how many different arrangements are there of eight peo- ple seated at a round table, where two arrangements are considered the same if one can be obtained from the other by a rotation?

The equations without absolute value for the given conditions are: 1. y = -3x + 6 if x > 5; 2. y = -x - 6 if x < -2; 3. y = x - 6 if 3 ≤ x ≤ 5, and y = -x - 6 if x < 3.

1. When x > 5, the expression (x - 3) is positive, (x + 2) is positive, and (x - 5) is positive. Thus, to get absolute value we can rewrite the equation as:

y = (x - 3) + (x + 2) - (x - 5)

Simplifying this, we get:

y = 2x - 4

2. When x < -2, the expression (x - 3) is negative, (x + 2) is negative, and (x - 5) is negative. Thus, we can rewrite the equation as:

y = -(x - 3) - (x + 2) + (x - 5)

Simplifying this, we get:

y = -2x + 6

3. When -2 ≤ x ≤ 3, the expression (x - 3) is negative, (x + 2) is positive, and (x - 5) is negative. Thus, we can rewrite the equation as:

y = -(x - 3) + (x + 2) - (x - 5)

Simplifying this, we get:

y = 10 - x

When x > 3, the expression (x - 3) is negative, (x + 2) is positive, and (x - 5) is positive. Thus, we can rewrite the equation as:

y = -(x - 3) + (x + 2) + (x - 5)

Simplifying this, we get:

y = -2x + 6

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The theoretical probability of not picking the silver coin will be 0.38 .

Given,

200 silver coins and 123 gold coins are filled in a bag .

Now,

Total number of coins in a bag = gold + silver coins

Total number of coins in a bag  = 200 + 123

Total number of coins in a bag  = 323

Further ,

Probability of taking silver coin = 200/323

Probability of taking silver coin = 0.619.

probability of taking gold coin = 123/323

probability of taking gold coin  = 0.38

Hence the probability of not selecting silver coin is 0.38 .

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The value of x in the triangle can be found by using the fact that the sum of all angles in a triangle is 180 degrees. Simplifying the equation 142 degrees + 112 degrees + x = 180 degrees, we get x = 26 degrees.

To find the value of x in the triangle, we use the fact that the sum of all angles in a triangle is 180 degrees.

Let's call the third angle of the triangle "x".

Then, we have:

142 degrees + 112 degrees + x = 180 degrees

Simplifying this equation, we get:

x = 180 degrees - 142 degrees - 112 degrees

x = 26 degrees

Therefore, the value of x in the triangle is 26 degrees.

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Answer:

z ≥ 9

Step-by-step explanation:

z ≥ 9

(The number z is greater than or equal to 9)

...

The probability that a student chosen randomly from the class is an only child is 0.23 or 23%.

What is the probability?

To find the probability that a student chosen randomly from the class is an only child, we need to add up the number of students who do not have a brother and do not have a sister, and then divide by the total number of students in the class.

From the table, we can see that there are 6 students who do not have a sister and do not have a brother. Therefore, the probability that a student chosen randomly from the class is an only child is:

P(only child) = number of only children / total number of students

= 6 / (2 + 13 + 5 + 6)

= 6 / 26

= 0.23 (rounded to two decimal places)

Therefore, the probability that a student chosen randomly from the class is an only child is 0.23 or 23%.

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The hot or cold, and they can be served in a variety of containers, including cups, bottles, and cans.

There is no sample size or other information provided in the question, so the probability of 45 or more people in the sample having consumed alcoholic beverages cannot be calculated. More information is needed to solve this problem.What is probability?Probability is a branch of mathematics that deals with calculating the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 representing impossibility and 1 representing certainty. A probability of 0.5 represents a 50% chance of the event occurring. Probability is used in a variety of fields, including statistics, finance, and engineering.What are beverages?Beverages are drinks that are intended for human consumption. Beverages come in a variety of types, including alcoholic and non-alcoholic. Beverages can be made from a variety of ingredients, including water, fruit juice, and milk. They can be hot or cold, and they can be served in a variety of containers, including cups, bottles, and cans.

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Answer:

[tex]2 \sqrt{2(6 + \sqrt{3} )} [/tex]

Step-by-step explanation:

There's your answer.

A pushdown automata that recognizes {wwr | w is a string over {0, 1} such that w does not contain 0110 as a substring} can be constructed as follows:

We construct the PDA in two stages:

First, we design a machine that accepts the language (0 + 1)*0110(0 + 1)*.

We can construct a machine that accepts this language as follows:

Initially, we push a marker $ onto the stack.

For each 0 we read, we push a symbol A onto the stack.

