when the sample size is small, the main assumptions of parametric tests may be violated. State True or False

Answer:

The quadrilateral KLMN is a parallelogram.

Step-by-step explanation:

To find the slopes and lengths of the sides of the quadrilateral formed by the points K(7,-9), L(5,0), M(-1,7), and N(1, -2), we can use the formulas for slope and distance between two points.

Slope of KL:

The slope of KL can be calculated as (y2 - y1) / (x2 - x1) using the coordinates of points K and L. Substituting the values, we have (0 - (-9)) / (5 - 7) = 9 / (-2) = -4.5.

Slope of LM:

Using the coordinates of points L and M, we have (7 - 0) / (-1 - 5) = 7 / (-6) = -7/6.

Slope of MN:

The slope of MN is ( -2 - 7) / (1 - (-1)) = -9 / 2 = -4.5.

Slope of NK:

Using the coordinates of points N and K, we have (-9 - (-2)) / (7 - 1) = -7 / 6.

Length of KL:

The length of KL can be found using the distance formula, which is √[(x2 - x1)^2 + (y2 - y1)^2]. Substituting the values, we get √[(5 - 7)^2 + (0 - (-9))^2] = √[4 + 81] = √85.

Length of LM:

Using the distance formula with the coordinates of points L and M, we get √[(-1 - 5)^2 + (7 - 0)^2] = √[36 + 49] = √85.

Length of MN:

The length of MN is √[(1 - (-1))^2 + (-2 - 7)^2] = √[4 + 81] = √85.

Length of NK:

Using the distance formula, we find √[(7 - 1)^2 + (-9 - (-2))^2] = √[36 + 49] = √85.

Based on the slopes and lengths, the quadrilateral KLMN is a parallelogram. A parallelogram has opposite sides that are parallel and equal in length.

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The system that sought to ensure the availability of a subservient agricultural labor supply controlled by white people.

Slavery is the practice of forcing individuals to work without pay or freedom. Historically, it has been used as a means of exploiting people for economic gain, and it has been justified on the basis of race, ethnicity, religion, or social status.

In the transatlantic slave trade, which lasted from the 16th to the 19th century, millions of Africans were captured and forcibly transported across the Atlantic Ocean to the Americas, where they were sold into slavery. Slaves were treated as property and denied basic human rights, such as the right to freedom, education, and family.

The system that sought to ensure the availability of a subservient agricultural labor supply controlled by white people is known as "slavery." Slavery was a brutal and inhumane practice that existed in many parts of the world throughout history. In the United States, slavery was primarily used to support the Southern agricultural economy, with enslaved people being forced to work on plantations producing crops such as cotton, tobacco, and sugar cane. The abolition of slavery in the United States was a long and difficult struggle that culminated in the Civil War and the passage of the 13th Amendment to the US Constitution in 1865.

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The width of the rectangle is 7m and the length of the rectangle is 10m.

A rectangle is a quadrilateral that is a four sided polygon with two opposite sides parallel and equal.

Let the width of the rectangle be x.

Therefore the length of the rectangle = x + 3.

Area of a rectangle = length * width

Area = (x + 3) (x)

Open bracket;

Area = x² + 3x

We are given the area = 70 m².

Therefore,

70 = x² + 3x

x² + 3x - 70 = 0

Solve quadratically using the factorization method by finding two factors of -70 that add up to give 3 the coefficient of x.

Factors = 10 and -7 which add up to 3.

Rewrite the equation;

x² + 10x - 7x - 70 = 0

x( x + 10) - 7 ( x + 10) = 0

(x - 7) (x + 10) = 0

x - 7 = 0 or x + 10 = 0

x = 7 or x = -10

x = 7m because the width can't be negative.

Therefore,

Length = x + 3 = 7 + 3 = 10 m

Therefore, the width of the rectangle is 7m and the length of the rectangle is 10m.

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There are a total of 3 x 10 x 10 = 300 possible combinations of suits, ties, and shirts that a person can select from. However, when selecting a traveling wardrobe, there are only 10 possible suit combinations, 10x10 = 100 possible tie combinations, and 10x10x10 = 1000 possible shirt combinations. This makes a total of 10 x 100 x 1000 = 100,000 possible selections of two suits, four ties and six shirts.

