fourier transform of [tex]x(t)[/tex]

[tex]Y(w) = H(w) X(w)[/tex]

[tex]Y(w)[/tex] is the Fourier transform of the output [tex]y(t)[/tex].

Using the given frequency response function, we have:

[tex]H(w) = 1/(jw^3)[/tex]

Taking the Fourier transform of the input [tex]x(t)[/tex], we have:

[tex]X(w)[/tex] = Fourier transform of [tex]x(t)[/tex]

And multiplying [tex]H(w)[/tex] and[tex]X(w)[/tex], we get:

[tex]Y(w) = H(w) X(w) = 1/(jw^3) X(w)[/tex]

Taking the inverse Fourier transform of [tex]Y(w)[/tex], we get the output [tex]y(t)[/tex]:

[tex]y(t)[/tex] = inverse Fourier transform of [tex]Y(w)[/tex]

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From the figures, AB is a tangent to the C because they make a right angles (90⁰)

Recall that in n Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs.

We shall be determining the angle at C to see if it gives 90⁰

Using trigonometrical ratios of tangent

TanB = Opposite/Adjacent

Tan B. = 4.8/7.2

Tan B = 0.6667

B = Tan⁻¹0.6667

<B = 33.69⁰

Also in the same manner,

TanS = opp/Adj

Tan S = 7.2/4.8

Tan S = 1.5

S = Tan⁺¹1.5

< S = 56.31⁰

Npw <S + <B = 56.32 + 33.69 = 89.9999247 = 90⁰

Therefore AB makes tangent at C

20.  

Tan C = Opp/Adj

Tan C = 15/11.2

Tan C = 1.3393

C = Tan⁺¹1.3393

< C = 53.25

Also, Tan B = 11.2/15

Tan B = 0.7467

B = 36.75

<B + <C = 36.75 + 53.25 = 89.9986 = 90⁰

Therefore AB makes a tangent at C

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Answer: The function that has real zeros at x = 3 and x = 7 is:

f(x) = (x - 3)(x - 7)

Expanding this function using FOIL (First, Outer, Inner, Last) method:

f(x) = x^2 - 10x + 21

Therefore, the answer is:

f(x) = x^2 - 10x + 21

Step-by-step explanation:

Answer:

-6/7

Step-by-step explanation:

The value of a for which the solution of the inequality is all real numbers is a = 5.

We have to first simplify the inequality:

A(x + 3) < 5x + 15 - x

Ax + 3A < 4x + 15

Ax - 4x < 15 - 3A

Simplifying further:

x(A - 4) < 15 - 3A

Now, we need the inequality to hold for all real values of x. This means that the coefficient of x, (A - 4), must have a fixed sign, and that the right-hand side, 15 - 3A, must be unbounded.

For the coefficient of x to have a fixed sign, we need either A - 4 < 0 or A - 4 > 0. This means that A must be less than 4 or greater than 4.

For the right-hand side to be unbounded, we need 15 - 3A to be equal to positive or negative infinity. Since 15 - 3A is a linear function of A, this only occurs when A = 5.

So, the solution to the inequality for all real numbers is:

if A < 4, then the solution is x < (15 - 3A) / (4 - A)

if A > 5, then the solution is x > (15 - 3A) / (4 - A)

if A = 5, then the solution is all real numbers.

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The area swept clean by the rear window wiper blade is approximately 91.37 square inches.

We'll calculate the area swept clean by the rear window wiper blade using the given information.
Convert the angle from degrees to radians:

115 degrees * (π radians / 180 degrees) = (23π/36) radians.
Find the length of the arc that the wiper blade traces out:

Arc length = (radius * angle) = (10 inches * (23π/36) radians) ≈ 20.08 inches.
Calculate the area of the sector formed by the arc and the pivot point:

Sector area = (1/2) * (radius² * angle) = (1/2) * (10 inches² * (23π/36) radians) ≈ 100.42 square inches.
Find the length of the arc that the mounting point of the blade traces out:

Arc length = (radius * angle) = (3 inches * (23π/36) radians) ≈ 6.02 inches.
Calculate the area of the sector formed by this arc and the pivot point:

Sector area = (1/2) * (radius² * angle) = (1/2) * (3 inches² * (23π/36) radians) ≈ 9.05 square inches.
Subtract the smaller sector area from the larger one to get the area swept clean by the wiper blade:

Area swept clean = 100.42 square inches - 9.05 square inches ≈ 91.37 square inches.

