Which of the following is an even function?
f(x) = (x - 1)^2
f(x) = 8x
f(x) = x^2-x
f(x) = 7

The variance of the population according to the given table is option B 41.

The spread or dispersion of a set of data around its mean is measured by variance. It has the same units as the original data and is calculated as the average of the squared deviations from the mean. Variance is a frequently used statistical term to describe the diversity or variability of a population or sample. When the variance is modest, the data points are closely grouped around the mean, whereas when the variance is great, the data points are widely dispersed.

The variance is given by the formula:

variance = (sum of squared deviations from the mean) / (number of observations)

Using the table we have sum of squared deviations from the mean:

81 + 1 + 1 + 81 = 164

variance = 164 / 4 = 41

Hence, the variance of the population according to the given table is option B 41.

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Based on the information given, we can use the Pythagorean theorem to determine the distance traveled by the northbound car.

Let's denote the distance traveled by the northbound car as 'x' kilometers.

According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (the straight-line distance between the two cars) is equal to the sum of the squares of the other two sides (the distances traveled by each car).

In this case, the northbound car's distance is 'x' kilometers and the eastbound car's distance is 5 kilometers.

So we have the equation:

x^2 + 5^2 = 13^2

Simplifying, we get:

x^2 + 25 = 169

Subtracting 25 from both sides, we get:

x^2 = 144

Taking the square root of both sides, we get:

x = 12

So the northbound car has traveled 12 kilometers.

Answer: 12 km

Step-by-step explanation:

As seen in the figure the distance that the northbound car traveled equals to the distance from point N to the parking lot.

pythagorean: [tex]\sqrt{13^{2}-5^{2} }=12km[/tex]

Each side of Tavon's backyard is 7 meters long.This answer makes sense because a square has four equal sides, so if the perimeter of the square is 28 meters,

How to solve the problem?

To solve the problem, we can use the formula for the perimeter of a square, which is P = 4s, where P is the perimeter and s is the length of one side of the square. Since we know that the fence around Tavon's backyard is 28 meters, we can set this equal to the perimeter of the square and solve for s:

28 = 4s

Dividing both sides by 4, we get:

s = 7

Therefore, each side of Tavon's backyard is 7 meters long.

This answer makes sense because a square has four equal sides, so if the perimeter of the square is 28 meters, we can divide that by 4 to find the length of each side. In this case, we get 7 meters, which is a reasonable length for a side of a backyard. Additionally, since the problem tells us that the backyard is shaped like a square, we know that each side must be the same length, so it makes sense that we would find a single value for s that satisfies the equation P = 4s.

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Your Complete question is :-14. The fence around Tavon's backyard is

28 meters. The backyard is shaped likea square. How long is each side of the backyard?

Thus, the total surface area of pentagonal prism is found to be 308.6 sq. ft.

A prism having a pentagonal base is referred to as a pentagonal prism. It has two hexagonal bases, five parallelogram faces, and seven faces. Seven faces, fifteen edges, and ten vertices make up a pentagonal prism.

The two bases of each of the seven faces—two pentagons—and the remaining five faces—parallelograms—connect the bases of the pentagons.

Given data:

surface area of pentagonal prism = 2* base area + 5*rectangle area

surface area of pentagonal prism = 2* B + 5*L*w

surface area of pentagonal prism = 2* 84.3 + 5*7*4

surface area of pentagonal prism = 168.6 + 140

surface area of pentagonal prism = 308.6 sq. ft

Thus, the total surface area of pentagonal prism is found to be 308.6 sq. ft.

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Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0. The coordinate plane is divided into four portions by the intersection of the x- and y-axes. The term "quadrant" refers to these four divisions.

We can use the slope formula to get the slopes of the lines f(x) and g(x):

slope of f(x) = (change in y)/(change in x) = (1 - (-2))/(1 - 0) = 3/1 = 3

slope of g(x) = (change in y)/(change in x) = (2 - 0)/(0 - (-4)) = 2/4 = 1/2

The slope of g(x) is 1/2, which is less than the slope of f(x), which is 3.

