Which amount is bigger? x^0, 1/x or x^-1, assuming that x > 1

since we have found an element (48) in S that is not in T, we can conclude that S is not equal to T.

To prove that S is not equal to T, we need to show that there I an element in either S or T that is not in the other set.

Let's first look at the elements in S. We know that S is the set of all integers that can be expressed as 24 times some other integer. So, for example, 24, 48, 72, -24, -48, -72, etc. are all in S.

Now, let's look at the elements in T. We know that T is the set of all integers that can be expressed as 4 times some integer and 6 times some integer. We can find some examples of numbers in T by finding the multiples of the LCM of 4 and 6, which is 12. So, for example, 12, 24, 36, -12, -24, -36, etc. are all in T.

Now, let's consider the number 48. We know that 48 is in S, since it can be expressed as 24 times 2. However, 48 is not in T, since it cannot be expressed as 4 times some integer and 6 times some integer. This is because the only common multiple of 4 and 6 is 12, and 48 is not a multiple of 12.

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The ratio of boy to girl who play kickball at race is 6 to 2. There are 18 girl on the team. the number of boys who play kickball at race is 12 boys.

The ratio of boy to girl who play kickball at race is 6 to 2

6 boys: 2 girls

Multiply the number of girls by the ratio:

18 girls x (6 boys / 2 girls) = 18 x 3 = 54

Subtract the number of girls from the total to get the number of boys:

54 - 18 = 36

Therefore, there are 12 boys who play kickball at race.

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To plot with a range 2 to 20 and y=x using the matplotlib library, the following code can be written:
import matplotlib.pyplot as plt

x = range(2, 21)
y = x

plt.plot(x, y)
plt.show()
``The above code imports the matplotlib library using the alias `plt`. It then creates a range of values for `x` from 2 to 20 using the `range()` function. The values of `y` are set equal to the values of `x`.The `plot()` function is used to create the plot with the `x` and `y` values passed as arguments. The `show()` function is then called to display the plot.

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The charge per cubic foot is $0.05. The equation for the total cost of a resident's water is C(x) = 0.05x + 40. The number of cubic feet of water used that would lead to a bill of $130 is 2200.

We will use the given data to calculate the charge per cubic foot:Let x be the number of cubic feet of water used by a household and let y be the corresponding bill amount.

Case 1: When a household using 1000 cubic feet was billed $90.

Case 2: When one using 1600 cubic feet was billed $105.Subtracting case 1 from case 2, we get:$$105 - 90 = 15$$$$1600 - 1000 = 600$$So, the charge per cubic foot is:$$\frac{15}{600} = 0.025$$$$\implies 0.05 \text{ (for two decimal place)}$$ Hence, the charge per cubic foot is $0.05.

To write an equation for the total cost of a resident's water as a function of cubic feet of water used, we will use the given data:

$$\text{Fixed amount = } $40$$\text{Charge per cubic foot of water used = } $0.05$$\text{Number of cubic feet used = } x$$

Therefore, the equation for the total cost of a resident's water as a function of cubic feet of water used is:

$$C(x) = \text{(Charge per cubic foot of water used)}\times\text{(Number of cubic feet used)}+\text{(Fixed amount)}$$$$C(x) = 0.05x + 40$$

To find out how many cubic feet of water used would lead to a bill of $130, we will use the equation obtained above:

$$C(x) = 0.05x + 40

= $130$$$$\implies 0.05x

= $90$$$$\implies x

= \frac{90}{0.05}

= 1800$$

Therefore, the number of cubic feet of water used that would lead to a bill of $130 is 1800.

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Step-by-step explanation:

\(\frac{-x^{2}+9}{x+3} \\ \\ \frac{-(x^{2}-9)}{x+3} \\ \\ \frac{-(x-3)(x+3)}{x+3} \\ \\ -x(x-3)\)

Answer:

Please check explanations

Step-by-step explanation:

Using the difference of two squares, the lowest common multiple becomes;

1-sin^2 a

Thus, we have that;

cos a (1-sin a) + cos a (1 + sin a) /1 - sin^2 a

1 - sin^2 a = cos^2 a

That means;

{cos a - cos a sin a + cos a + cos a sin a}/ cos^2 a

= 2cos a / cos^2 a

= 2/cos a

but 1/cos a = sec a

Thus;

2/ cos a = 2 sec a

ANSWER

Horizontal asymptote: y = -3

EXPLANATION

The horizontal asymptote is the value the function takes when x→∞ or x→-∞. In this case, when x→∞ the function goes to ∞, but when x→-∞:

The equation of the horizontal asyptote is y = -3

The requried, survey will most likely suffer from Non-response bias. Option C is correct.