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The area swept clean by the rear window wiper blade is approximately 31.53 square inches.

To determine the area swept clean by the rear window wiper blade, we first need to find the length of the arc covered by the blade. We can use the formula:

arc length = radius * angle in radians

To convert the angle from degrees to radians, we multiply by[tex]\pi /180[/tex]:

115 degrees x [tex]\pi /180[/tex] = 2.007 radians

The radius is the length of the wiper arm, which is 13 inches minus the distance from the pivot point to the blade, which is 3 inches. Therefore, the radius is:

13 inches - 3 inches = 10 inches

Now we can calculate the arc length:

arc length = 10 inches x 2.007 radians = 20.07 inches

So the area swept clean by the wiper blade is approximately equal to the area of the sector formed by the arc and the two radii. The formula for the area of a sector is:

area = (angle in radians / [tex]2\pi[/tex]) x [tex]\pi r^2[/tex]

Plugging in values we have:

area = (2.007 / [tex]2\pi[/tex]) x [tex]\pi[/tex][tex](10 inches)^2[/tex] = 31.53 square inches

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For all given Quadrilaterals none has enough information provided in the problem to definitively say - if they are a parallelogram.Hence, option E is correct for all.

If a quadrilateral is a parallelogram, it satisfies the following properties:

It is important to note that in order to definitively conclude that a quadrilateral is a parallelogram, all four properties must be satisfied. If only one or some of the properties are met, it does not necessarily guarantee that the quadrilateral is a parallelogram.

Figure 1-: Adjacent angles are 105 and 75 degrees, which satify the condition of opposite angles being equal but except this no other information is provided, Hence, we don't have enough information to say figure 1 is a parallelogram.

Figure 2-: Diagonals bisect each other and make angle 65 degree with each other. Given that Diagonal 1 bisects Diagonal 2 and the opposite sides of the quadrilateral are equal, by using SAS criterion, the congruency of triangles formed by the diagonals can be derived to say that the opposite angles of the quadrilateral are also equal . However, we still need more information about parallelism of sides to definitively say given quadrilateral is a parallelogram.

Figure 3-: One pair of opposite side is equal in length ,while other pair of line is parallel to each other.This information is insufficient to determine if given quadrilateral is a parallelogram.

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If Cara's calculation of the sum of the squared differences i.e. 1370 from the mean is incorrect, that would be the first error she made in computing the variance.

As the steps for finding the variance are not provided, it is difficult to determine the first error Cara made.

However, the formula for calculating the variance is:

Variance = (sum of the squared differences from the mean) / (number of observations)

The first error Cara may have made is in calculating the sum of the squared differences from the mean.

The correct steps to find the variance are:

Find the mean:

Mean = (87 + 46 + 90 + 78 + 89) / 5 = 78

Calculate the differences from the mean for each observation:

87 - 78 = 9

46 - 78 = -32

90 - 78 = 12

78 - 78 = 0

89 - 78 = 11

Square each difference:

[tex]9^2 = 81[/tex]

[tex](-32)^2 = 1024[/tex]

[tex]12^2 = 144[/tex]

[tex]0^2 = 0[/tex]

[tex]11^2 = 121[/tex]

Find the sum of the squared differences:

81 + 1024 + 144 + 0 + 121 = 1370

Divide the sum of squared differences by the number of observations:

Variance = 1370 / 5 = 274.

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The correct answer is (c) 1.9

To calculate the test statistic in this example, we can use the formula for a z-test for proportions:

[tex]z = (p - P) / \sqrt{[P(1-P) / n][/tex]

where:

p is the sample proportion of vegetarians (140/1000 = 0.14)

P is the hypothesized population proportion of vegetarians (0.12)

n is the sample size (1000)

Substituting these values into the formula, we get:

[tex]z = (0.14 - 0.12) / \sqrt{[0.12(1-0.12) / 1000][/tex]

z = 0.02 / 0.0110

z = 1.818 (rounded to three decimal places)

Therefore, the test statistic in this example will be approximately equal to 1.818. The answer closest to this value is (c) 1.9

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If M is the midpoint of the leg CG, then the

a) Area of ABD = 18.75 ft^2

b) Area of MOC = 15 ft^2

To solve this problem, we need to use the properties of trapezoids and their diagonals. Let's start with finding the area of ABD.