For each 1 we read, we remove a symbol A from the stack. When we read 01 in the input, we push B onto the stack. When we read 10 in the input, we replace a single symbol A on the stack with a B.

Finally, when we read 0110 in the input, we remove B from the stack if it is on top. If we reach the end of the input and the stack is empty, the machine accepts. Otherwise, it rejects.

Now, let us turn our attention to the problem at hand. We want to create a machine that accepts {wwr | w is a string over {0, 1} such that w does not contain 0110 as a substring}.

It is equivalent to constructing a PDA that accepts the language

L = { wwr | w is a string over {0, 1} and w does not contain 0110 as a substring}.

First, we divide the string w into two parts: a prefix and a suffix.

For w to be a word in L, the suffix must be the reverse of the prefix, and w cannot contain 0110 as a substring.Next, we try to use the PDA that accepts (0 + 1)*0110(0 + 1)* to ensure that w does not contain the substring 0110.

We maintain a buffer on the stack, and the input is processed one symbol at a time. Initially, we push $ onto the stack. If we read 0 or 1, we push the symbol A onto the stack.

If we read 01, we push B onto the stack. If we read 10, we replace an A with B. Finally, when we read 0110, we pop B from the stack. If we reach the end of the input and the stack is empty, we accept.

If we reach the end of the input and the stack is non-empty, we reject.

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According to the information provided, k and m are crossing lines with an angle of 86°. We know this because k and m are straight lines.

The angles add up to 180 degrees.

Then we receive,

[tex]a + 86 =180[/tex]

Or, a = 180 -86

Or, a = 94°.

As a result, an is 94°.

The angle an is 94 degrees.

Supplementary angle are formed when two angles add to 180 degrees. When additional angles are added together, they form a straight angle, or 180 degrees. In these other words, if indeed the sum of angles 1 and 2 equals 180 degrees, angles 1 and 2 are supplementary. Angles 1 and 2 are referred to as "supplements" to one another in this context.

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Therefore, the area of the polygon is 24 square units.

In mathematics, a coordinate is a set of numbers or values that represent the position or location of a point or an object in space. Typically, coordinates are used to describe points in two-dimensional (2D) or three-dimensional (3D) space.

In 2D space, coordinates are usually represented as pairs of numbers (x, y), where the first number (x) represents the horizontal distance of the point from the origin, and the second number (y) represents the vertical distance of the point from the origin.

by the question.

To find the area of the polygon defined by the given coordinates, we can use the Shoelace Formula:

[tex]Area = 1/2 * |(x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1)|[/tex]

where?[tex](x_{1} ,y_1), (x_2,y_2), ..., (x_n,y_n)[/tex] are the coordinates of the vertices listed in order.

Plugging in the given coordinates in order, we get:

[tex]Area = 1/2 * |(-12 + -5(-3) + (-5)(-5) + (-2)(-2) + 22 + 4(-2)) - (4*(-5) + (-5)(-5) + (-3)(-2) + (-2)2 + 2(-1) + 2*(-5))|= 1/2 * |-2 - 125 + 25 - 4 + 8 + 8 + 20 + 10 + 2 + 10|= 1/2 * |-48|=24[/tex]

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The regression line is a statistical tool that can be used to analyze the relationship between two variables.

It helps identify trends in the data and can be used to make predictions about future values. It can also be used to assess the accuracy of the model and to determine the strength of the relationship between the two variables.

By examining the slope of the regression line, we can assess the direction and strength of the linear relationship between the two variables.

Additionally, the y-intercept of the regression line can provide insight into the value of the dependent variable when the independent variable is equal to zero.

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The height of the water is increasing at the rate of 3 meters per minute.

We know that a cylindrical tank with radius r and height h has a volume of V = πr²h.

The rate at which the water is being filled in the tank is given as dV/dt = 2πr²( dh/dt).

On rearranging the above equation we get dh/dt = (dV/dt) ÷ (2πr²)

Given: Radius of the cylindrical tank, r = 3 m

Rate at which the water is being filled,

dV/dt = 54π cubic meters per minute.

we

Height of the cylindrical tank, h = ?

We need to find out how fast is the height of the water increasing.

This can be calculated using the formula.

dh/dt = (dV/dt) ÷ (2πr²)

Substitute the values of dV/dt  and r in the above formula,

we get,

dh/dt = (54π) ÷ (2π x 3²)

dh/dt = 54/18

dh/dt = 3 m/min

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The second urn contains 16 green balls and 46 blue balls.

Let's first find the probability of drawing two green balls, which we'll denote as P(G,G).