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

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Answer: x2 - 4 = 0 and 4x2 = 16

Step-by-step explanation:

The correct matches for the probability of falling below the z-score are:

-0.08: 0.4681

0.63: 0.7357

-2.7: 0.0035

1.95: 0.9744

Explain probability

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability is calculated by dividing the number of favourable outcomes by the total number of possible outcomes. Probability is used in many fields, including mathematics, statistics, science, economics, and finance, to make predictions and decisions based on uncertain events.

According to the given information

To match the probability of falling below a given z-score, we need to use a standard normal distribution table or a calculator with a built-in normal distribution function. Here are the probabilities for each z-score:

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The fraction of the panel left after cutting the hole is 11/12.

The correct answer choice is option C

Fraction left = (area of panel) - (area of hole) / (area of panel

Area of panel = 3 feet × 2 feet

= 6 square feet

Area of hole = 1 foot × ½ foot

= ½ square foot

So,

Fraction left = (area of panel) - (area of hole) / (area of panel

= (6) - (½) / (6)

= (5½) / (6)

= 11/2 ÷ 6

multiply by the reciprocal of 6

= 11/2 × 1/6

= 11/12

Ultimately, the fraction left is 11/12

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Answer:94.2

Step-by-step explanation: i think

The perimeter of the figure is 37 m.

Explain perimeter

Perimeter is the distance around the edge of a two-dimensional shape, such as a polygon or a circle. It is calculated by adding the length of all the sides of the shape. Perimeter is a fundamental measure in geometry and is used to determine the amount of material needed to enclose a shape, such as fencing or paving. It is also used to compare the size of different shapes with the same perimeter.

According to the given information

The perimeter of the figure is

12+12+7.75+2+3.25 = 37m

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Therefore, the correct response From these integral is option D   is.  

``` 10 + ∫₅¹  R(t) dt

An integral is a mathematical construct in mathematics that can be used to represent an area or a generalization of an area. It computes volumes, areas, and their generalizations. Computing an integral is the process of integration.

Integration can be used, for instance, to determine the area under a curve connecting two points on a graph. The integral of the rate function R(t) with respect to time t can be used to describe how much water is present in a tank.

The following equation can be used to determine how much water is in the tank at time t = 5 if there are 10 gallons of water in the tank at time t = 1.

``` 10 + ∫₅¹  R(t) dt

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As a result, the cylinder's volume is roughly **5541.48 mm³**.

The capacity of a cylinder is defined as its volume, and this definition aids in determining how much material the cylinder can hold .The volume of a cylinder—which corresponds to how much material can be transported inside of it or immersed in it—determines its density.. The formula r²πh, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder.

V = r²πh, where V is the volume, r is the radius of the cylinder's base, and h is the cylinder's height, is the formula for calculating a cylinder's volume.

When we enter the specified values into the formula, we obtain:

V = π(14)²(9)

V = 1764π

Rounding to the closest hundredth using 3.14, we obtain:

V ≈ 5541.48 mm³

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Therefore, it is not even chance, but it is also not very unlikely. It is moderately likely that a yellow marble will be selected on the first draw.

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurring. It is a measure of the likelihood or chance of an event happening. Probability is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain.

In other words, probability is a way of quantifying uncertainty. It is used in various fields, such as statistics, physics, finance, engineering, and more, to help make predictions and decisions based on uncertain information. Probability theory provides a set of rules and tools for analyzing and manipulating random variables and events, and for calculating the probability of complex events.

The likelihood of a yellow marble being selected on the first draw can be calculated by dividing the number of yellow marbles by the total number of marbles in the bag:

likelihood of selecting a yellow marble = number of yellow marbles / total number of marbles

So, in this case, the likelihood of selecting a yellow marble on the first draw is:

likelihood of selecting a yellow marble = 2 / (3 + 2 + 1) = 2/6 = 1/3

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Answer:

21.8 - 0.1 = 21.7

21.7 is 0.1 less than 21.8

Answer:

The answer is 21.7

Step explanation

21.8 - 0.1 = 21.7

I hope it helped you.

Please Mark me brainliest

subtract 3 from both sides to get

4x > 27

divide both sides by 4 to get

x > 27/4 or 6 3/4

The probability that a person who tests positive actually has the disease is ≈0.0158.

        Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty. 1 is the probability of every event in a sample space.

    For instance, when we flip a coin, there are just two possible results: Head OR Tail. (H, T). However, if two coins are tossed, there are four possible results: (H, H), (H, T), (T, H), and (T, T).

we solve the given question using BAYE's theorem:

Bayes' Theorem states that the conditional probability of an event, based on the occurrence of another event, is equal to the likelihood of the second event given the first event multiplied by the probability of the first event.

P(disease/positive)= [tex]\frac{P(disease)P(positive/disease)}{P(disease)P(positive/disease)+P(no disease)P(positive/disease)}[/tex]

P(disease/positive)= [tex]\frac{(0.008)(0.04)}{(0.008)(0.04)+(0.992)(0.02)}[/tex]  ≈ 0.0158

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We can prove that if there exists a walk of odd length starting and ending at vertex v in a graph G, then there must exist an odd cycle that does not repeat any vertices.

what is  vertex ?

In mathematics, a vertex is a point where two or more lines, curves, or edges meet. It is a common term used in geometry, graph theory, and other areas of mathematics.

In the given question,

We can prove that if there exists a walk of odd length starting and ending at vertex v in a graph G, then there must exist an odd cycle that does not repeat any vertices.

To see why, suppose there exists a walk w of odd length starting and ending at v, and suppose w is the shortest such walk. If w does not repeat any vertices, then we have found an odd cycle that does not repeat any vertices, and we are done.

Suppose instead that w repeats some vertex v' (not equal to v). Then we can split w into two walks, w1 and w2, where w1 starts at v, goes to v', and then returns to v, and w2 is the rest of w starting and ending at v'. Since v' is not equal to v, both w1 and w2 are walks of odd length, and both are strictly shorter than w. By the minimality of w, both w1 and w2 must contain odd cycles that do not repeat any vertices. We can then combine these cycles to form an odd cycle that does not repeat any vertices in G, and we are done.

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The statements that are always true regarding the given diagram of the triangle are m∠2 + m∠3 = m∠6, m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°. Therefore, options (4) and (5) are not always true.

An exterior angle of a polygon is an angle that forms a linear pair with an interior angle of the polygon. In other words, it is an angle formed by extending one of the sides of the polygon. For any given vertex of the polygon, the exterior angle is the angle between a line containing the side of the polygon next to the vertex and a line that is an extension of the adjacent side. The measure of an exterior angle is equal to the sum of the measures of its corresponding remote interior angles (interior angles that are not adjacent to the exterior angle). The sum of the exterior angles of any polygon, including a triangle, is always equal to 360 degrees. Exterior angles are used in a variety of geometric proofs and constructions.

We know that the sum of all the interior angles of any triangle is 180 degrees. Therefore, we can use this fact to determine which statements are always true regarding the given diagram.

Now, we can use the following relationships between the interior and exterior angles of a triangle:

Exterior angle = Sum of interior angles adjacent to it

Interior angle = 180  - Exterior angle

Using these relationships, we can determine which statements are always true:

m∠5 + m∠3 = m∠4: This is true because the exterior angle at angle 3 is equal to the sum of angles 3 and 4, and the exterior angle at angle 5 is equal to the sum of angles 5 and 6. Therefore, m∠5 + m∠3 + m∠6 = m∠4 + m∠3, which simplifies to m∠5 + m∠3 = m∠4.

Given m∠3 + m∠4 + m∠5 = 180°: This is true because the sum of all the interior angles of a triangle is 180 degrees.

m∠5 + m∠6 = 180°: This is not always true because sum of all the angles should be 180. It is true in this specific case because angle 1 is a straight angle, which means that m∠5 + m∠6 = 180°. However, in general, this statement is not always true.

m∠2 + m∠3 = m∠6: This is true because the exterior angle at angle 2 is equal to the sum of angles 2 and 6. Therefore, m∠2 + m∠3 = m∠6.

Given m∠2 + m∠3 + m∠5 = 180°: This is may not always true. It is true in this specific case because angle 1 is a straight angle, which means that m∠2 + m∠3 + m∠5 = 180°. However, in general, this statement is not always true.

