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The correct statement is: c. Median is less than or equal to [tex]18[/tex].

Let's analyze the given range of values, which is [tex]5 \ to \ 18[/tex], and evaluate the statements:

a. Mean is less than [tex]6[/tex]:

To determine if the mean is less than [tex]6[/tex], we need to find the average of the given range.

The mean can be calculated as:

[tex]\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \][/tex]

In this case, the sum of the values is [tex]5 + 6 + 7 + \ldots + 18[/tex], and the number of values is [tex]18 - 5 + 1[/tex] (inclusive).

b. Range is greater than [tex]18[/tex]:

The range is the difference between the maximum and minimum values in a dataset. In this case, the range is [tex]18 - 5 = 13,[/tex] which is less than 18.

c. Median is less than or equal to [tex]18[/tex]:

The median is the middle value in a dataset when the values are arranged in ascending order. In this case, since the range starts from [tex]5[/tex] and ends at 18, the median is less than or equal to [tex]18[/tex].

d. IQR is greater than or equal to [tex]6[/tex]:

The interquartile range (IQR) is the difference between the first quartile (Q1) and the third quartile (Q3) of a dataset. Since we don't have the actual dataset or specific values beyond the range, we cannot determine if the IQR is greater than or equal to [tex]6[/tex].

Therefore, based on the given range, the correct statement is:

c. Median is less than or equal to [tex]18[/tex].

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The value of s in the circle is 11.

We have,

When two chords in a circle have the same arc length intercepted by the chords, it means that the distances from each endpoint of the chords to the center of the circle are equal.

Now,

The arc length XY and WZ are the same.

This means,

Chord XY and Chord WZ are equal.

Now,

2s = s + 11

Solve for s.

2s - s = 11

s = 11

Thus,

The value of s in the circle is 11.

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The true statements regarding the probability are:

Based on the given information, it is likely that the bag has at least one black marble (with a probability of 0.1). It is not certain or impossible, as the probability is not 0 or 1.

It is not certain or unlikely that the bag has at least one pink marble, as the probability is not 0 or 1. However, the probability of the bag having at least one pink marble is relatively high (0.79), so it is more likely than not that the bag has a pink marble.

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To make both triangles equal, their corresponding angles must be equal and when x = 106 degrees, the second angle in triangle 2 is equal to the third angle in triangle 1, which refutes Terry's claims.

To determine the value of x that refutes Terry's claims, we need to examine the angles of the triangles and find a valid configuration where triangle 1 is similar to triangle 2.

In triangle 1, the given angles are 18 degrees and 96 degrees. The third angle can be found using the property that the sum of the angles in a triangle is always 180 degrees:

Third angle in triangle 1 = 180 - (18 + 96) = 180 - 114 = 66 degrees.

let's find the value of x that will make both triangles similar to one another or their corresponding angles to be equal.

Since we already know one angle in triangle 2 is 8 degrees, we can find the second angle as follows:

Second angle in triangle 2 = 180 - (8 + x) = 180 - 8 - x = 172 - x degrees.

To refute Terry's claims, we need to find a value of x such that the second angle in triangle 2 (172 - x degrees) is equal to the third angle in triangle 1 (66 degrees).

Setting up the equation:

172 - x = 66

Solving for x:

172 - 66 = x

106 = x

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Mark's accusation is incorrect. Based on the blood type combinations, it is possible for the children to have the observed blood types without any infidelity. Mark owes his wife an apology for the false accusation.

Mark has blood type AB, which means he has one A allele and one B allele.

Mark's wife has blood type O, which means she has two O alleles.

One child has blood type A, indicating they have inherited one A allele.

One child has blood type B, indicating they have inherited one B allele.

One child has blood type O, indicating they have inherited two O alleles.

Child 1:

Mark's allele: A

Wife's allele: O

Possible combinations: AO

Child 2:

Mark's allele: B

Wife's allele: O

Possible combinations: BO

Child 3:

Mark's allele: A or B (since Mark has AB blood type)

Wife's allele: O

Possible combinations: AO or BO

From the possible combinations, we can see that it is possible for the children to have blood types A, B, and O without any issues.

