For the following regression model Y = α + βX + u
-Discuss the difference between one-tailed and two-tailed tests for β=1.

Glacial HVAC, Inc. had a relative market share of 54.39% in Fulton County in 2010, based on the sale of 3,295 air conditioning units, compared to their largest competitor, Estes Heating and Air.

To calculate the relative market share, we need to divide Glacial HVAC's sales by the total market sales. The formula for relative market share is:

Relative Market Share = Glacial HVAC's Sales / Total Market Sales.

In this case, Glacial HVAC sold 3,295 units, and their largest competitor, Estes Heating and Air, sold 2,759 units. So the total market sales would be the sum of these two figures, which is 3,295 + 2,759 = 6,054 units.

Now, we can calculate the relative market share:

Relative Market Share = 3,295 / 6,054 * 100%.

Evaluating the expression, we find that Glacial HVAC's relative market share is approximately 54.39% when rounded to two decimal places.

This means that Glacial HVAC had a market share of 54.39% in Fulton County in 2010, indicating their position in the market relative to their largest competitor.

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Answer:

28.26

Step-by-step explanation:

The formula for finding the circumference is C=2pi(radius) and the radius is half of the diameter, which in our case is 4.5. So 2*3.14*4.5=28.26

(a) The area between the curve of f(x) and the x-axis best describes the result of integrating a positive function f(x).

(b) The general antiderivative of the function f(x) = 23 + 8x is 2x³ + 4x² + C.

Hence, option (C) is the correct answer.

(c) An odd function satisfies f(-x) = -f(x). Thus, for an odd function f(x), the integral from -a to a is equal to zero because f(x) and -f(x) will have opposite signs, and the areas will cancel each other out. Hence, option (A) is the correct answer.

(d) To use the substitution u = 4x + 2, we need to find dx in terms of du.du = d/dx (4x + 2) dx= 4dxIntegrating both sides gives ∫du/4 = ∫dx/ (4x + 2). Therefore, the given expression becomes, ∫ 1/(4x + 2) dx = (1/4)∫du/u= (1/4)ln|u|+C= (1/4) ln|4x + 2| + C. Hence, (1/4) ln|4x + 2| + C is true by using the substitution 4x + 2 = u.

(e) The given function can be graphed as below: [tex]\int_0^1 (x^2 + 1) dx = \frac{4}{3}[/tex] We need to use the disk method to find the volume of the solid generated by rotating the region bounded by the curves about the x-axis. We need to consider an elemental area, find its volume, and integrate it over the region of interest. We know that the volume of the disk is given by V = πr²h, where r is the radius and h is the height of the disk. Let us consider an elemental area, A of the region rotated about the x-axis. If we rotate this area through a small angle, θ, then the area of the sector generated is given by d A = πr²dθ/2π = r²dθ/2. The radius of the disk is x, and the height is given by g(x) - f(x). Thus, V = ∫[g(x) - f(x)]²πx²dx.In this case, we have g(x) = x + 1 and f(x) = x². Substituting these values, V = π∫(x + 1 - x²)² x² dx. The limits of integration are from 0 to 1.

Therefore, V = π∫[x⁴ - 2x³ + x² + 2x + 1]dx= π[x⁵/5 - x⁴/2 + x³/3 + x² + x]₀¹= π[(1/5) - (1/2) + (1/3) + 1 + 1]

The volume of the solid obtained is, V = π[(8/15) + 2] = (14π/15).

Hence, the volume of the solid obtained when the area bounded by the curves below is rotated about the x-axis is (14π/15).

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1. is a central angle, therefore, the arc will have the same measurement as the angle. Set the equation:

Arc = Central Angle

2x - 7 = 47

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, add 7 to both sides of the equation:

2x - 7 (+7) = 47 (+7)

2x = 47 + 7

2x = 54

Next, divide 2 from both sides of the equation:

(2x)/2 = (54)/2

x = 54/2 = 27

27 is your answer.

2. is a inscribed angle, meaning that the angle measurement will be half of the arc. Set the equation:

212 = 2(13x - 24)

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, divide 2 from both sides of the equation:

(212)/2 = (2(13x - 24))/2

106 = 13x - 24

Next, add 24 to both sides of the equation:

106 (+24) = 13x - 24 (+24)

106 + 24 = 13x

130 = 13x

Finally, divide 13 from both sides of the equation:

(130)/13 = (13x)/13

x = 130/13

x = 10

10 is your answer.