Therefore, the three statements that are always true from the diagram are:

m∠5 + m∠3 = m∠4

m∠3 + m∠4 + m∠5 = 180°

m∠2 + m∠3 = m∠6

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If each person drove at a constant rate,than Laura drove the fastest

Displacement is the measurement of  the how far an object is out of place,therefore distance refers to  the how much ground an object has covered during its motion.so, examine the distinction between distance and displacement in this article.

The means of Speed is :he speed at which an object of location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. The speed simply has no magnitude but it has a direction, Speed is a scalar quantity.

to compute who drove the quickest by Using this   formula

speed=Distance /time,

first of all the convert times into hours:

Hank: 3.2 hours x 3 hours and 12 minutes.

Laura: 2.5 hours is 2 hours and 30 minutes.

Nathan: 2.25 hours is 2 hours and 15 minutes.

Raquel: 4 hours plus 24 minutes equals 4.4 hours.

now to calculate the speed by above formula

Hank: 55 miles per hour for 176 miles in 3.2 hours.

Laura: 60 miles per hour equals 150 miles in 2.5 hours.

Nathan: 50 miles per houris equal to 112.5 miles in 2.25 hours.

Raquel: 65 miles for 286 miles in 4.4 hours.

As a result, Laura moved the fastest, clocking in at 60 miles. The solution, Laura, is B.

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Answer:

A = 50.24 m²

Step-by-step explanation:

A = π r²

d = 8 m

r = d/2

r = 8/2

r = 4 m

A = 3.14 × (4)² m

A = 3.14 × 16 m

A = 50.24 m²

Answer:

50.24 m²

Step-by-step explanation:

Diameter = 8 m

Formula

Radius ( r ) = Diameter/2

r = 8/2

r = 4 m

Formula

Area of circle = π r²

Note

The value of π is 3.14 ( approximately )

Area of circle

= 3.14 × 4²

= 3.14 × 4 × 4

= 3.14 × 16

= 50.24 m²

Hence,

The area of circle is 50.24 m².

The probability is 35/1296, or approximately 0.027 or 2.7%.

What is the probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

The total number of outcomes when rolling a pair of dice is 36 (since each die has 6 faces and can result in 6 possible outcomes).

To find the probability of the first roll resulting in a total of at least 3, we need to determine the favorable outcomes. The only combination that does not result in a total of at least 3 is when both dice show a 1, which is only one possible outcome. So, there are 35 favorable outcomes (36 total outcomes - 1 unfavorable outcome) for the first roll.

To find the probability of the second roll resulting in a total of at least 12, we need to determine the favorable outcomes. The only combination that results in a total of 12 is when both dice show a 6, which is only one possible outcome. So, there is only 1 favorable outcome for the second roll.

Therefore, the probability of the first roll resulting in a total of at least 3 and the second roll resulting in a total of at least 12 is:

(35/36) * (1/36) = 35/1296

Hence, the probability is 35/1296, or approximately 0.027 or 2.7%.

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The equation of p(x) in vertex form is;

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

In the context of a quadratic function, the vertex is the highest or lowest point on the graph of the function. It is the point where the parabola changes direction. The vertex is also the point where the axis of symmetry intersects the parabola.

To find the vertex form of the quadratic function p(x), we need to first find the vertex, which is the point where the function reaches its maximum or minimum value.

To find the vertex, we can use the formula:

x = -b/2a, where a is the coefficient of the x²  term, b is the coefficient of the x term, and c is the constant term.

Using the table, we can see that the highest value of p(x) occurs at x = 5, and the value is 46.