We can break it down into two cases:

Case 1: A green ball is drawn from the first urn and a green ball is drawn from the second urn.

The probability of drawing a green ball from the first urn is 4/10, and the probability of drawing a green ball from the second urn is 16/(16+N). Therefore, the probability of this case is (4/10) x (16/(16+N)).

Case 2: A blue ball is drawn from the first urn and a blue ball is drawn from the second urn.

The probability of drawing a blue ball from the first urn is 6/10, and the probability of drawing a blue ball from the second urn is N/(16+N). Therefore, the probability of this case is

(6/10) x (N/(16+N))

The probability of drawing two balls of the same color is the sum of the probabilities of these two cases, which we know to be 0.58:

P(G,G) + P(B,B) = 0.58

We can solve for P(G,G) as follows:

P(G,G) = 0.58 - P(B,B)

= 0.58 - (6/10) x (N/(16+N))

Now, we can set P(G,G) equal to the probability of drawing two green balls from the urns that we found earlier:

(4/10) x (16/(16+N)) = 0.58 - (6/10) x (N/(16+N))

By simplifying this equation, we get:

64 = 58(16+N) - 60N

By solving for N, we get:

N = 46

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Question:

An urn contains 4 green balls and 6 blue balls. A second urn contains 16

green and N blue balls. A single ball is drawn at random from each urn. The probability that both balls are of the same colour is 0.58. Find N.

Answer:

(- 1, 1 )

Step-by-step explanation:

x = 6y - 7 → (1)

4x + y = - 3 → (2)

substitute x = 6y - 7 into (2)

4(6y - 7) + y = - 3 ← distribute parenthesis and simplify left side

24y - 28 + y = - 3

25y - 28 = - 3 ( add 28 to both sides )

25y = 25 ( divide both sides by 25 )

y = 1

substitute y = 1 into (1)

x = 6(1) - 7 = 6 - 7 = - 1

solution is (- 1, 1 )

Answer:

(-1,1)

Step-by-step explanation:

4(6y-7)+y=-3

24y+y=-3+28 (put them in like terms)

25y/25=25/25 (divide both side by 25)

y=1

x=6×1-7(already we get y and replace it by 1)

x=-1

(-1,1)

Answer:

Sure! The perimeter of a rectangle is calculated by adding the lengths of all four sides. Since the length of the rectangle is given as (5x²y) and the width is given as (3x²y), we can calculate the perimeter as follows:

Perimeter = 2 * Length + 2 * Width = 2 * (5x²y) + 2 * (3x²y) = 10x²y + 6x²y = 16x²y

So, the perimeter of this rectangle is 16x²y.

Step-by-step explanation:

The probability of at least one visit during a given minute is 86.47%.

Given that the average rate of visits per minute is two.

To find the probability of at least one visit during a given minute, we can use Poisson distribution.

Poisson distribution is a probability distribution that is used to determine the probability of a certain number of events occurring in a fixed time period when the events are rare and random.

The Poisson probability distribution is given by;

[tex]P(X=x) = (e^{-\lambda} \times \lambda ^x) / x![/tex]

Where; λ is the average rate of events, x is the number of events that occurred, and e is the base of the natural logarithm,

e ≈ 2.7183

We can find the probability of at least one visit in a minute using the complement rule.

The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

Therefore;

P(at least one visit) = 1 - P(no visit)P(no visit)

= P(X=0)   = [tex](e^{-\lambda} \times \lambda^0) / 0![/tex]  = [tex]e^{-\lambda}[/tex] = [tex]e^{-2}[/tex] = 0.1353

Therefore;

P(at least one visit) = 1 - P(no visit)

= 1 - 0.1353

= 0.8647 = 86.47%

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the function d(t) represents the total distance (in miles) traveled by Carrie after t hours, where t is the time elapsed since the start of her journey.

To write a piecewise function to represent the total distance Carrie has traveled after t hours, we need to break down her journey into different parts and calculate the distance covered during each part.

Let's define the three different parts of her journey:

•Part 1: The first hour, during which she averaged 30 miles per hour

•Part 2: The next 4 hours, during which she averaged 65 miles per hour

•Part 3: The remaining 2 hours, during which she averaged 52 miles per hour

For Part 1, the distance covered can be calculated as:

d1 = 30t (where t is the time spent in the first hour, t ≤ 1)

For Part 2, the distance covered can be calculated as:

d2 = 260 + 65(t - 1) (where t is the time spent in the next 4 hours, 1 < t ≤ 5)

For Part 3, the distance covered can be calculated as:

d3 = 520 + 52(t - 5) (where t is the time spent in the remaining 2 hours, 5 < t ≤ 7)

Now, we can combine these three equations to form a piecewise function for the total distance traveled by Carrie:

d(t) = 30t, 0 ≤ t ≤ 1

d(t) = 260 + 65(t - 1), 1 < t ≤ 5

d(t) = 520 + 52(t - 5), 5 < t ≤ 7

Therefore, the function d(t) represents the total distance (in miles) traveled by Carrie after t hours, where t is the time elapsed since the start of her journey.