First, notice that ABD and COD are similar triangles because they share angle O. Thus, we can write

AB/CD = AD/CO

Since AD = BC (opposite sides of a trapezoid are parallel), we can simplify to:

AB/CD = BC/CO

We also know that the area of AOD is 15 ft^2

Area of ABD/ Area of COD = AB/CD

We can substitute the ratio AB/CD from the similarity relation above to get

Area of ABD/ Area of COD = BC/CO

Since the bases of the trapezoids are parallel

Area of ABD/ Area of COD = BD/CO

Finally, we can use the fact that the altitudes from B and O to the longer base are in a 5:3 ratio to write

Area of ABD/ Area of COD = 5/3

Area of ABD = 5/8 × Area of COD

We know that the area of AOD is 15 ft^2, so the area of COD is twice that, or 30 ft^2. Therefore

Area of ABD = 5/8 × 30 = 18.75 ft^2

Next, we need to find the area of MOC. To do this, we can use the fact that the diagonals of a trapezoid divide it into four triangles, and the areas of these triangles are proportional to the lengths of the diagonals.

Let x be the length of OC, and let y be the length of OG. Then we have

Area of MOC/ Area of MOG = x/y

Also, since M is the midpoint of CG, we have

x = 2y

Substituting this into the first equation, we get

Area of MOC/ Area of MOG = 2

We know that the area of MOG is half the area of AOD, so

Area of MOG = 15/2 ft^2

Therefore, we have

Area of MOC = 2 × Area of MOG = 15 ft^2

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Answer:

Step-by-step explanation:

1 + 1 divided by 3 x 3.5 = 4.66 or 4 2/3

The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance is 10.76.

The critical value can be determined using a statistical table.

The degrees of freedom for the blocks is 4 (df_b = 5 - 1 = 4) and for the treatments is 2 (df_t = 3 - 1 = 2).

The critical value for a 5% level of significance is 10.76.

This value can be found in the statistical table given in the textbook.

The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance can be calculated by using the F-test statistic.

The F-test is used to compare the variance between the blocks (SSBL) and the variance between the groups (SSB).

The F statistic is calculated by dividing the variance between the blocks (SSBL) by the variance between the groups (SSB).

In this case,

The F statistic is 3738/1048.93 = 3.56.

The critical value for a 5% level of significance can be found using a statistical table.

According to the table,

The critical value for an F statistic of 3.56 with four degrees of freedom in the numerator and four degrees of freedom in the denominator is 10.76

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The sample mean for 100 pell grant recipients is more likely to be within $80 of $2,600 for State A, given the relatively smaller population size and the use of the t-distribution.

To compare the two states, we need to calculate the probability of the sample mean for 100 pell grant recipients being within $80 of $2,600 for each state.

For State A, with only 4,000 pell grant recipients, the sample size of 100 is relatively large, but not enough to use the normal distribution. Therefore, we need to use the t-distribution, which has fatter tails than the normal distribution, making it more likely to produce extreme values. This means that the probability of the sample mean for 100 pell grant recipients being within $80 of $2,600 is higher for State A than for State B.

For State B, with a larger population of 200,000 pell grant recipients, the sample size of 100 is a small fraction of the population, allowing us to use the normal distribution. However, as the distribution is narrower than the t-distribution, the probability of the sample mean for 100 pell grant recipients being within $80 of $2,600 is lower for State B than for State A.

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Answer:

The correct answer is:

10√2

Explanation:

In a right triangle, the hypotenuse is the side opposite the right angle and is also the longest side. The other two sides are called the legs.

In this problem, the hypotenuse of the resulting triangles is given as 20 inches. Since the quilt squares are cut on the diagonal to form triangular quilt pieces, the hypotenuse of each triangle is formed by the diagonal cut of a square.

Let's denote the side length of each square as "s" inches.

According to the Pythagorean Theorem, which relates the sides of a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

In this case, the hypotenuse is 20 inches, so we have:

20^2 = s^2 + s^2 (since the two legs of the right triangle are the sides of the square)

400 = 2s^2

Dividing both sides by 2, we get:

200 = s^2

Taking the square root of both sides, we get:

s = √200

Since we are looking for the side length of each piece in simplified radical form, we can further simplify √200 as follows:

√200 = √(100 x 2) = 10√2

So, the side length of each quilt piece is 10√

The side length of each piece of the triangular pieces of quilt cut from squares will be 10√2 inches.