The sample space of a sample statistic is the collection of all conceivable results. A random experiment's associated event is a subset of the sample space.

Here,
The survey is suffering from non-response bias since only 285 out of 300 surveys were returned, meaning that 15 surveys were not returned. The opinions of those 15 students who did not respond are unknown and may differ from the opinions of those who did respond. Therefore, the sample may not be representative of the population, and the results may be biased.

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Answer:

A student group on a college campus wanted to create a survey about parking availability on campus. The student group randomly selected 300 students to take the survey. One of the questions read, “Many students believe the lack of available parking is a major problem. Do you agree or disagree?” Of the 300 students that took the survey, 285 surveys were returned.

This survey will most likely suffer from which of the following types of bias?

Selection bias

There is no bias in the way this survey is carried out.

Response bias - Answer

Non-response bias

RATIONALE

By putting a response inside of the question which may lead survey participants to a given response, this is a good example of response bias.

CONCEPT

Step-by-step explanation:

The length of the smallest part of the line segment is 12 cm.

The line segment of length 96 cm is divided into 3 parts with the ratio of 2:9:5. The given ratio is a part-to-whole ratio. We can find the lengths of the parts by applying the formula:

Part = Whole × Ratio

Part 1 = 96 cm × (2/16)

= 12 cm

Part 2 = 96 cm × (9/16)

= 54 cm

Part 3 = 96 cm × (5/16)

= 30 cm

Therefore, the length of the smallest part of the line segment is 12 cm.

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Answer:

x=27

Step-by-step explanation:

2x+6 = 60 because equaliteral triangle has 60 degrees per angle, and trangle with sum of all angles = 180 degrees

60=2x+6

54=2x

x=27

Answer:

4

Step-by-step explanation:

lol

Answer:

-42

Step-by-step explanation:

Hope it helps!

The 90% confidence interval estimate for the overall difference in the percentages of Democrats and Republicans who prioritize protecting the environment is between X% and Y%.

To estimate the overall difference in the percentages of Democrats and Republicans who consider protecting the environment a top priority, we can use the concept of confidence intervals.

Confidence intervals provide a range of values within which we can be reasonably confident that the true population parameter lies. In this case, we want to estimate the difference in the proportions of Democrats and Republicans who prioritize protecting the environment.

The provided information states that in a random sample of 950 Democrats, 817 consider protecting the environment a top priority, while in a random sample of 800 Republicans, 384 share the same view. To construct a 90% confidence interval, we need to calculate the margin of error, which is determined by the sample sizes and proportions.

Using the formulas for the margin of error, we find that the margin of error is 3. With this information, we can state that we are 90% confident that the difference between the percentage of Democrats and Republicans who prioritize protecting the environment lies between X% and Y%.

The confidence interval estimate gives us a range within which we can reasonably expect the true difference to fall. However, it does not provide an exact value for the difference. The range allows for some uncertainty due to the sampling variability inherent in survey data.

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Dilations involve scaling the figure uniformly along a given center and factor. This process results in an enlarged or reduced version of the original figure, while maintaining the same proportions and shape.

A dilation is a type of geometric transformation that alters the size or shape of a figure while preserving its proportions. It involves scaling the figure uniformly in all directions from a specific center of dilation. The scaling factor determines whether the figure will be enlarged or reduced.

When dilating a figure, each point is moved along a line that passes through the center of dilation. The distance between the original point and the center is multiplied by the scaling factor to determine the new position of the point. If the scaling factor is greater than 1, the figure will be enlarged, while a scaling factor between 0 and 1 will result in a reduction.

The center of dilation can be any point on the plane, and it serves as the reference point from which the scaling occurs. If the center of dilation is outside the figure, the shape will change along with the size. However, if the center is inside the figure, only the size will be affected, and the shape will remain the same.