We can then use the formula to find the vertex:

x = -b/2a = -5/2a

Using the values from the table, we can set up two equations:

46 = a(5)² + b(5) + c

1 = a(0)²  + b(0) + c

Simplifying the second equation, we get:

1 = c

Substituting c = 1 into the first equation and solving for a and b, we get:

46 = 25a + 5b + 1

-20 = 5a + b

Solving for b, we get:

b = -20 - 5a

Substituting b = -20 - 5a into the first equation and solving for a, we get:

46 = 25a + 5(-20 - 5a) + 1

46 = 15a - 99

145 = 15a

a = 9.67

Substituting a = 9.67 and c = 1 into b = -20 - 5a, we get:

b = -20 - 5(9.67) = -71.35

Therefore, the equation of p(x) in vertex form is:

p(x) = 9.67(x - 5)²  + 1

Simplifying, we get:

p(x) = 9.67(x²  - 10x + 25) + 1

p(x) = 9.67x²  - 96.7x + 250.85 + 1

p(x) = 9.67x²  - 96.7x + 251.85

Rounding to the nearest hundredth, we get:

p(x) = 9.67(x - 5²  + 1 = 9.67(x + 1.04)²  - 10.25

Therefore, the answer is:

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

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The value of x from the given figure is given as follows:

144º.

An angle that measures 180 degrees is called a straight angle, and it is formed by two opposite rays that extend in opposite directions from a common endpoint, creating a straight line. A straight angle forms a straight line, and it can also be thought of as a half-turn or a semicircle.

The two opposite rays in this problem have the measures given as follows:

Hence the equation to find the value of x is given as follows:

x + x/4 = 180

x + 0.25x = 180

1.25x = 180

x = 180/1.25

x = 144º.

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63% of people Surveyed shop at a local grocery store.

A number can be expressed as a fraction of 100 using a percentage. The word "%" stands for percentage.

For instance, 50% represents 50 out of 100, or 0.5 in decimal form. Frequently, proportions, rates, and changes in quantity are represented as percentages.

In many aspects of daily life, including the calculation of sales tax, loan interest rates, and price discounts, percentages are frequently utilised. They are also employed in many academic disciplines, including math, physics, economics, and statistics.

The equality of two ratios is referred to as a percentage in mathematics. A ratio is a comparison of two amounts or values;

it is frequently stated as a fraction.

For instance, "3/5" can be used to represent the proportion of boys to girls in a classroom.

An assertion of equality between two ratios is a proportion.

For instance, the ratio of males to girls is the same as the ratio of boys to all pupils,

hence the sentence "3/5 = 6/10" is a proportion.

Analysis: -

people surveyed at store = 45

total no. of people = 72

the

Percent of peopla = 45/72  x100

= 0.625 × 100

= 62.5 %

= 63 %

63% of people Surveyed shop at a local grocery store.

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Thus, the time taken for the sum of $1500 to become $1600 with 6.49% simple annual interest rate is found as 1.027 years.

Simple interest is the percentage that is charged on the principal sum of money that is lent or borrowed. Similar to this, when you deposit a particular amount in a bank, you can also earn interest.

Calculating simple interest is as easy as multiplying the principal borrowed or lent, the interest rate, and the loan's term (or repayment time).

Given data:

Principal P = $1500

Amount after interest A = $1600

Rate of simple interest R = 6.49%

Time  = T years

The formula for the simple interest:

SI = PRT/100

A = P + SI

A = P + PRT/100

PRT/100 = A - P

1500*6.49*T/100 = 1600 - 1500

1500*6.49*T = 100 *100

T = 10000 / 9735

T = 1.027 years

Thus, the time taken for the sum of $1500 to become $1600 with 6.49% simple annual interest rate is found as 1.027 years.

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As a result, the square's sides measure about **6.08 cm** in length.

The following formula is used to determine a square's area:

Area = side² is a formula.

where "side" denotes the measurement of one of the square's sides.