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The exact values are:

sin(α + β) = (-6√5 - 8)/25

cos(α + β) = (4√5 - 6)/25

sin(α - β) = (-6√5 + 8)/25

tan(α - β) = (-9√5 + 45)/4

We have,

Recall the trigonometric identities:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

tan(a - b) = (tan(a) - tan(b))/(1 + tan(a)tan(b))

Using these identities, we can find the exact values of the expressions given.

(a) Sin (α + β)

sin(α + β) = sin(α)cos(β) + cos(α)sin(β)

= (√5/5)(-3/5) + (2/5)(-4/5) (using the values given for sin and cos)

= -6√5/25 - 8/25

= (-6√5 - 8)/25

(b) Cos (α + β)

cos(α + β) = cos(α)cos(β) - sin(α)sin(β)

= (2/5)(-3/5) - (√5/5)(-4/5) (using the values given for sin and cos)

= -6/25 + 4√5/25

= (4√5 - 6)/25

(c) Sin (α - β)

sin(α - β) = sin(α)cos(β) - cos(α)sin(β)

= (√5/5)(-3/5) - (2/5)(-4/5) (using the values given for sin and cos)

= -6√5/25 + 8/25

= (-6√5 + 8)/25

(d) tan (α - β)

tan(α - β) = (tan(α) - tan(β))/(1 + tan(α)tan(β))

= ((√5/5) - (-4/5))/(1 + (√5/5)(-4/5)) (using the values given for sin and cos)

= (9√5/5)/(1 - 4/5√5)

= (-9√5 + 45)/4

Therefore,

The exact values are:

sin(α + β) = (-6√5 - 8)/25

cos(α + β) = (4√5 - 6)/25

sin(α - β) = (-6√5 + 8)/25

tan(α - β) = (-9√5 + 45)/4

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The answer is 23/24

there are 23 out of the 24 crayons that arent light blue and that gives you the odds against the light blue crayon

The value of the sides are;

c = 35. 5, y = 32. 2, <H = 65 degrees

Option D

We have that the ratios of the trigonometric identities are;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the information given, we have that;

Using sine identity

sin 25 = 15/c

cross multiply the values, we get;

c = 35. 5

Then, using tan identity;

tan 25 = 15/y

cross multiply

y = 32. 2

Sum of angles in a triangle is equal to 180 degrees.

Then, we have that;

90 + 25 + <H = 180

collect the terms

<H = 65 degrees

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The domain and range of a function for the area of a rectangle indicates;

(a) Range; 0 ≤ y < ∞

(b) Domain; 0 ≤ x < ∞

A function is a definition or rule that maps the values of an input unto the values of the output variables.

The area of a rectangle, A = Length, L × Width, W

Therefore;

The area of a rectangle is directly proportional to the width of a rectangle

A ∝ W

The graph of the area to the length of the width of the rectangle indicates that we get;

(a) The domain is the set of the possible x-values of the function

The proportional relationship between the area and the width of a rectangle indicates;

The domain is; 0 ≤ x < ∞

(b) The range is the set of the possible output values of the graph, which is the set of the y-values

The proportional relationship between the area, y and the width, x , the range is; 0 ≤ y < ∞

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The value of x is 53.  

We have,

From the figure,

There are two parallel lines.

This means,

44 and angle M are corresponding angles.

And,

We can consider a triangle as:

M + P + P = 180

Where P is the angle opposite to the equal sides.

So,

44 + P + P = 180

44 + 2P = 180

2P = 180 - 44

2P = 36

P = 18

Now,

x is the exterior angle.

This means,

x = 35 + P

x = 35 + 18

x = 53

Thus,

The value of x is 53.  

