A sampling distribution of the sample means of many large samples of a probability distribution is normally distributed. Which statement is true according to the Central Limit Theorem?
A the original PD can have any shape
B the original PD must also be normal
C the original PD must be uniform
D the original PD must be symmetric

Generalization refers to a set of procedures in which the sample size and sample statistics are used to make estimates of population values or facts.

Statistics is a branch of applied mathematics that involves the collection, description, analysis, and conclusion of conclusions from quantitative data. Sample size determination is the act of choosing the number of compliances or replicates to include in a statistical sample.

Statistical conception involves statistically calculating the likely parameters of a population using data from an arbitrary sample of that population.

One of the primary operations for data conception is when you need to analyze data that you've collected, but also need to ensure the sequestration of the individualities who are included in that data.

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The length, width and area of the smaller rectangle are 18 cm, 14 cm and 252 cm² respectively.

A rectangle is a polygon in two dimension with four sides with opposide sides are equal and all the angles are right angles.

Given smaller rectangle is 1/2 scale drawing of the original figure. So the dimensions of the smaller rectangle will be half of the dimensions of the bigger rectangle.

For bigger rectangle,

Length = 36 cm

Width = 28 cm

Area = 1,008 cm²

So for smaller rectangle,

Length = 36/2 = 18 cm

Width = 28/2 = 14 cm

Area = 18 × 14 = 252 cm²

Hence the length, width and area of the smaller rectangle are 18 cm, 14 cm and 252 cm².

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The Valley of Ashes symbolizes the emotional turmoil and feelings of the characters the working class who enable the lifestyles of the wealthy the negative economic impact of prohibition laws Gatsby's fears organized crime

On the north shore of Long Island, the valley of ashes was a two to three thousand acre marshland that encircled the Flushing River mouth. This small river primarily serves as an inlet into Flushing Bay, which is an arm of the East River, with tidal water flowing through it rather than fresh water.

It is a metaphor for the moral and societal decay brought on by the unrestrained pursuit of wealth, as the wealthy indulge in only their own pleasure. The emotional turmoil and feelings of the characters from the working class that support the lifestyles of the wealthy are symbolized by The Valley of Ashes. the damaging effects of prohibition laws on the economy Gatsby worries about organized crime.

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The percent of her monthly pay that goes to rent will be 20%.

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.

In this situation, Dimple gets paid $4,800 per month and then she pays $960 a month for rent.

The percent of her monthly pay that goes to rent will be:

= 960 / 4800 × 100

= 20%

The percentage is 20%.

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The volume of the cylinder generated by rotating the region bounded by y = x³ , y = 8 , x = 0 and x = 9 be, 1608.25 cubic units.

Given, a cylinder generated by rotating the region bounded by the given curves about the specified axis

y = x³ , y = 8 , x = 0 and x = 9

we have to find the volume of the cylinder generated by the given region,

So, using the concept of integration, we get

Volume of the cylinder =  Integrating y from x³ to 8 then integrating x from 0 to 9.

Volume of the cylinder = ∫∫dy dx

Volume of the cylinder = ∫(x³ - 8) dx

Volume of the cylinder = x^4/4 - 8x

Volume of the cylinder = (9)^4/4 - 8(4)

Volume of the cylinder = 1640.25 - 32

Volume of the cylinder = 1608.25

So, the volume of the cylinder be 1608.25 cubic units.

Hence, volume of the cylinder be 1608.25 cubic units.

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It can be any distribution from the exponential family is true about the distribution of the response variable in a logistic regression model.

Logistic regression is a popular method for solving prediction and classification issues. Among these use cases are: Fraud detection: Logistic regression methods can assist teams in identifying data abnormalities that suggest fraud. The logistic model is a statistical model that represents the chance of an event occurring by making the event's log-odds a linear combination of one or more independent variables. Logistic regression is used in regression analysis to estimate the parameters of a logistic model.

Here,

The distribution of the response variable in a logistic regression model can be any distribution from the exponential family.

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Answer:

The square's area will be larger

Step-by-step explanation:

Let's say that a square's side length is 10.

To find the perimeter of a square, we add up all of the sides.

10 + 10 + 10 + 10 = 40

The perimeter of the square would be 40.

Now let's figure out the area of this square.

To find the area, we multiply the length by the width.

10 × 10 = 100

The area of the square is 100.