3. is a central angle. The arc and the angle will, therefore, have the same measurement:

137 = 3x + 5

First, subtract 5 from both sides of the equation:

137 (-5) = 3x + 5 (-5)

137 - 5 = 3x

132 = 3x

Next, divide 3 from both sides of the equation to isolate the variable, x:

(132)/3 = (3x)/3

x = 132/3 = 44

44 is your answer.

4. is a inscribed angle. The arc will be twice the measurement of the angle.

86 = 2(2x + 3)

First, isolate the variable x by dividing 2 from both sides of the equation.

(86)/2 = (2(2x + 3)/2

43 = 2x + 3

Next, subtract 3 from both sides of the equation:

43 (-3)  = 2x + 3 (-3)

40 = 2x

Finally, divide 2 from both sides of the equation:

(40)/2 = (2x)/2

x = 40/2 = 20

20 is your answer.

~

Answer:

the answer is B

Step-by-step explanation:

because you just put 100 underneath

Answer:

B, 71/100

Step-by-step explanation:

To do this, just put each fraction into a calculator, and whichever fraction results in the decimal you're looking for will be your answer.

The volume of the cylinder inside the given sphere is 8 cubic units.

To determine the volume of the cylinder inside the given sphere, we need to find the limits of integration and set up the integral.

Let's analyze the equations:

Cylinder equation:[tex]r^2 + y^2 = 4[/tex]

Sphere equation: [tex]r^2 + y^2 + 2^2 = 16[/tex]

From the equations, we can see that the cylinder is centered at the origin (0, 0) with a radius of 2 and an infinite height along the y-axis. The sphere is centered at the origin as well, with a radius of 4.

To find the limits of integration, we need to determine where the cylinder intersects the sphere. By substituting the cylinder equation into the sphere equation, we can solve for the values of r and y:

[tex](2^2) + y^2 + 2^2 = 16\\4 + y^2 + 4 = 16\\y^2 = 8[/tex]

y = ±√8

We can see that the cylinder intersects the sphere at y = √8 and y = -√8. Since the cylinder has infinite height, the limits of integration for y will be from -√8 to √8.

Now we can set up the integral to calculate the volume of the cylinder:

V = ∫∫∫ dV

  = [tex]\int_0^ 2 \int_{\sqrt -8} ^ {\sqrt 8}\int _{\sqrt-(16 - r^2 - y^2)} ^{\sqrt (16 - r^2 - y^2)} dz dy dr[/tex]

Since the integrand is equal to 1, we can simplify the integral to:

V = [tex]\int_0 ^ 2 \int _{-\sqrt8} ^ {\sqrt8} 2\sqrt{(16 - r^2 - y^2)}[/tex] dy dr

Evaluating this integral will give us the volume of the cylinder inside the sphere.

To evaluate the integral and calculate the volume, we can integrate the given expression with respect to y first and then with respect to r.

[tex]\int_0 ^ 2 \int _{-\sqrt8} ^ {\sqrt8} 2\sqrt{(16 - r^2 - y^2)}[/tex]

Let's begin by integrating with respect to y:

[tex]\int_{-\sqrt8} ^ {\sqrt8} 2\sqrt(16 - r^2 - y^2) dy[/tex]

We can simplify the integrand using the trigonometric substitution y = √8sinθ:

dy = √8cosθ dθ

y = √8sinθ

Replacing y and dy in the integral:

[tex]\int _{-\pi /2} ^{\pi/2} 2\sqrt(16 - r^2 - (\sqrt 8sin\theta)^2) \sqrt 8cos\theta d\theta[/tex]

= 16[tex]\int _{-\pi /2} ^ {\pi /2} \sqrt(1 - (r/4)^2 - sin^2\theta)[/tex]cosθ dθ

To simplify the integral further, we can use the trigonometric identity [tex]sin^2\theta + cos^2\theta = 1:[/tex]

16[tex]\int _{-\pi /2} ^ {\pi /2} \sqrt(1 - (r/4)^2 - sin^2\theta)[/tex]cosθ dθ

= 16 [tex]\int _{-\pi /2} ^ {\pi /2} \sqrt(r^2/16)[1 - cos^2\theta][/tex]cosθ dθ

= 4r[tex]\int _{-\pi/2} ^ {\pi/2}[/tex] sinθ cosθ dθ

= 4r [tex][ -cos^2\theta/2[/tex] ]| [-π/2 to π/2 ]

= 4r [ [tex]-cos^2(\pi/2)/2 + cos^2(-\pi/2)/2[/tex] ]

= 4r [ -1/2 + 1/2 ]

= 4r

Now, we can integrate with respect to r:

[tex]\int_0 ^ 2[/tex] 4r dr

= 2[tex]r^2[/tex]| [0 to 2]

= 2[tex](2^2 - 0^2)[/tex]

= 2(4)

= 8

Therefore, the volume of the cylinder is 8 cubic units.