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Answer:

68°

Step-by-step explanation:

since the ball is placed or comes from a straight line (which is the wall) it means that when you add all those angles the final answer has to be 180 because angles in a straight line add up to 180°

68°+44°+1=180

112°+1=180

1=180-112

=68°

I hope this helps

The measure of ∠1 is 68 degrees.

We have Lisa who kicked a ball against the wall at the indicated angle.

We have to determine the measure of the angle 1 in degrees.

A straight line has an angle of 180 degrees.

According to question, we have -

∠3 = 68 degrees

∠2 = 44 degrees

Therefore -

∠3 + ∠2 + ∠1 = 180

68 + 44 + ∠1 = 180

112 + ∠1 = 180

∠1 = 180 - 112

∠1 = 68 degrees

Hence, the measure of ∠1 is 68 degrees.

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The radius is that goes from the chord to the center point is r= 8.2 units

The chord of a circle is a line segment that joins any two points on the circumference of the circle. The diameter is the longest chord that passes through the center of the circle

A line from the center of a circle intersecting a chord makes an angle of 90 degrees at the point of intersection

Using Pythagoras theorem

r² = c² + h²

r² = 8² + 2²

r²= 64 + 4

r² = 68

Making r the subject of the relation we have that

r = √68

r= 8.2 units

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The volume of the solid obtained by rotating the region under the curve y = x√(4 − x²) from x = 0 to x = 2 about the y-axis is 32π/15 cubic units.

Let's consider a thin disk or washer-shaped slice of the solid, with thickness Δx and radius y = x√(4 − x²). To find the volume of this slice, we can use the formula for the volume of a disk:

Volume of disk = πr²Δx

where r is the radius of the disk. In this case, the radius of the disk is y = x√(4 − x²), so the volume of the slice is:

Volume of slice = π(x√(4 − x²))²Δx

= πx²(4 − x²)Δx

To find the total volume of the solid, we need to add up the volumes of all of the thin slices. To do this, we can use an integral:

Total volume = ∫[from 0 to 2] πx²(4 − x²) dx

Evaluating this integral gives us the total volume of the solid:

Total volume = π∫[from 0 to 2] (4x² − x⁴) dx

= π[4x³/3 − x⁵/5] [from 0 to 2]

= π(32/3 − 32/5)

= 32π/15

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Complete Question:

Find the volume of the solid obtained when the region under the curve y = x √ 4 − x² from x = 0 t o x = 2 is rotated about the y-axis.

Option - B : Decision support system is a flexible tool for data analysis, since its reports do not have a fixed format.

  Decision support systems, a subset of business intelligence, are created to help organisations make sensible business decisions based on vast volumes of analysed data. Huge volumes of data are analysed using an interactive information system called a decision support system (DSS) to aid in the direction of business choices. A DSS aids management, operations, and planning levels of an organisation in making better decisions by assessing the importance of uncertainties and the tradeoffs involved in selecting one option over another. A DSS uses a variety of raw data, papers, personal knowledge, and/or business models to aid users in making decisions. A DSS may make use of relational data sources, cubes, data warehouses, electronic health records (EHRs), income projections, sales projections, and other sources.

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The residual for each of the coordinate pairs, (x, y) are-

a) -3.1; b) -0.2; c)  0.32; d) 0; e) -0.1; f) -6.96.

For the stated question;

Data is given by the line of best fit as;

y = 1.1x + 3.4

Then, the residual for the given coordinates are found as;

Residual = y - (1.1x + 3.4)

a. (5,8.8)

Residual = 5.8 - (1.1(5) + 3.4)

Residual = -3.1

b. (2.5,5.95)

Residual = 5.95 - (1.1(2.5) + 3.4)

Residual = -0.2

c. ((0,3.72)

Residual = 3.72 - (1.1(0) + 3.4)

Residual = 0.32

d. (1.5,5.05)

Residual = 5.05 - (1.1(1.5) + 3.4)

Residual = 0

e. (-3,0)

Residual = 0 - (1.1(-3) + 3.4)

Residual = -0.1

f. (-5,-4.86)

Residual = -4.86 - (1.1(-5) + 3.4)

Residual =  -6.96

Thus, the residual for each of the coordinate pairs, (x, y) are found.

