Can someone please help me find the domain and range thank you all so much for the help

The z-scores for the observations 16, 11, 13, 22, 15, and 19 are approximately 0, -1.37, -0.82, 1.64, -0.27, and 0.82, respectively.

To compute the z-scores for each observation in the sample, we need to first calculate the mean and standard deviation of the data set.

Given the sample with observations: 16, 11, 13, 22, 15, and 19.

Calculate the mean (μ):

Add up all the observations and divide by the total number of observations.

Mean (μ) = (16 + 11 + 13 + 22 + 15 + 19) / 6 = 96 / 6 = 16.

Calculate the standard deviation (σ):

Subtract the mean from each observation.

Deviation = Observation - Mean

Square each deviation.

Squared Deviation = Deviation²

Calculate the average of the squared deviations.

Average Squared Deviation = (Squared Deviation1 + Squared Deviation2 + ... + Squared Deviation6) / 6

Take the square root of the average squared deviation.

Standard Deviation (σ) = √(Average Squared Deviation)

Let's calculate each step:

Deviation1 = 16 - 16 = 0

Deviation2 = 11 - 16 = -5

Deviation3 = 13 - 16 = -3

Deviation4 = 22 - 16 = 6

Deviation5 = 15 - 16 = -1

Deviation6 = 19 - 16 = 3

Squared Deviation1 = 0² = 0

Squared Deviation2 = (-5)² = 25

Squared Deviation3 = (-3)² = 9

Squared Deviation4 = 6² = 36

Squared Deviation5 = (-1)² = 1

Squared Deviation6 = 3² = 9

Average Squared Deviation = (0 + 25 + 9 + 36 + 1 + 9) / 6 = 80 / 6 = 13.33

Standard Deviation (σ) = √13.33 ≈ 3.65

Now that we have the mean (μ = 16) and standard deviation (σ ≈ 3.65), we can calculate the z-score for each observation.

The z-score (Z) for an observation (X) is calculated using the formula:

Z = (X - μ) / σ

Let's calculate the z-scores for each observation:

Z1 = (16 - 16) / 3.65 = 0 / 3.65 = 0

Z2 = (11 - 16) / 3.65 = -5 / 3.65 ≈ -1.37

Z3 = (13 - 16) / 3.65 = -3 / 3.65 ≈ -0.82

Z4 = (22 - 16) / 3.65 = 6 / 3.65 ≈ 1.64

Z5 = (15 - 16) / 3.65 = -1 / 3.65 ≈ -0.27

Z6 = (19 - 16) / 3.65 = 3 / 3.65 ≈ 0.82

So, the z-scores for the observations 16, 11, 13, 22, 15, and 19 are approximately 0, -1.37, -0.82, 1.64, -0.27, and 0.82, respectively.

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Answer:

B.   {1, 6, 7, 8} ∩ {6, 8, 9} = {6, 8}

Step-by-step explanation:

The intersection of two sets is a set containing the elements that are present in both sets.

{1, 6, 7, 8} ∩ {6, 8, 9} = {6, 8}

The length of the arc KL in the given circle is 3.49 units

In a circle whose radius is R, the length of an arc defined by an angle x is given by:

Length = (x/360)*2*3.14*R

Here we know that the radius is 2 units, and the angle for the arc KL is 100°, then we can replace these values in the formula above so we get that the length of the arc is:

Length = (100/360)*2*3.14*2

Lenght = 3.49 units.

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A z-score of 0 indicates that the person's score is equal to the mean, so they are right at the Average Performance level.the z-score of a person who scored 300 on the exam is 0.

The z-score of a person who scored 300 on the exam, we can use the formula:

z = (x - μ) / σ

where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.

In this case, the person scored 300 on the exam, which is equal to the mean (μ). Therefore, we can substitute these values into the formula:

z = (300 - 300) / 40

Simplifying the equation, we have:

z = 0 / 40

Since any number divided by zero is undefined, we can conclude that the z-score of a person who scored 300 on the exam is 0.

The z-score measures the number of standard deviations a data point is away from the mean. In this case, a z-score of 0 indicates that the person's score is equal to the mean, so they are right at the average performance level.

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No, the inference is not necessarily valid. The fact that a comedian received the most votes in an online poll does not guarantee that they are the funniest comedian in the nation.

The poll's results are influenced by various factors such as the sample size, the demographics of the voters and potential biases in the voting process.