Now let's move on to the rectangle.

The rectangle has a side length of 12, and 8.

Let's figure out the perimeter of this rectangle.

12 + 12 + 8 + 8 = 40

The perimeter of the rectangle is 40, which means that the perimeters are the same.

Now let's figure out the area.

If you remember, to find the area we multiply the side length by the width.

12 × 8 = 96

The area of the rectangle is 96.

If the area of the square is 100, and the area of the rectangle is 96, then we can conclude that the area of a square is larger.

If a rectangle and a square have the same perimeter then Square will have a larger area.

Suppose length of rectangle is 6 cm and breadth is 2 cm.

So, Area of a rectangle = length ×  breadth

                                  =(6×2) cm²

                                  = 12 cm²

Given that,

Perimeter of rectangle = Perimeter of square

2× (length + breadth)   =  4×side

Side = [tex]\frac{2 ( length + breadth)}{4}[/tex]

Side =  [tex]\frac{2 (6+2)}{4}[/tex]

Therefore, side = 4 unit.

Now,  Area of Square = (side)²

                                    = ( 4 )²

                                      16 unit²

Hence, Area of square (16) is more than area of rectangle (12).

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A figure in the flag has rotational symmetry if the figure can be mapped onto itself by a rotation between 0° and 360° about the center of the figure.

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Answer: Part 1) Option A

Part 2) Option B

Part 3) Option C

Part 4) Option C

Part 5) Option D

Part 6) Option B

Part 10)  Option B

Part 11) Option A  

Part 13) Option A

Part 14) Option D

Part 15) Option D

Part 16) Option C

Part 17) Option D

Part 18) Option D

Part 19) Option D distribute the  to the  and ; distribute the  to the  and

Part 20) Option B  

Step-by-step explanation:

Part 1) we have

solve for x

Part 2) we have

solve for x

Part 3) we have

solve for x

Part 4) we have

solve for x

Part 5) we have

solve for x

Part 6) we have

solve for x

remember that

convert to mixed number

Part 7) The model is not included

Part 8) The model is not included

Part 9) The model is not included

Part 10) we have

solve for x

Part 11) we have

solve for x

Part 12) The model is not included

Part 13) we have

solve for r

Part 14) and  Part 15)

the answer is the option D

Look for parenthesis and apply the distributive property; combine like terms; move your variable terms to one side and constants to the other side of the equal sign; go in reverse PEMorDAorS to isolate the variable using inverse operations

Part 16)

Let

n------> the number

we know that

-----> algebraic expression that represent the situation

solve for n

Part 17) we have

solve for y

Part 18) we have

solve for x

Part 19) we have

 ------> distribute the  to the  and ; distribute the  to the  and

Part 20) we have

step 1

distribute the  to the  and ; distribute the  to the  and

step 2

Group terms that contain the same variable and move the constant to the other side

step 3

Combine like terms

step 4

Divide by  both sides

Answer:  The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC if and only if the distances between the points meet the requirements of the equation AB + BC = AC

When two system of linear equations solved by Sara represents the lines parallel to each other then the equations have no solution.

Step by Step explanation:

Given system of two linear equations :

Let us consider system of two linear equation with Sara has :

y =  3x + 7

y = 3x + 9

Here both the lines have same slope = 3

Lines are parallel to each other.

Solve the equation by elimination method :

y =  3x + 7

y = 3x + 9

0 = 0x - 2

⇒ -2 = 0 which is not possible and has no solution.

Therefore, when the system of linear equations with Sara has no solution it represents lines are parallel to each other.

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The three side lengths; 9m, 12m, 15m as given in the task content would form a right triangle.

It follows from the task content that the type of triangle formed by the side lengths given is to be determined.

On this note, recall that given three side lengths, a, b and c where c is the longest of all three side-lengths;

if; c² > a² + b² .....Obtuse triangle.

if; c² < a² + b².......Acute triangle.

if; c² = a² + b²........Right triangle.

On this note, since;

15² = 12² + 9²

225 = 144 + 81

225 = 225.

The three side lengths in discuss would form a right triangle.

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None of the Options are true both the given functions are parabolic functions.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given function are,  f(x)=-15x²+32 and g(x)= -17x²+5x+32,
Zeros for the functions are,
x = ± 1.461 and x = -1.233 and 1.527,
Where g(x) has a higher maximum than f(x), the Intercept of f(x) is greater than g(x). As shown in the graph.