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This formula calculates the value corresponding to a 90% confidence level using the T.INV function. The first argument, 0.95, represents 1 minus the desired confidence level (0.05 for a 90% confidence level). The second argument, `COUNT(A2:A89)-1`, calculates the degrees of freedom by subtracting 1 from the count of data points.

To find the value from the appropriate probability table to construct a 90% confidence interval in cell B8, you can use the T.INV function in Excel. Here's how you can do it:

1. In cell B8, enter the formula:

  ```

  =T.INV(0.95, COUNT(A2:A89)-1)

  ```

  This formula calculates the value corresponding to a 90% confidence level using the T.INV function. The first argument, 0.95, represents 1 minus the desired confidence level (0.05 for a 90% confidence level). The second argument, `COUNT(A2:A89)-1`, calculates the degrees of freedom by subtracting 1 from the count of data points.

Make sure to adjust the cell references in the formula based on the actual location of your data in the spreadsheet.

Note: The T.INV function returns the value from the Student's t-distribution, which is used for small sample sizes or when the population standard deviation is unknown.

If you have a large sample size (usually considered more than 30), you can use the Z.INV function instead to calculate the value from the standard normal distribution.

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Answer:

See explanations below

Step-by-step explanation:

evaluate sin 60. cos 30 sin +sin 30 .cos 60 what is the value of sin(30-60) what can you conclude​

According to the trigonometry identity

Sin 30  = 1/2

Sin 60 = √3/2

Cos 30 = √3/2

Cos 60 = 1/2

sin 60. cos 30 +sin 30 .cos 60

= √3/2(√3/2) + 1/2(1/2)

= √9/4 + 1/4

= 3/4 + 1/4

= 4/4

= 1

sin(30-60) = sin30cos60 - cos30sin60

sin(30-60) =1/2(1/2) - √3/2(√3/2)

sin(30-60) = 1/4 -  √9/4

sin(30-60) = 1/4 - 3/4

sin(30-60) = (1-3)/4

sin(30-60) = -2/4

sin(30-60)  = -1/2

hence the former fraction gives a positive values while the later gives a negative

There are no points in C for which the function g(z) is holomorphic.

The functions given are :

f(z) = z² and g(z) = x² - y² + 2xy (where z = x + iy)

We need to determine the points in C for which the functions are holomorphic.

(a) To check whether f(z) = z² is holomorphic or not, we will verify the Cauchy-Riemann equations (CRE) which are:

u x = v y and v x = - u y

Let us assume that f(z) = u(x, y) + iv(x, y)

Substituting in f(z) = z², we have f(z) = (x + iy)²= x² + 2ixy - y²

Now comparing with u(x, y) + iv(x, y), we get :

u(x, y) = x² - y² and v(x, y) = 2xy

Now applying the CRE, we get :

u x = 2xv

y = 2xu

y = - 2yv

x = 2y

We can see that both the CRE are satisfied.

Hence, f(z) = z² is holomorphic for all values of z in C.

(b) Similarly, for g(z) = x² - y² + 2xy (where z = x + iy), we have g(z) = u(x, y) + iv(x, y)

Substituting in g(z) = x² - y² + 2xy, we have g(z) = x² - y² + 2ixy

Now comparing with u(x, y) + iv(x, y), we get :

u(x, y) = x² - y² and v(x, y) = 2xy

Now applying the CRE, we get :

u x = 2xv

y = 2xu

y = - 2yv

x = 2x

Since the CRE are not satisfied, g(z) = x² - y² + 2xy (where z = x + iy) is not holomorphic at any point in C.

Therefore, we can say that there are no points in C for which the function g(z) is holomorphic.

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Answer:

the answer is 35

Step-by-step explanation:

because if BC is 35 that means AB will have to be that same because it's a triangle

The required value of AB is 33 units for the given right triangle.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Triangle ACB is a right-angle triangle. The length of AC is 12 and BC is 35.

Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.

Assume BC is the hypotenuse,

Since this is a right triangle, use the formula AB² + AC² = BC² and substitute values of AC = 12 and BC = 35.

AB² + AC² = BC²

AB² + (12)² = (35)²

AB² + 144 = 1225

AB² = 1225 -144

AB² = 1081

AB = 32.8785

Rounded to two decimal places,

AB = 33 units

Therefore, the required value of AB is 33 units.

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Answer:

Hey I know this isn’t an answer but your bf Jordan told me to tell you he is looking for you and he needs to talk to you. Sorry again for wasting ur time but he kinda worried

Step-by-step explanation:

The cross product of

[tex](i+j) \times k[/tex]= 0.