The sheer number of possible combinations indicates how important it is to choose wisely. The two suits should be complementary and appropriate to the occasion; the four ties can be chosen to match the suits, and the six shirts should be selected to mix and match with the ties and suits. Care should be taken to avoid repeating clothing items, and the person should also consider the climate and purpose of the trip in order to select the most suitable wardrobe.

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There are 7 degrees of freedom.

In performing the pooled-variance t test, the degrees of freedom can be calculated using the formula:
df = (n1 - 1) + (n2 - 1)

Substituting the given values:
df = (4 - 1) + (5 - 1)
df = 3 + 4
df = 7

Therefore, there are 7 degrees of  freedom.

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There are 7 degrees of freedom for the pooled-variance t-test.

To perform a pooled-variance t-test, we need to calculate the degrees of freedom. The formula for degrees of freedom in a pooled-variance t-test is:

\(\[\text{{df}} = n_1 + n_2 - 2\]\)

where \(\(n_1\)\) and \(\(n_2\)\) are the sample sizes of the two independent samples.

In this case, \(\(n_1 = 4\)\) and \(\(n_2 = 5\)\). Substituting these values into the formula, we get:

\(\[\text{{df}} = 4 + 5 - 2 = 7\]\)

In a pooled-variance t-test, we combine the sample variances from two independent samples to estimate the population variance. The degrees of freedom for this test are calculated using the formula \(df = n1 + n2 - 2\), where \(n_1\)and \(n_2\) are the sample sizes of the two independent samples.

To understand why the formula is \(df = n1 + n2 - 2\), we need to consider the concept of degrees of freedom. Degrees of freedom represent the number of independent pieces of information available to estimate a parameter. In the case of a pooled-variance t-test, we subtract 2 from the total sample sizes because we use two sample means to estimate the population means, thereby reducing the degrees of freedom by 2.

In this specific case, the sample sizes are \(n1 = 4\) and \(n2 = 5\). Plugging these values into the formula gives us \(df = 4 + 5 - 2 = 7\). Hence, there are 7 degrees of freedom for the pooled-variance t-test.

Therefore, there are 7 degrees of freedom for the pooled-variance t-test.

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Given:

Consider the below figure attached with this question.

To find:

The equation of the graph in slope-intercept form.

Solution:

From the graph it is clear that, the line passes through (0,450) and (3,350).

So, the equation of line is

\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)

\(y-450=\dfrac{350-450}{3-0}(x-0)\)

\(y-450=\dfrac{-100}{3}x\)

Add 450 on both sides.

\(y=-\dfrac{100}{3}x+450\)

Therefore, the correct option is A.

Answer:

A

Step-by-step explanation:

donno

Answer:

385$

Step-by-step explanation:

30% off of 600 is 180. 600-180=420. Then, 35$ off would be 385.

Line segment is a a measurable part of a line that consists of two points, called endpoints.

a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Given that measurable part of a line that consists of two points, called endpoints is a line segment.

A line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints.

Hence, line segment is a a measurable part of a line that consists of two points, called endpoints.

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Answer:

5y

Step-by-step explanation:

10

Answer:

60.25 then 34.5

Step-by-step explanation:

Answer:

60.75 and 119.25

Step-by-step explanation:

Answer:

168 unlimited-ride passes.

Step-by-step explanation:

50x+20y=10680

x+y=282

Multiply.

20(x+y=282)

20x+20y=5640

Subtract.

50x-20x+20y-20y=10680-5640.

30x=5040

x=168

Hope this helps plz hit the crown :D

It's C, I took the test and got it right.

Answer:

To calculate the value of v using the equation v = u + at, we can substitute the given values:

u = 2 (initial velocity)

a = -5 (acceleration)

t = 1/12/22 (time)

v = u + at

v = 2 + (-5)(1/12/22)

First, let's simplify the time expression:

t = 1/12/22

t = 1 ÷ 12 ÷ 22

t = 0.00297619 (approximately)

Now we substitute the values into the equation:

v = 2 + (-5)(0.00297619)

Calculating the multiplication:

v = 2 - 0.01488095

Finally, let's add the values:

v ≈ 1.98511905

Therefore, the value of v is approximately 1.98511905.