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Answer is attached

hope it helps you ⬆️

The experimental probabilities have their values to be P(3) = 1/12, P(6) = 1/4 and P(Less than 4) = 1/2

Experimental probability of 3

From the table of values, we have

n(3) = 1

Total = 12

So, we have

P(3) = 1/12

Experimental probability of 6

From the table of values, we have

n(6) = 3

Total = 12

So, we have

P(6) = 3/12

P(6) = 1/4

Experimental probability of less than 4

From the table of values, we have

n(Less than 4) = 6

Total = 12

So, we have

P(Less than 4) = 6/12

P(Less than 4) = 1/2

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The percentage of people who do not like to listen to radio as well as watch the television is 65%.

It is important to note that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

From the information, 36% like to listen to radio as well as watch the television.

Therefore, the percentage of the people who do not like to listen to radio as well as watch the television will be:

= 1 - 35%

= 65%

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In a survey of a community. 55% of the people like to listen the radio, 65% like to watch the television and 35% like to listen the radio as well as watch the television

Find the percentage of the people who do not like to listen radio as well as watch the television.

11.5 and 15 are the values that are part of the solution set of the inequality.

Inequality is defined as relationship between non-equal numbers or expressions. The solution of an inequality is the set of values that satisfies the given inequality.

To determine the solution set of the given inequality, isolate the variable to one side and simplify.

-4x + 24 < -2x + 2

-4x + 2x < -24 + 2

-2x < -22

22 < 2x

11 < x

Hence, the solution set of the given inequality is the set of numbers greater than 11. Among the given choices, 11.5 and 15 are both greater than 11.

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A linear transformation t defined by a square matrix a is an isomorphism if and only if a is nonsingular.

To prove this statement, we first recall that an isomorphism is a linear transformation that is both injective (one-to-one) and surjective (onto). If t is an isomorphism, then it is invertible, which means that there exists another linear transformation t^-1 such that t(t^-1(x)) = x and t^-1(t(x)) = x for all vectors x in the domain of t. In matrix notation, this means that aa^-1 = a^-1a = I, where I is the identity matrix.

Now suppose that a is nonsingular, which means that its determinant det(a) is nonzero. This implies that a^-1 exists and is also a square matrix. If we can show that t is injective and surjective, then we can conclude that t is an isomorphism. To prove injectivity, suppose that t(x) = t(y) for some vectors x and y. Then ax = ay, which implies that a(x - y) = 0. Since det(a) is nonzero, it follows that x - y = 0, which means that x = y. Thus, t is injective. To prove surjectivity, let z be an arbitrary vector in the range of t. Then there exists a vector y such that t(y) = z.

This implies that ay = z, which means that y = a^-1z. Thus, every vector in the range of t can be written as t(a^-1z), which shows that t is surjective. Therefore, we can conclude that t is an isomorphism if a is nonsingular. Conversely, if t is an isomorphism, then it must be invertible, which implies that a must be nonsingular, as we showed earlier. Thus, t is an isomorphism if and only if a is nonsingular.

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Answer: When we use the change of variables u=x2,v=y3,w=z�=�2,�=�3,�=� to find the volume of the solid enclosed by the ellipsoid x24+y29+z2=1�24+�29+�2=1 above the xy−��− plane, we are essentially transforming the original equation of the ellipsoid into a new equation that is easier to work with.

Step-by-step explanation:

The new equation becomes u/4+v/9+w/1=1. We can now use this equation to find the volume of the solid by integrating over the region in uvw-space that corresponds to the region in xyz-space above the xy−��− plane. This region is a solid bounded by a plane, two planes perpendicular to the uvw-axes, and the surface of the ellipsoid. To integrate over this region, we can use triple integrals in uvw-space.
The triple integral would have limits of integration of 0 to 1 for u, 0 to (1-4u/9) for v, and 0 to sqrt(1-4u/9-v) for w. Integrating this triple integral would give us the volume of the solid enclosed by the ellipsoid above the xy−��− plane. In summary, the change of variables transforms the original equation into a simpler equation that can be used to set up a triple integral to find the volume of the solid. The region of integration in uvw-space corresponds to the region in xyz-space above the xy−��− plane, and we can use triple integrals to integrate over this region and find the volume.
Using the change of variables u = x^2, v = y^3, w = z, we can rewrite the equation for the ellipsoid as u/24 + v/29 + w^2 = 1. We want to find the volume of the solid enclosed by this ellipsoid above the xy-plane, which means we're looking for the region where w ≥ 0.