Thus, none of the options are true because both of the supplied functions are parabolic.

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Answer: 0, 1, 5, -2 ,-4

Step-by-step explanation: hope it helps

An explicit description of Nul A is given by the set of vectors {[0, 0, 1, 0], [0, 0, 0, 1]}.

What is the explicit description of a null space matrix?

To find an explicit description of the null space of matrix A, we can find a spanning set of vectors that span the null space.

The null space of matrix A, denoted Nul A, is the set of all vectors x that satisfy the equation Ax = 0. In other words, the null space consists of all vectors that are mapped to the zero vector by the matrix A.

To find a spanning set for Nul A, we can use the following steps:

Row reduces the matrix A to a reduced row-echelon form using elementary row operations.

Identify the free variables in the row-reduced matrix.

For each free variable, create a vector with a 1 in the position corresponding to the free variable and 0's in all other positions.

The set of vectors created in step 3 form a spanning set for Nul A.

For example, consider the matrix A = [1, 2, 3, 0; 0, 0, 1, 0]. To find a spanning set for Nul A, we can row reduce the matrix to reduced row-echelon form:

[1, 2, 3, 0] -> [1, 2, 3, 0]

[0, 0, 1, 0] -> [0, 0, 1, 0]

The matrix is already in reduced row-echelon form, so there are no more elementary row operations to perform. The free variables in this matrix are the third and fourth columns, which correspond to the variables x3 and x4, respectively. Therefore, we can create the following vectors:

x3 = [0, 0, 1, 0]

x4 = [0, 0, 0, 1]

These vectors form a spanning set for Nul A, as they are linearly independent and span the null space.

Hence, an explicit description of Nul A is given by the set of vectors {[0, 0, 1, 0], [0, 0, 0, 1]}.

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The correct conclusion is A. Since the p-value is greater than the significance level, there is not sufficient sample evidence to conclude that the full-time placement rate is now less than 87% because the p-value is greater than 0.05.

For the null hypothesis, 87% of the graduates find full-time employment in their field within the first year of graduation. It is tested if the proportion is still of 0.87, so:

H₀: p = 0.87

For the alternative hypothesis, less than 87% of the graduates find full-time employment in their field within the first year of graduation. It is tested if it has decreased, so:

H₁: p < 0.87

Since the p-value is greater than the significance level (p-value is greater than 0.0), we do not reject the null hypothesis, and thus, the correct conclusion is A.

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Hence the minimum value of x is 18 cm

a minimal requirement of coverage that is applicable to employment-based health plans. You cannot receive a premium tax credit if you purchase a Marketplace insurance plan if your employer's plan satisfies this criterion and is deemed "affordable."

given,

Within 10 cm of the A, a laser beam will pierce the water.

Snell's law permits us to state:

[tex]n_{1}sin\alpha ^{2} = n_{2}sin\beta^{2}[/tex]

Where,

is equal to 1, which is air's refractive index.

a measure of water's refractive index is [tex]n_{2}[/tex] = 1.33

At the interface, we can formulate a formula using Sell's law.

θ[tex]_{2}[/tex] = 38.7°

x= 18 cm

hence the minimum value of x is 18 cm.

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Answer:

The graph

Step-by-step explanation:

The graph has a slope of 4, the equation has a slope of 3, the table has a slope of 2.

Charge required to levitate a ball is [tex]1*10^{-2}C[/tex] given by the cross section of your pen 10 [tex]mm^{2}[/tex], which is of order 10 squared.

The flow of air is drawn toward the ball by the low pressure area that surrounds it. As a result, the fluid (air) jet flows across the ping pong ball's curved surface. The "Coandă effect" refers to this phenomena.

The airflow's propensity to stick to the ball's surface is the Coandă effect in this situation. This indicates that the streamlines are curved at the ball's surface, with a radius of curvature roughly equal to the ball's radius. This curvature produces a pressure gradient, much like it does in the theory of lift, which I assume to be constant over the surface:

The equilibrium point, when the net forces acting on the ball cancel, is indicated by this, which points radially inward. Gravity causes the ball to hang below this spot during practice.

The Charge required to levitate a ball is [tex]1*10^{-2}C[/tex] given by the cross section of your pen 10 [tex]mm^{2}[/tex], which is of order 10 squared.