Answer: 3,020,000

Step-by-step explanation:

three million twenty thousand

Answer: 3,020,000

Step-by-step explanation: 3,000,000 + 20,000 = 3020000

The probability that a randomly selected datum falls within 2 standard deviations of the mean as required is; 0.95.

By observation, it follows that the distribution as represented in the task content above is a normal distribution.

On this note, the empirical rule applies as follows;

For a standard normal distribution, 68% of the observations (datum) fall within 1 standard deviation of the mean; 95% of the datum lie within two standard deviation of the mean; and 99.9% lie within 3 standard deviations of the mean.

On this note, when expressed as a percentage; the probability that the randomly selected datum falls with 2 standard deviations is; 95/100 = 0.95.

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Answer:

It's - 28

Step-by-step explanation:

6*-7=-42-4=-28

Answer:

y is -46

Step-by-step explanation:

y= 6x -4 ....means

y =6 *x -4......so replace x with -7

y = 6*-7 -4

y=-42 -4

y= -46

The maximum number of individual areas that may be created from the plot and have dimensions larger than 1 m each is 216.

A dimension in mathematics is the lengths or breadth of a region, area, or space as seen from a single angle. It only comprises its length, width, and height of an item. A typical approach to describe dimensions is by length. Height, depth, and other dimensions represent example of dimensions. The dimensions of a line, a square, and a cube are all one, two, and three dimensions, respectively (3D).

ab > 1

So, a = 1

b = 2

Number is 27/1 * 16/2

= 27 * 8

= 216

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Answer:

2x^2 +4x -4

Step-by-step explanation:

(2x^2 - 2x) + (6x - 4)

Combine like terms

2x^2 +6x-2x -4

2x^2 +4x -4

Answer:

let

f(x) = x^2 - 10x – 24=0

x^2 - 10x – 24=0

x^2 -12x+2x-24=0

x(x-12)+2((x-12)=0

(x+2)(x-12)=0

either

x=-2

or

x=12

Step-by-step explanation:

therefore the other solution of the function is f(12).

Answer: c

Step-by-step explanation:

The point (7,84) represents a precise location on a graph or coordinate plane.

A coordinate is a set of values that specifies the position or location of a point in a geometric space.

The point (7,84) represents a specific location on a graph or coordinate plane. The first number, 7, represents the point's position on the x-axis, which is a horizontal line that runs left to right. The second number, 84, represents the point's position on the y-axis, which is a vertical line that runs up and down. Together, the two numbers give us a precise location for the point.

In this situation, we don't have enough context to know what the point (7,84) represents. It could be the location of a city on a map, the amount of rainfall in inches on a specific day, or the price of a stock at a particular time. However, regardless of the situation, the point (7,84) is simply a specific location in a two-dimensional space that has been identified using coordinates.

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Complete Question:

What does the point (7,84) represent in the graph?​ And define the explanation for each value.

(a) The partial derivative of the utility function with respect to x_2 is:
∂U/∂x_2 = -(1-α)ρx_2^(-ρ-1)(αx_1^(-ρ) + (1-α)x_2^(-ρ))^(-1/ρ - 1)

(b) The expression is MRS = αρx_1^(-ρ) / (1-α)ρx_2^(-ρ)

(c) the preferences represented by this function are homothetic.

(a) To find the marginal utility of both goods, we need to take the partial derivatives of the utility function with respect to each good.

The partial derivative of the utility function with respect to x_1 is:
∂U/∂x_1 = -αρx_1^(-ρ-1)(αx_1^(-ρ) + (1-α)x_2^(-ρ))^(-1/ρ - 1)

Similarly, the partial derivative of the utility function with respect to x_2 is:
∂U/∂x_2 = -(1-α)ρx_2^(-ρ-1)(αx_1^(-ρ) + (1-α)x_2^(-ρ))^(-1/ρ - 1)

(b) The Marginal Rate of Substitution (MRS) represents the rate at which a consumer is willing to substitute one good for another while maintaining the same level of utility.