Also, humor is subjective and what one person finds funny may not be the same for someone else. Therefore, determining the funniest comedian based solely on the number of votes in an online poll is an oversimplified and flawed approach.

To improve the poll, several steps can be taken which are:

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Answer:    D.   <4 and <7

Step-by-step explanation:

Consecutive means one after the other

Interior means within the parallel lines

So we are looking for 2 to angles inside the parallelel lines that are 1 after the other on the same side

D.   <4 and <7

The solutions are : solution of the following system of equations are:

(- 1/2, 1/2)

(- 1, 2)

Here, we have,

The given system of equations is expressed as

y = 2x²- - - - - - - - - - - - - - -1

y = - 3x - 1- - - - - - - - - -- - - -2

We would apply the method of substitution by substituting equation 1 into equation 2. It becomes

2x² = - 3x - 1

2x² + 3x + 1 = 0

We would find two numbers such that their sum or difference is 3x and their product is 2x².

The two numbers are 2x and x. Therefore,

2x² + 2x + x + 1 = 0

2x(x + 1) + 1(x + 1) = 0

2x + 1 = 0 or x + 1 = 0

x = - 1/2 or x = - 1

Substituting x = - 1/2 into equation 1, it becomes

y = 2(-1/2)² = 1/2

Substituting x = - 1 into equation 1, it becomes

y = 2(-1)² = 2

Hence, The solutions are : solution of the following system of equations are:

(- 1/2, 1/2)

(- 1, 2)

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Answer:

The correct answer is:

(A) enlargement

John will have to pay $12.24 in interest at the end of the loan.

To calculate the amount of interest John will have to pay at the end of the loan, we can use the formula for simple interest:

Interest = Principal * Rate * Time

Given:

Principal (P) = $4,300.00

Rate (R) = 13.75% per annum

Time (T) = 8 days

First, we need to convert the rate from an annual percentage to a daily rate. Since there are 365 days in a year:

Daily Rate = (Rate / 100) / 365 = (13.75 / 100) / 365 = 0.0003767

Now we can calculate the interest:

Interest = Principal * Rate * Time

= $4,300.00 * 0.0003767 * 8

= $12.24

Therefore, John will have to pay $12.24 in interest at the end of the loan.

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A graph of the image of polygon DGF after a dilation centered at the origin with a scale factor of 1.5 is shown below.

In Geometry, a dilation is a type of transformation which typically changes the dimension (size) or side lengths of a geometric figure, but not its shape.

This ultimately implies that, the side lengths of the dilated geometric figure would be enlarged or reduced based on the scale factor applied.

In this scenario an exercise, we would dilate the coordinates of the polygon by applying a scale factor of 1.5 that is centered at the origin as follows:

D (-2, 0) → (-2 × 1.5, 0 × 1.5) = D' (-3, 0).

G (0, 2) → (0 × 1.5, 2 × 1.5) = G' (0, 3).

F (2, -2) → (2 × 1.5, -2 × 1.5) = F' (3, -3).

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The arrangement of the side length of the triangles from the least to the greatest is DF <  DE < EG <  EF <  GF.

The arrangement of the lengths of the triangle from the least to the greatest is determined as follows;

The size of the length of a triangle increases as the size of the angle opposite to the length increases.

That is the greater the size of the angle opposite the side length of a triangle, the greater the size of the side length of the triangle.

From the given diagram, we can arrange the size of the side length of the triangle as follows;

angle D = 180 - (57 + 58 )

angle D = 65⁰ (this is opposite to length EF)

So the arrangement of the side length of the triangles are;

length DF < Length DE < length EG < length EF < length GF

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A plane intersecting a rectangular prism can create different cross-sectional shapes depending on the orientation of the plane. A plane intersects the pyramid parallel to its base. The cross section is a rectangle  A plane intersects the pyramid perpendicular to its base and through the top vertex. The cross section is a triangle

A plane intersecting a rectangular prism can create different cross-sectional shapes depending on the orientation of the plane. Let's explore the two scenarios you mentioned:

Plane parallel to the base: When a plane intersects the rectangular prism parallel to its base, the resulting cross section is also a rectangle. The shape of the cross section will have the same dimensions as the base of the rectangular prism.

Plane perpendicular to the base and through the top vertex: In this case, the cross section will be a triangle. The shape of the cross section will be determined by the intersection of the plane with the three sides of the rectangular prism. The base of the triangle will be formed by the side of the rectangular prism, while the other two sides will be formed by the edges connecting the top vertex of the pyramid to the corresponding vertices of the base.