To calculate the cross product of (i+j) and k,

Step 1: Assign unit vectors to the given vectors:

(i+j) = i + j + 0k

k = 0i + 0j + k

Step 2: Apply the cross product formula:

(i+j) × k = (i × 0i) + (i × 0j) + (i × k) + (j × 0i) + (j × 0j) + (j × k) + (0k × 0i) + (0k × 0j) + (0k × k)

Step 3: Simplify the cross product using the properties of the cross product:

(i × 0i) = (j × 0j) = (0k × 0i) = (0k × 0j) = 0

(i × k) = - (k × i)

(j × k) = - (k × j)

(k × k) = 0

Step 4: Substitute the simplified cross products into the formula:

(i+j) × k = 0 + 0 + (i × k) + 0 + 0 + (j × k) + 0 + 0 + 0

= 0 + 0 + (i × k) + 0 + 0 + (j × k) + 0 + 0 + 0

= (i × k) + (j × k)

Step 5: Calculate the cross products:

(i × k) = (0 - 0)k - (0 - 0)j = 0k - 0j = 0k

(j × k) = (0 - 0)i - (0 - 0)k = 0i - 0k = 0i

Step 6: Substitute the calculated cross products into the formula:

(i+j) × k = 0k + 0i

= 0k + 0

= 0

Therefore k=0.

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Answer: good luck

Step-by-step explanation:

The preliminary sample size is undefined since the projected misstatement is zero.

In determining the appropriate sample size for testing inventory valuation using MUS, the following steps are taken;

Given that the population has 2,620 inventory items valued at $12,625,000 and the tolerable misstatement is $500,000 at a 10% ARIA, we can calculate the preliminary sample size using the formula;

Preliminary sample size = (Confidence Factor2 × Tolerable Misstatement)/Projected misstatement.

Considering that no misstatements are expected in the population, the projected misstatement will be zero.

Thus; the Preliminary sample size = (2.31 × 500,000)/0. Preliminary sample size = (2.31 × ∞) / 0. The preliminary sample size is undefined.

In conclusion, the preliminary sample size is undefined since the projected misstatement is zero.

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Answer:

y - 6

Step-by-step explanation:

y is the number and  it is less than 6 so 6 has to be negative:

y - 6

Answer:

I have

Step-by-step explanation:

The statistic provides an estimate of the parameter based on the information obtained from the sample.

In this scenario, the population refers to the entire group of customers of the local store.

The sample is a subset of this population and consists of the 82 customers who were randomly surveyed.

The variable of interest is the age of the customers, as the store owner wants to determine the mean age.

Age is a continuous numerical variable since it represents a quantitative measurement.

The parameter is the unknown mean age of all customers of the local store, while the statistic is the calculated mean age of the 82 surveyed customers.

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Answer:

See Explanation

Step-by-step explanation:

The question has missing details, as the scale factor is not given. However, I will give a general explanation on how to calculate the area and perimeter of a dilated shape (triangle).

The following assumptions, apply:

(1) Scale factor of 1/2 from the blue to the yellow triangle.

(2) The dimension of the blue triangle are:

[tex]Base = x[/tex]

[tex]Sides= y\ and\ z[/tex]

[tex]Height= h[/tex]

First, calculate the dimensions of the yellow triangle.

The dimension will be the product of the scale factor and the dimensions of the blue triangle.

So, we have:

[tex]Base = \frac{1}{2} * x = \frac{1}{2}x[/tex]

[tex]Sides = \frac{1}{2}y\ and\ \frac{1}{2}z[/tex]

[tex]Height = \frac{1}{2}h[/tex]

The perimeter of the blue triangle is:

[tex]P_1 =Base + Sides[/tex]

[tex]P_1 = x + y + z[/tex]

The perimeter of the yellow triangle is:

[tex]P_2 =Base + Sides[/tex]

[tex]P_2 = \frac{1}{2}x + \frac{1}{2}y + \frac{1}{2}z[/tex]

Factorize

[tex]P_2 = \frac{1}{2}[x + y + z][/tex]

Recall that: [tex]P_1 = x + y + z[/tex]

So:

[tex]P_2 = \frac{1}{2}*P_1[/tex]

This implies that the perimeter of the yellow triangle is a product of the scale factor and the perimeter of the blue triangle.