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After considering the given data we conclude that the area of the given figure is 62.2 cm², under the condition that x = 5 cm

Since the given figure comprises of two right angled triangle and one rectangle we can split them and calculate their area separately then apply summation at the ending.
Let us proceed with the triangle
Let us first name the whole figure, ABCD is the whole diagram out of which first we will deal with triangle CDG,
In triangle CDG
The height length (DG) = 7.5 cm
The base  length ( CG) = 2.4 cm
Then the area of the triangle CDG
[tex]Area =1/2 * base *height[/tex]
= 1/2 × 2.4 ×7.5
= 1/2 × 18
= 9 cm²
Now moving on to the other triangle ABE
The height length (AE) = 7.5 cm
The base  length (EB) = 4.2 cm
Then the area of the triangle ABE
[tex]Area =1/2 * base *height[/tex]
= 1/2 × 4.2 × 7.5
=1/2 × 31.5
= 15.7 cm²
Finally moving onto the rectangle AEGD,
Given
Length of the rectangle (DG) = 7.5 cm
Breadth of the rectangle ( GE) = x = 5 cm
Placing the values in the formula
[tex]Area = length * breathe[/tex]
Area = 7.5 × 5
Area = 37.5 cm²

Now applying summation to evaluate the total area of the quadrilateral ABCD
Area of CDG + Area of ABE + Area of AEGD
= ( 9 + 15.7 + 37.5)
= 62.2 cm²
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1. The two cylinders have the same height and the same cross-sectional area at every point along that height, so they have the same volume. Sue is correct.

2. The two stacks of quarters have the same height and the same cross-sectional area at every point along that height, so they have the same volume.

3. The two triangular prisms have the same height and the same cross-sectional area at every point along that height, so they have the same volume. This can also be explained using Cavalieri's principle.

The two stacks of quarters have the same height and the same cross-sectional area at every point along that height, so they have the same volume.

This can be explained using Cavalieri's principle, which states that two solids have the same volume if they have the same height and the same cross-sectional area at every point along that height.

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Answer:

72 1/2

Step-by-step explanation:

so, she ran 2 miles in 8 3/4 minutes each.

3 miles in 9 minutes each.

2 miles in 9 1/4 minutes each.

1 mile in 9 1/2 = 9 2/4 minutes.

in total that means

2×(8 3/4) + 3×9 + 2×(9 1/4) + 9 2/4 =

= 16 6/4 + 27 + 18 2/4 + 9 2/4 =

= 16 + 27 + 18 + 9 + 6/4 + 2/4 + 2/4 =

= 70 + 10/4 = 70 + 2 + 2/4 = 72 2/4 = 72 1/2 minutes

Answer:

The original price of the shirt was Ksh 500 and it was sold for Ksh 550.

The discount is the difference between the original price and the selling price, which is Ksh 500 - Ksh 550 = Ksh -50.

To find the percentage discount, we can use the formula:

percentage discount = (discount ÷ original price) × 100%

percentage discount = (-50 ÷ 500) × 100%

percentage discount = -10%

Therefore, the percentage discount is 10%.

The Binomial coefficients, we get:

(2x+5y)^3 = 8x^3 + 60x^2y + 150xy^2 + 125y^3

Therefore, (2x+5y)^3 expands to 8x^3 + 60x^2y + 150xy^2 + 125y^3.

To expand (2x+5y)^3, we can use the Binomial Theorem, which states that:

(a + b)^n = nC0a^n + nC1a^(n-1)b + nC2a^(n-2)b^2 + ... + nCn-1ab^(n-1) + nCn b^n

where nCk represents the binomial coefficient, which is the number of ways to choose k items from a set of n items.

In this case, we have:

a = 2x

b = 5y

n = 3

So, we can apply the Binomial Theorem as follows:

(2x+5y)^3 = 3C0 (2x)^3 + 3C1 (2x)^2(5y) + 3C2 (2x)(5y)^2 + 3C3 (5y)^3

Simplifying each term using the binomial coefficients, we get:

(2x+5y)^3 = 8x^3 + 60x^2y + 150xy^2 + 125y^3

Therefore, (2x+5y)^3 expands to 8x^3 + 60x^2y + 150xy^2 + 125y^3.