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Answer:

------------------------------------

Use trigonometry.

Since all three sides are known, you may choose either sine, cosine or tangent.

We'll use sine here:

The minimum sample size required to estimate the mean duration time of TR classes is t distribution confidence interval.

The confidence interval is 75.0694 and 76.9306.

Given that

(a) This is t-distribution confidence interval because sample standard deviation is given and also sample size is less than 30.

(b)

CI for 95%

n 28

mean 76

value of 95% CI and df = 27 (using  table) 2.0518

std. dev. 2.4

SE = standard deviation/n² 0.45356

ME = t*SE 0.93062

Lower Limit = Mean - ME 75.06938

Upper Limit = Mean + ME 76.93062

95% CI (75.0694 , 76.9306 )

95% CI=75.0694 , 76.9306

(c)The 95% confidence interval estimate of the population mean is within 75.0694 and 76.9306 (lower bound and upper bound)

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The equation is y =  45.5+ 1.7x₁ + 11.5x₂+ 16.7x₃ when x₂ = x₃ = 0.

What is meant by equation?

In math, equation refers a mathematical statement that is made up of two expressions connected by an equal sign.

Here we have given that,  x1 is a quantitative variable and x2 and x3 are dummy variables describing a qualitative variable at three levels using the coding scheme.

and we need to find the correct equation when the value of x₂ = x₃ = 0.

Here while we looking into the given question we have identified that the value of x₂ =0 and x₃ = 0.

Then the given equation will be remain same withouth any changes.

Therefore, the resulting equation of the given condition is written as,

=> y =  45.5+ 1.7x₁ + 11.5x₂+ 16.7x₃

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Answer:

8 [tex]\frac{9}{10}[/tex]

Step-by-step explanation:

substitute x = [tex]\frac{2}{3}[/tex] into the expression

(6 × [tex]\frac{2}{3}[/tex] ) + 4 [tex]\frac{9}{10}[/tex]

= (2 × 2) + 4 [tex]\frac{9}{10}[/tex]

= 4 + 4 [tex]\frac{9}{10}[/tex] ( add the whole numbers )

= 8 [tex]\frac{9}{10}[/tex]

Note that:

For 1) To compute the average rate (AR), divide the change in y-values by the change in x-values. That is:

AR = (5-2)/5-4)

= 3/1

= 3ft/sec.

For 2) we must use the same formula above:
(2-5)/(10-7)

= -1 ft/sec.

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Full Question:

See attached graph

Yes, the inverse of the matrix exist and a11 = 13 , a12 = -5 , a21 = -5 and a22 = 2

The inverse of matrix is another matrix, which on multiplication with the given matrix gives the multiplicative identity.

The matrix whose determinant is non-zero and for which the inverse matrix can be calculated is called an invertible matrix.

According to the question,

The matrix given is [tex]\left[\begin{array}{cc}2&5\\5&13\end{array}\right][/tex]

Let Matrix be A

To check if its inverse exist , We have to find out the determinant

|A| = 13(2) - 5(5)

=> 26 - 25

=> 1

Determinant is non zero

Hence , Inverse exist

(b) To find the inverse , we have to find the adjoint of A

adj A = [tex]\left[\begin{array}{cc}13&-5\\-5&2\end{array}\right][/tex]

Inverse is ratio of adj A and determinant A

A⁻¹ = adj A / |A|

=>  [tex]\left[\begin{array}{cc}13&-5\\-5&2\end{array}\right][/tex] / 1

=> A⁻¹ = [tex]\left[\begin{array}{cc}13&-5\\-5&2\end{array}\right][/tex]

a11 = 13 , a12 = -5 , a21 = -5 and a22 = 2

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Answer: See below

Step-by-step explanation:

C=20t+100

t= number of months

C= total cost over t number of months

Table of values

t                C

1                 120

2                140

3                160

4                 180

5                 200

Answer:

-15

Step-by-step explanation:

Answer:

y = 650

Step-by-step explanation:

0.9y = 585

y = 650

Answer:

[tex]y = 650[/tex]

Step-by-step explanation:

[tex]1.25y-0.35y=585[/tex]

[tex]0.9y=585[/tex]

[tex]y = \frac{585}{0.9}[/tex]

[tex]y = 650[/tex]