In this case, the MRS is the negative ratio of the partial derivatives of the utility function:
MRS = -∂U/∂x_1 / ∂U/∂x_2

= (-αρx_1^(-ρ-1)(αx_1^(-ρ) + (1-α)x_2^(-ρ))^(-1/ρ - 1)) / (-(1-α)ρx_2^(-ρ-1)(αx_1^(-ρ) + (1-α)x_2^(-ρ))^(-1/ρ - 1))

Simplifying the expression, we get:
MRS = αρx_1^(-ρ) / (1-α)ρx_2^(-ρ)

(c) Homothetic preferences mean that the consumer's preferences do not change with changes in their income.

To determine whether the preferences represented by this function are homothetic, we need to check whether the MRS depends on the ratio of x_1 to x_2 or on the levels of x_1 and x_2 individually.

By looking at the expression for MRS, we can see that it depends on the ratio of x_1 to x_2 (x_1/x_2), not on their individual levels.

Therefore, the preferences represented by this function are homothetic.

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Problem 7

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

Work Shown:

p(x) = x^4+x^3-kx-x+6

If (x-2) is a factor of p(x), then x = 2 is a root of p(x). This is a special case of the remainder theorem.

This means p(2) = 0

Replace every x with 2 and solve for k

p(x) = x^4+x^3-kx^2-x+6

p(2) = 2^4+2^3-k(2)^2-2+6

p(2) = 16+8-4k-2+6

p(2) = 28-4k

0 = 28-4k .... replace p(2) with 0

4k = 28

k = 28/4

k = 7

The polynomial

p(x) = x^4+x^3-7x^2-x+6

has the factor (x-2)

============================================

Problem 8

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

Work Shown:

Check out the diagram below to see the synthetic division table. We're after the remainder which is highlighted in yellow.

An alternative is to use direct substitution

p(x) = 2x^4+4x^3-x^2-5

p(-3) = 2(-3)^4+4(-3)^3-(-3)^2-5 ... replace every x with -3

p(-3) = 2(81)+4(-27)-9-5

p(-3) = 162-108-9-5

p(-3) = 40  

This helps confirm we got the right remainder and the right answer.

Answer:

1/8 of males as females are 7 times of males are x then females are 7x so the fraction of males x will be 1/8

Step-by-step explanation:

Answer:

Solution is in the photo

Answer:\

\(10^{7}\)

Step-by-step explanation:

keep the number, add the exponents

Answer:

499

Step-by-step explanation:

Answer:

so if the printer can print 10 pages per min. then the equation would be 10*m.

Step-by-step explanation:

Answer:

The 3rd one

Step-by-step explanation:

Plug it in

The rate of change of the perimeter of the square is 11.2 cm/min when the side length is 6 cm.

Step 1: The area of a square is A = s2, where s is the side length.

Step 2: The rate of change of the area of the square is 28 cm2/min.

Step 3: The perimeter of the square is

P = 4s.

Step 4: Substitute s = 6 into the equation for P to get

P = 24 cm.

Step 5: Differentiate P with respect to time to get the rate of change of

the perimeter:

dP/dt = 4ds/dt.

Step 6: Substitute the rate of change of the area (dA/dt = 28 cm2/min) into the equation for dP/dt to get dP/dt = 4(28 cm2/min)/dt.

Step 7: Simplify the equation to get

dP/dt = 112 cm/min.

Conclusion: The rate of change of the perimeter of the square is 112 cm/min when the side length is 6 cm

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In Liam's cylindrical container,  Liam has collected approximately 155.2 grams of the trace element.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that consists of two parallel, congruent circular bases connected by a curved surface. The curved surface is usually called the lateral surface, and it can be formed by taking a rectangle and wrapping it around the circumference of the base. The line segment that connects the centers of the circular bases is called the axis of the cylinder.

Now,

The first step is to find the volume of Liam's container. We know that it's in the shape of a right cylinder with a diameter of 14 cm and a height of 13.6 cm, so we can use the formula for the volume of a cylinder:

V = πr²h

where r = radius and h = height. So

r = 14 / 2

= 7 cm

h = 13.6 cm

V = π(7 cm)²(13.6 cm) = 2,773.2 cubic centimeters

Next, we need to figure out how much of the trace element is in this sample. We know from the information given that there are 0.056 grams of the trace element for every cubic centimeter of water. So:

0.056 grams/cubic centimeter x 2,773.2 cubic centimeters = 155.194 grams

Therefore, Liam has collected approximately 155.2 grams of the trace element.

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