This is a simple mathematics problem that can be solved using the Pythagoras theorem. This theorem states that in a right-angled triangle, the square root of the sum of the two perpendicular sides (p,b) is equal to the longest side, called the hypotenuse (h).

[tex]h = \sqrt{p^2 + b^2}[/tex]

Since the triangle pieces have been cut from a square, they will be right-angled triangles, and the two perpendicular sides will be equal, i.e., p = b.

20 = √2p²  (since p and b are equal, b can be taken as p)

On squaring both sides,

400 = 2p²

p² = 400/2

p² = 200

p = √200

p = 10√2 = b

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Answer: 94 square inches 2

Step-by-step explanation:

2×(5×4 + 5×3 + 4×3) = 94 sq in 2

length x width x height

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have a good day!

The score to be made on the 4th quiz in order to have a mean quiz score of exactly 90 is equal to 88.

Let us consider the score that Tim needs to get on his fourth quiz be x.

Score he needs to get in order to have a mean quiz score of 90,

Set up an equation using the formula for the mean ,

(mean score) = (sum of scores) / (number of scores)

If Tim wants his mean quiz score to be 90, then we have,

⇒ 90 = (86 + 92 + 94 + x) / 4

Multiplying both sides by 4, we get,

⇒360 = 86 + 92 + 94 + x

Simplifying this equation, we get,

⇒ x = 360 - 272

⇒ x = 88

Therefore, Tim needs to get a score of 88 on his fourth quiz in order to have a mean quiz score of exactly 90.

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Answer: A. 5,220,000 songs were downloaded in the year 2020.

Step-by-step explanation: The interpretation of s(2020) = 5,220,000 is that in the year 2020, 5,220,000 songs were downloaded. The function s(d) represents the number of songs downloaded in a year d, so plugging in 2020 for d gives us the specific number of songs downloaded in that year.

Step-by-step explanation:

18-2x<3(2x-1)-3

21-2x<6x-3

24<8x

3<x

Interval notation

(3, ∞)

The measures of center and variability that would be most appropriate to describe the given distribution is D) Median and IQR.

The middle value in a set of data is represented by the median, a measure of central tendency. It is the value that, when a dataset's values are ranked from lowest to highest, distinguishes the lower from the upper half of the dataset.

The middle 50% of a dataset's interquartile range (IQR) is a measure of variability that captures this dispersion. It is the difference between the data's first (Q1) and third (Q3) quartiles. The number that divides the lowest 25% of the data from the remaining data is known as the first quartile, and the value that separates the highest 25% of the data from the remaining data is known as the third quartile.

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The complete question is:

There are 64 degrees of freedom for the test for independence in this contingency table.

To find the degrees of freedom for a test for independence in a contingency table, you can use the following formula:
Degrees of freedom (df) = (number of rows - 1) * (number of columns - 1).
In your case, the contingency table has nine rows and nine columns. Using the formula:
df = (9 - 1) * (9 - 1)
df = 8 * 8
df = 64.

In a contingency table, the degrees of freedom (df) for the test of independence are calculated as:

df = (number of rows - 1) x (number of columns - 1)

In this case, the contingency table has nine rows and nine columns, so the degrees of freedom are:

df = (9-1) x (9-1) = 64

This means that there are 64 degrees of freedom for the test of independence.

Degrees of freedom are important because they determine the critical values for the test statistic, which in turn affects the decision to reject or fail to reject the null hypothesis.

In general, as the degrees of freedom increase, the critical values decrease, making it easier to reject the null hypothesis.

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There are 64 degrees of freedom for the test for independence in a contingency table with nine rows and columns.

To determine the degrees of freedom for the test for independence in a contingency table with nine rows and columns, we use the formula df = (r-1)(c-1), where r is the number of rows and c is the number of columns.

Substituting in the values, we get:df = (9-1)(9-1)df = 8 x 8df = 64A contingency table is a table that shows the frequency distribution of two or more categorical variables.

A test for independence is a statistical test that checks whether the variables are related or not.

Therefore, there are 64 degrees of freedom for the test for independence in a contingency table with nine rows and columns.

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