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The correct statements are:

If "positive" end behaviour:

The arrows point in the same direction.

The right arrow is up.

The graph hits the y-axis.

If "negative" end behaviour:

The arrows point in opposite directions.

The right arrow is down.

The graph hits the X-axis.

In mathematics, a graph is a visual representation of a set of data, which consists of points, called vertices or nodes, and lines connecting them, called edges or arcs.

Graphs are often used to represent mathematical functions, data sets, or relationships between objects, and they can be used to model real-world phenomena.

Graphs can be drawn on a coordinate plane or in a more abstract form, and they can be used to analyze and understand complex systems and relationships.

The correct statements are:

If "positive" end behaviour:

The arrows point in the same direction.

The right arrow is up.

The graph hits the y-axis.

If "negative" end behaviour:

The arrows point in opposite directions.

The right arrow is down.

The graph hits the X-axis.

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The per-unit reactance of the transformer is 0.0444 pu.

To calculate the per-unit reactance of the transformer, we need to use the following formula:

Xpu = X / (Vbas[tex]e^2[/tex] / Sbase)

where X is the reactance in ohms, Vbase is the base voltage in volts, and Sbase is the base power in volt-amperes.

In this case, the rated power of the transformer is 5 kVA, and the rated voltage on the high side is 400V. Therefore, the base power and base voltage are:

Sbase = 5 kVA

Vbase = 400V

The reactance of the transformer referred to the low voltage side is given as 2Ω. To convert this to per-unit, we substitute the values in the formula:

Xpu = 2Ω / (300[tex]V^2[/tex] / 5 kVA)

Xpu = 0.0444 pu

Therefore, the per-unit reactance of the transformer is 0.0444 pu.

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Answer and Step-by-step explanation:

The given polygon can be referred to in multiple ways, though not all names may prove to be an accurate description:

1. Quadrilateral: A four-sided figure is accurately called a quadrilateral, as it includes any shape with four sides.

2. Rectangle: A type of quadrilateral with four right angles and opposite sides parallel.

3. Square: A special type of rectangle with all sides equal in length.

4. Parallelogram: A quadrilateral with opposite sides that are parallel.

5. Rhomboid: A parallelogram with no right angles and sides of unequal length.

6. Kite: A quadrilateral with two pairs of adjacent sides that are of equal length.

7. Irregular Quadrilateral: A quadrilateral that does not fit in any of the defined categories above.

It's important to note that some names provided in the question do not correctly classify a four-sided polygon:

- Rhombus: A quadrilateral with all sides of equal length and opposite sides parallel. However, it has been provided as a separate entry.

- Trapezoid: A quadrilateral with one pair of parallel sides. However, it has been provided as a separate entry.

- Pentagon: An incorrect classification for a four-sided figure as it refers to a five-sided polygon.

Hope that helps.

The value of x in the circle using the intersecting secants and tangents equation is 4

From the question, we have the following parameters that can be used in our computation:

The circle

The value of x in the circle can be calculated using the intersecting secants and tangents equation

So, we have

6² = x * (x + 5)

When expanded, we have

x² + 5x - 36 = 0

When factored, we have

(x + 9)(x - 4) = 0

Using the zero product property , we have

x = -9 or x = 4

The valiue of x cannot be negative

So, we have

x = 4

Hence, the value of x in the circle is 4

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The area of the whole quilt is 441 in². of the whole quilt is 441 in².

We are given that;

Measure= 7*7

Now,

To find the area of the whole quilt, you need to multiply the length and width of the quilt.

The length and width of the quilt are both 7 times 3 in,

which is 21 in. So, the area of the quilt is 21 in x 21 in

= 441 in².

Therefore, by the area the answer will be 441 in².

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The probability that both marbles are the same color is 1/3.