It's important to note that a rectangular prism is different from a pyramid. A rectangular prism has six rectangular faces, while a pyramid has a polygonal base (in this case, a rectangle) and triangular faces converging to a single point called the apex or top vertex.

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The value of x in trapezoid KFGJ is 40.

Given information:

KFGJ is a trapezoid.

KF = 20

JG = x

MN is midsegment of trapezoid KFGJ.

MN = 30

To find the value of x in trapezoid KFGJ, we can use the fact that the midsegment MN of a trapezoid is parallel to the bases and its length is equal to the average of the lengths of the bases.

In this case, MN is given as 30, and we know that KF is one of the bases with a length of 20. To find the length of the other base JG, we can use the formula for the midsegment of a trapezoid:

MN = (KF + JG) / 2

Substituting the given values, we have:

30 = (20 + x) / 2

To solve for x, we can multiply both sides of the equation by 2:

60 = 20 + x

Subtracting 20 from both sides:

x = 60 - 20

x = 40

Therefore, the value of x in trapezoid KFGJ is 40.

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The probability is solved and the tree diagram is given

Given data ,

The tree diagram to draw 3 cards out of 52 cards from the given probability details are:

The two events, drawing a spade, and not drawing a spade. These two events have to branches which are the same, drawing a spade and not drawing a spade. Once again these two branches have two more branches for each, drawing another spade and not drawing a spade.

        _______ Draw a Spade _______

              /                              \

      ______/______                  ______\_______

     /              \                /               \

   /                  \            /                   \

 /                      \        /                       \

Spade                 Not Spade             Spade             Not Spade

 |                        |                |                   |

Draw another Spade   Not Draw a Spade  Draw another Spade  Not Draw a Spade

Hence , the probability of deck of cards is solved

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These atomic formulas represent basic assertions or relationships between elements or sets.

In logic and mathematical logic, "atomic formulas" refer to the simplest, indivisible formulas that do not contain any logical connectives or quantifiers.

They are the building blocks from which more complex formulas are constructed.

In set theory, the atomic formulas are typically statements about membership or equality.

For example, "x belongs to y" (x ∈ y) and "x equals y" (x = y) are atomic formulas in set theory.

Using logical connectives (such as conjunction, disjunction, negation, implication, and equivalence) and quantifiers (such as "for all" (∀) and "there exists" (∃)), we can combine atomic formulas to form more complex formulas, enabling us to express a wide range of logical statements and mathematical properties.

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Answer:

  See attached

Step-by-step explanation:

You want the given numbers classified as to Natural, Whole, Integer, Rational, Irrational, and/or Real.

All the given numbers are real.

The number √2 is irrational. All the others are rational.

The values √16 = 4, 0, and -5 are integer values. Whole numbers are non-negative integers, so exclude -5. Natural numbers are positive integers, so exclude 0 and -5.

The Xs indicate the categories each number belongs to.

Answer:

When the cab travels 0 miles, the total fee will be $10.00.

Step-by-step explanation:

We Know

2 miles = $13.00

5 miles = $17.50

3 miles = 17.50 - 13.00 = $4.50

1 mile = 4.50 / 3 = $1.50

So, for every 1-mile go, the cost is increasing by $1.50; this is the slope.

What does the y-intercept mean in this situation?

It is the total fee that Tyrell pays when the cab goes 0 miles (when he first steps in the cap).

So, the answer is D. When the cab travels 0 miles, the total fee will be $10.00.

Answer:

20cm

Step-by-step explanation:

The translation used to create the image A'B'C'D', from the pre image ABCD is T(7, 0), which corresponds with the option;

7 units to the right

The coordinates of the vertices of the polygon ABCD are;

A(-2, -1), B(0, -4), C(4, -4), D(2, -1)

The coordinates of the vertices of the polygon A'B'C'D' are;

A'(5, -1), B'(7, -4), C'(11, -4), D'(9, -1)

The coordinates of the vertices of the image indicates;

The difference between the coordinates are;

A'(5, -1) - A(-2, -1) = (5 - (-2), -1 - (-1)) = (7, 0)

B'(7, -4) - B(0, -4) = (7 - 0, -4 - (-4)) = (7, 0)

C'(11, -4) - C(4, -4) = (11 - 4, -4 - (-4)) = (7, 0)

D'(9, -1) - D(2, -1) = (9 - 2, -1 - (-1)) = (7, 0)

The translation that is used to create the image is therefore;

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