The area of the blue triangle is:

[tex]A_1 = \frac{1}{2}* Base * Height[/tex]

[tex]A_1 = \frac{1}{2} * x* h[/tex]

[tex]A_1 = \frac{1}{2} xh[/tex]

The area of the yellow triangle is:

[tex]A_2 = \frac{1}{2} * Base * Height[/tex]

[tex]A_2 = \frac{1}{2}* (\frac{1}{2}x) * (\frac{1}{2}h)[/tex]

Rewrite as:

[tex]A_2 = \frac{1}{2}* \frac{1}{2} [\frac{1}{2}x h][/tex]

[tex]A_2 = (\frac{1}{2})^2 *[\frac{1}{2}x h][/tex]

Recall that:[tex]A_1 = \frac{1}{2} xh[/tex]

So:

[tex]A_2 = (\frac{1}{2})^2 *A_1[/tex]

This implies that the area of the yellow triangle is a product of the square of the scale factor and the area of the blue triangle.

Answer:

3(y-9)^2

Step-by-step explanation:

Answer:

See in the picture mark brainliest if correct

Answer:$15 per yard

Step-by-step explanation: $825 divided by 55 = $15

Answer:

1

Step-by-step explanation:

The probability which is in a random sample of 133 people from State College, more than 50 are not college students is 0.0000313 (rounded to 4 decimal places).

Given that in State College, Pennsylvania, the proportion of college students in the population is 71.1%.

We need to find the probability that in a random sample of 133 people from State College, more than 50 are not college students.

We need to round the final answer to at least 4 decimal places and intermediate z-value calculations to 2 decimal places.

The proportion of college students in State College, Pennsylvania is 71.1%.

Therefore, the proportion of non-college students in State College, Pennsylvania is 100% - 71.1% = 28.9%.

Let X be the number of non-college students in a sample of 133 people from State College, Pennsylvania.

As the sample is random, X follows the binomial distribution with parameters n = 133 and p = 0.289.

The probability of getting more than 50 non-college students can be obtained using the normal distribution approximation to the binomial distribution.

Using the normal distribution approximation, we can convert the binomial distribution to a standard normal distribution using the following formula: Z = (X - np) / sqrt(npq)

Where q = 1 - p is the proportion of college students in the population, and np = 133 x 0.289

= 38.397 and npq = 133 x 0.289 x 0.711 = 9.728.

The probability of getting more than 50 non-college students is : P(X > 50)

= P(Z > (50 - 38.397) / sqrt(9.728))

= P(Z > 3.92)

= 0.0000313 (rounded to 4 decimal places).

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The total number of ways is: {Total number of ways} =[1120]

Let's say we have 7 candies and 14 stickers that need to be distributed among 4 children in such a way that each child gets at least 1 candy and more stickers than candies. So, let's divide the candies first. Then we can use the formula of stars and bars to distribute the remaining stickers.

Let's assume that the candies have already been divided into 4 groups such that each group contains at least 1 candy.

Then, the total number of ways of dividing 7 candies among 4 children is given by 3 stars and 4 bars (one less than the number of children). For example, the following diagram shows one possible distribution of the candies:
Each star represents one candy, and the bars represent the separations between the groups.

For example, the above diagram represents the distribution of candies as follows:

Child 1: 1 candy

Child 2: 2 candies

Child 3: 1 candy

Child 4: 3 candies

Now, we need to distribute the 14 stickers among the 4 children in such a way that each child gets more stickers than candies. We can do this by using the formula of stars and bars again. This time, we need to distribute 14 stickers among 4 children such that each child gets more than 1 candy. Let's represent the candies by stars and the stickers by bars, then we need to distribute 14 bars among 3 stars and 4 bars.

Here, the first three bars represent the stickers for the first child, the next two bars represent the stickers for the second child, the next bar represents the stickers for the third child, and the remaining eight bars represent the stickers for the fourth child.

So, the total number of ways of distributing 7 candies and 14 stickers among 4 children such that each child gets at least 1 candy and more stickers than candies is given by the product of the number of ways of distributing the candies and the number of ways of distributing the stickers.

Therefore, the total number of ways is: {Total number of ways} =[1120]

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[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

Here,

The two lines l and m are parallel,

cut by a transversat line t

So The two angles are supplementary each other.

we know that,

The sum of two supplementary angles are 180°

According to the question,

Therefore,

The value of x is 8°

Answer:

1/4 is x and 1 is b

Step-by-step explanation:

Answer:

7:00 = 6:60

Step-by-step explanation:

6:60 - 3:30 = 3 hours and 30 minutes

Answer: 22.94 cubic meters

I'm pretty sure it is this.

I think it's 25.23 cubic meters if not then I don't know

Answer: 891ft^3

Step-by-step explanation:

Answer:

she have 29 seed for the pasture

Answer:

One solution

I actually do not think you're going to give me brainliest