P(R₂ | R₁) = 1/3

The probability of both events happening together (drawing two red marbles) is the product of the probabilities of each event:

P(R₁ and R₂) = P(R₁) * P(R₂ | R₁)

= (1/2) * (1/3)

= 1/6

P(B₁) = 2/4 = 1/2

P(B₂ | B₁) = 1/3

Probability of B₁ and B₂

P(B₁ and B₂)

= P(B₁) * P(B₂ | B₁)

= (1/2) * (1/3)

= 1/6

P(Same color)

= P(R₁ and R₂) + P(B₁and B₂)

= 1/6 + 1/6 = 2/6

= 1/3

So, the probability that both marbles are the same color is 1/3.

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+* Answer *+

$5,590

*+Step-by-step explanation:*+

$5,000 x 5.9% = $295
$95 x 2 (months), = 590

5,000 + 590 = 5,590

So therefore you have $5,590 dollars.

hope this helps! : )

The division of the polynomial 3x³ - 2x² + x - 4 by x + 3 is:

Quotient: 3x² + 11x + 34

Remainder: -106/(x + 3)

When dividing a polynomial by a linear binomial of the form (x - c) or (x + c), where "c" is a constant, the process is known as synthetic division. This streamlined method of polynomial long division offers a faster and clearer method for dividing polynomials by linear factors.

The process of synthetic division involves arranging the coefficients of the polynomial in descending order and performing a sequence of simple arithmetic operations.

The result of the synthetic division is:

[tex]Quotient: 3x^2 + 11x + 34[/tex]

Remainder: -106/(x + 3)

Kindly find the step by step analysis below.

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The final equation of the given conic, after rotating the axes through the angle θ = arccos(3/5), is:

x^2 * cos(2θ) + y^2 * cos(2θ) = 2y

The equation of the conic in xy-coordinates when the axes are rotated through the given angle can be determined by using a rotation matrix. Given that the conic is represented by the equation:

x^2 - y^2 = 2y

And the rotation angle is θ = arccos(3/5), we can proceed as follows:

1. Rewrite the given equation in matrix form:

[x, y] * [1  0] * [x]  = [2y]

        [-1 0]   [y]      [0]

2. Define the rotation matrix using the given angle θ:

R(θ) = [cos(θ)  -sin(θ)]

          [sin(θ)   cos(θ)]

3. Apply the rotation matrix to the equation:

[x, y] * R(θ)^T * R(θ) * [x] = [2y]

        [1  0]     [-1 0]   [y]     [0]

[x, y] * R(θ)^T * [1  0] * R(θ) * [x] = [2y]

                              [-1 0]   [y]     [0]

[x, y] * [cos(θ) sin(θ)] * [1  0] * [cos(θ)  -sin(θ)] * [x] = [2y]

        [-sin(θ) cos(θ)]   [-1 0]     [sin(θ)   cos(θ)]   [y]     [0]

Simplifying the expression:

[x * cos(θ) + y * sin(θ)] * [x * cos(θ) - y * sin(θ)] - [x * sin(θ) - y * cos(θ)] * [x * sin(θ) + y * cos(θ)] = 2y

Expanding and rearranging terms:

x^2 * cos^2(θ) - y^2 * sin^2(θ) - x^2 * sin^2(θ) + y^2 * cos^2(θ) = 2y

Combining like terms:

x^2 * (cos^2(θ) - sin^2(θ)) + y^2 * (cos^2(θ) - sin^2(θ)) = 2y

Using the trigonometric identity cos^2(θ) - sin^2(θ) = cos(2θ):

x^2 * cos(2θ) + y^2 * cos(2θ) = 2y

The final equation of the given conic, after rotating the axes through the angle θ = arccos(3/5), is:

x^2 * cos(2θ) + y^2 * cos(2θ) = 2y

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After considering the given data we conclude that angle t as a function of the height x is θ = tan⁻¹ (x/300), and angle t in degrees when x is equal to 150, 300, and 600 meters is 63.4°, the graph represent a curve when drawn.