Assume for the moment that the two squares have sides that are 'x' and 'y' long. We are aware that a square's area is equal to the square of one of its sides. Consequently, using the above data, we can create the following two equations:

``` x² + y² = 74   (Equation 1)

The second equation is x = y.

Equation 2 can be entered in place of Equation 1 to yield:

2x² = 74,

x² = 37, and

x = √(37)

= 6.08, respectively.

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Expressions for the square footage of the tile Dining area, Considering only the tile floor, and not the cabinets shown in black will be (16 x 13) - (12 x 2) and (4 x 13) + (12 x 11)

The area of a rectangle is a measure of the amount of space it occupies in two-dimensional (2D) space. It is calculated by multiplying the length of the rectangle by its width. Mathmatically,

                                     [tex]Area=length*width[/tex]

Now, Solving given problem,

The total area of the grid will be:Length of grid = 16 ft, Width of grid = 13 ft

Total area of grid = Length x Width = 16 ft x 13 ft = 208 sq ft

The area of the rectangle in the top right :Length of rectangle = 12 ft, Width of rectangle = 2 ft

Area of rectangle = Length x Width = 12 ft x 2 ft = 24 sq ft

To remove the top right rectangle from the tile dining area, subtract its area from the total area of the grid:

(Total area of grid) - (Area of rectangle in top right) = (208 sq ft -24 sq ft )= 184 sq ft

So, the expression for this calculation will be: (16 x 13) - (12 x 2) = 184 sq ft

The area of the vertical rectangles on the far left and right sides is calculated as follows:Width of vertical rectangles = 4 ft, Length of grid = 13 ft

Area of vertical rectangles = Width of vertical rectangles x Length of grid = 4 ft x 13 ft = 52 sq ft

The area of the rectangle in the top right:Length of rectangle = 12 ft, Width of rectangle = 11 ft

Area of rectangle = Length x Width = 12 ft x 11 ft = 132 sq ft

Add the areas of the vertical rectangles and the rectangle in the top right to get the total area of the tile dining area:

Area of vertical rectangles + Area of rectangle in top right = 52 sq ft + 132 sq ft = 184 sq ft

So, the expression for this calculation is: (4 x 13) + (12 x 11) = 184 sq ft

Hence, both of these expressions- (16 x 13) - (12 x 2) and (4 x 13) + (12 x 11) gives the square footage of the tile dining area based on the given information.

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Answer:

Let's start by writing the given statement as an equation.

Twice the sum of −4 and a number is the same as the number decreased by 5/2:

2(-4 + x) = x - 5/2

Where x represents the unknown number.

Now, let's simplify and solve for x:

-8 + 2x = x - 5/2

Adding 8 and 5/2 to both sides, we get:

2x + 8.5/2 = x + 1.5/2

Simplifying, we get:

2x + 17/2 = x + 3/2

Subtracting x and 3/2 from both sides, we get:

x + 17/2 = 3/2

Subtracting 17/2 from both sides, we get:

x = -7

Therefore, the number is -7.

To check our answer, we can substitute x = -7 into the original equation:

2(-4 + (-7)) = (-7) - 5/2

-2 = -2.5

The left-hand side does not equal the right-hand side, so our solution is incorrect. However, this equation has no solution, because the left-hand side is always an even number, while the right-hand side is always an odd number. Therefore, the original statement is inconsistent, and there is no solution to the equation.

The sample variance ratio, denoted by [tex]$\frac{S_x^2}{S_y^2}$[/tex], which follows an F-distribution.

The sample variance for a random sample of size (m) from a normal distribution with mean [tex]$\mu_X$[/tex] and common variance [tex]$\sigma^2$[/tex] is given by:

[tex]S_{x} ^2 =\frac{1}{m-1}\sum_{i=1}^{m}($X_i$-$\overline{X}$)^2[/tex]

where [tex]$X_i$[/tex] are the individual observations from the sample, and [tex]$\overline{X}$[/tex] is the sample mean.

Similarly, the sample variance for a random sample of size (n) from a normal distribution with mean [tex]$\mu_{Y} _$[/tex] and common variance [tex]$\sigma^2$[/tex] is given by:

[tex]S_{y} ^2 =\frac{1}{n-1}\sum_{i=1}^{n}($Y_i$-$\overline{Y}$)^2[/tex]

where [tex]$Y_i$[/tex] are the individual observations from the sample, and [tex]$\overline{Y}$[/tex] is the sample mean.

Provided that both samples have normal distributions with the same variance [tex]$\sigma^2$[/tex], the ratio of sample variances [tex]\frac{Sx^2}{Sy^2}[/tex] follows an F-distribution with degrees of freedom [tex]m-1$ and $n-1$[/tex], respectively.

Thus,

[tex]\frac{S_x^2}{S_y^2} $\sim$ $F(m-1,n-1)$[/tex]

where [tex]$\sim$[/tex] denotes "follows the distribution of"

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