To do this, we will set up a triple integral over the given region using the Jacobian determinant to transform from (x, y, z) coordinates to (u, v, w) coordinates. The Jacobian determinant is given by:

J = |(∂(x,y,z)/∂(u,v,w))| = |(∂x/∂u, ∂x/∂v, ∂x/∂w; ∂y/∂u, ∂y/∂v, ∂y/∂w; ∂z/∂u, ∂z/∂v, ∂z/∂w)|

Computing the partial derivatives, we get J = |(1/2, 0, 0; 0, 1/3, 0; 0, 0, 1)| = 1/6.

Now, we can set up the triple integral:

Volume = ∫∫∫(u, v, w) dudvdw

The limits of integration for u will be 0 to 24, for v will be 0 to 29, and for w will be 0 to 1.

Volume = (1/6) ∫(0 to 24) ∫(0 to 29) ∫(0 to 1) dudvdw

Calculating this triple integral, we find the volume of the solid enclosed by the ellipsoid above the xy-plane:

Volume ≈ 58.8 cubic units.

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The value assigned to the variable iResult as a result of the statement int iResult = 10 + 56 / 5 + 3 % 12; will be 11.

To understand how this value is determined, let's break down the statement step by step:

1. 56 / 5 is the first operation. The division operation `/` calculates the quotient of 56 divided by 5, which is 11.

2. Next, we have 3 % 12. The modulus operation `%` calculates the remainder when 3 is divided by 12. In this case, the remainder is 3.

3. Finally, we add the results of the previous two operations: 10 + 11 + 3. The addition operation `+` adds the numbers together, resulting in 24.

Therefore, the value assigned to the variable iResult will be 11. I hope this helps! Let me know if you have any further questions.

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Answer:

41.8887 cm^2

Step-by-step explanation:

area of a circle
A = pi * r^2
A = pi * (3 + 4)^2
A = pi * 49
A = 153.94

120 / 360 = 1/3
153.94 / 3 = 51.3134

now area of inner circle
A = pi * 3^2
A = pi * 9
A = 28.274
28.274 / 3 = 9.4247

subtract
51.3134 - 9.4247 = 41.8887

Based on the team combination, the number of ways the team can be formed is  861,029,868,672 ways.

For the first team with 9 members, we need to select 9 members out of 32, which can be done in C(32, 9) ways.

Similarly, for the second team with 6 members, we need to select 6 members out of the remaining 32 - 9 = 23 members, which can be done in C(23, 6) ways.

For the third team with 7 members, we need to select 7 members out of the remaining 23 - 6 = 17 members, which can be done in C(17, 7) ways.

Finally, for the fourth team with 10 members, we need to select 10 members out of the remaining 17 - 7 = 10 members, which can be done in C(10, 10) ways.

Total number of ways = C(32, 9) × C(23, 6) × C(17, 7) × C(10, 10)

Using the combination formula C(n, r) = n! / (r! * (n - r)!), we can calculate the combinations:

Evaluating these expressions, we find:

C(32, 9) = 32,468,436

C(23, 6) = 1,352,128

C(17, 7) = 19,448

C(10, 10) = 1

Now, we can calculate the total number of ways:

Total number of ways = 32,468,436 × 1,352, 128 × 19,448 × 1

Total number of ways ≈ 861,029,868,672

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Answer:

-1/2

Step-by-step explanation:

Slope is change in x over change in y

so..

2-(-4)

over

-1-11

so...

-6/12 or -1/2

Answer:

d. The two triangles are not congruent because dilation is not a rigid motion.

Step-by-step explanation:

Triangle ABC is dilated about the origin b a factor of 2. It is then reflected and translated to form Triangle XYZ.

The new triangle formed is not congruent to ABC because the image is not the same size as the pre-image. It is only rigid transformations that preserve length, however dilation is not a rigid transformation.