The angle of elevation of the camera can be evaluated by

θ=tan⁻¹(x/2000)

Here, x = height of the rocket.

Hence, the angle t as a function of the height x is given by:

θ = tan⁻¹ (x/300)

To evaluate the angle t in degrees when x is equal to 150, 300, and 600 meters, we stage these values into the equation above:

θ = tan⁻¹ (150/300) = 26.6° (approximate to 1 decimal place)

θ = tan⁻¹ (300/300) = 45° (approximate to 1 decimal place)

θ = tan⁻¹ (600/300) = 63.4° (approximate to 1 decimal place)

To graph t as a function of x, we can plot the values of θ for different values of x. The graph will be a curve that starts at 0° when x=0 and increases as x increases.

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The commutative sets of transformations are two translations, refelction over the y-axis, dilation with center (2,2) and two reflections over the x-axis​. B, D, and E.

The sets of transformations that result in the same image when performed in any order are called "commutative."

A set of transformations is commutative if the order of the transformations doesn't matter;

Performing the transformations in a different order still results in the same final image.

Based on this definition can select the commutative sets of transformations from the given choices:

Translation and dilation with center (0,0) are not commutative.

The order of the transformations matters.

Two translations are commutative.

The order of the transformations doesn't matter.

Vertical translations and reflection over the y-axis are not commutative. The order of the transformations matters.

Reflection over the y-axis and dilation with center (2,2) are commutative.

The order of the transformations doesn't matter.

Two reflections over the x-axis are commutative.

The order of the transformations doesn't matter.

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Answer: A h = - 2

Step-by-step explanation:

Substitute -2 for h

4(-2) + 3 < 10

-8 + 3 < 10

-5 < 10 true

Answer:

-6

Step-by-step explanation:

[tex]\frac{x}{-3} = 2\\x = 2 * (-3)\\x = -6[/tex]

The answer is x equals negative 6

09. The total sample, 118 individuals set academic goals (regardless of gender), while 310 individuals did not set academic goals.

10. The total sample, 290 individuals have cats, while 306 individuals do not have cats. Furthermore, 312 individuals have dogs, while 284 individuals do not have dogs.

In order to find the marginal frequencies, we need to calculate the totals for each category separately.

For question 9:

The marginal frequency for "Set Academic Goals - yes" is 64 + 54 = 118. This represents the total number of individuals who answered "yes" to setting academic goals.

The marginal frequency for "Set Academic Goals - no" is 168 + 142 = 310. This represents the total number of individuals who answered "no" to setting academic goals.

The marginal frequency for "Male" is 64 + 168 = 232. This represents the total number of males.

The marginal frequency for "Female" is 54 + 142 = 196. This represents the total number of females.

Interpretation:

The marginal frequencies provide us with the total counts for each category in a contingency table. In this case, we can see that out of the total sample, 118 individuals set academic goals (regardless of gender), while 310 individuals did not set academic goals. Additionally, there were 232 males and 196 females in the sample.

For question 10:

The marginal frequency for "Cat - yes" is 104 + 186 = 290. This represents the total number of individuals who have cats.

The marginal frequency for "Cat - no" is 208 + 98 = 306. This represents the total number of individuals who do not have cats.

The marginal frequency for "Dog - yes" is 104 + 208 = 312. This represents the total number of individuals who have dogs.

The marginal frequency for "Dog - no" is 186 + 98 = 284. This represents the total number of individuals who do not have dogs.

Interpretation:

The marginal frequencies reveal the total counts for each category in the contingency table. In this case, we can observe that out of the total sample, 290 individuals have cats, while 306 individuals do not have cats. Furthermore, 312 individuals have dogs, while 284 individuals do not have dogs.

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Answer: 6

Step-by-step explanation:

set up a box plot.

To find the interquartile range: 3rd tile value subtracted by the first tile value. Basically: Q3-Q1=IQR

Q= Quartile

3 and 1 is the number

IQR = interquartile range

if you do incorrectly you should get 6 if not add me as a friend and I’ll show you and explain it better!