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Answer: m = 6/5

Step-by-step explanation:

Answer: m=6/5

Step-by-step explanation:

The employees work in the production, service, and sales sections is 3/4 of total number. 1/4 of the employees work in other sections. The total number of employees in the factory is 14,400. The number of cars produced in 2020 is 439,875. The production decreased by 2.25% from 2018 to 2020.

Let the total number of employees in the factory be represented by the variable x. Then, the fraction of employees in the production section is 1/3x, the fraction in the service section is 1/4x, and the fraction in the sales section is 2/5 of the remaining employees, which is (1 - 1/3 - 1/4) x = 7/60x. Therefore, the fraction of employees in the production, service, and sales sections is:

1/3x + 1/4x + 7/60x = 15/20x = 3/4x

The fraction of employees in other sections is the remaining fraction after accounting for those in the production, service, and sales sections:

1 - 3/4x = 1/4x

Let the number of employees in the sales section be represented by the variable y. Then, the number of employees in the production section is y + 6000, and the number of employees in the service section is (1/4)x. Therefore, the total number of employees in the factory is:

y + 6000 + (1/4)x + y + 7/60x + 3/4x = 1x

Simplifying this equation, we get:

5/12x + 2y = 6000

we can find their sum as:

x + y = (12/5)(6000) = 14,400

The number of cars produced in 2019 is:

450,000 x 1.15 = 517,500

The number of cars produced in 2020 is:

517,500 x 0.85 = 439,875

The percentage change in production from 2018 to 2020 is:

[(439,875 - 450,000)/450,000] x 100% = -2.25% (rounded to two decimal places)

Therefore, the production decreased by 2.25% from 2018 to 2020.

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Null hypothesis: No statistically significant relationship between stock splits and the value of shares held

Alternative Hypothesis: Statistically significant relationship between stock splits and the value of shares held

Probability of the shares held being worth

The null and alternative hypotheses are as follows:Null Hypothesis (H0): There is no statistically significant relationship between stock splits and the value of shares held.Alternative Hypothesis (Ha): There is a statistically significant relationship between stock splits and the value of shares held.The probability that the shares held will be worth more after the split can be determined through statistical analysis. The null hypothesis assumes that there is no relationship between stock splits and the value of shares held, while the alternative hypothesis suggests that there is a statistically significant relationship between the two variables.Therefore, the probability of the shares held being worth more after the split is based on the results of the statistical analysis of the null and alternative hypotheses.

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Remember, accurate interpretation of the results is essential for the success of Laura's dissertation.

The sum of squares for the factor in Laura Van Ertia's experiment can be found in the ANOVA display. ANOVA stands for Analysis of Variance, and it is a statistical method used to compare the means of two or more groups. The sum of squares is a measure of the variation within the data, and it helps to determine whether the differences between groups are statistically significant.

In the given question, you have not provided the actual ANOVA display, which is necessary to determine the sum of squares for the factor. The ANOVA table typically consists of columns for sources of variation (such as between groups and within groups), degrees of freedom, sum of squares, mean squares, F-ratio, and p-value. The sum of squares for the factor can be found in the 'sum of squares' column corresponding to the between-group variation row.

Once you have the ANOVA display, locate the sum of squares for the factor and use it in your analysis to understand the results of the experiment and its implications on the unified theory.

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Answer:

Step-by-step explanation:

You want to know the side lengths of the triangles shown if DE = 8.

Side DE is marked as x+6. If its length is 8, then we have ...

  x +6 = 8

  x = 2 . . . . . subtract 6

The unknown side lengths are then ...

  PQ = x+1 = 3

  QR = x+3 = 5

  EF = x+8 = 10

__

Additional comment

These are both 3:4:5 right triangles. The larger is twice the size of the smaller. You can guess this because a 3:4:5 right triangle is the only one with a side length of 4 and integer lengths for the other sides.

In the question given, The inequality will be h₂< h₁<h₃. Thus, Daniel is tallest.

In Mathematics, Inequality defines the relationship between two values that are not equal. When two values are not equal, we use “not equal sign (≠)”. But if there is a comparison between two values, whether it is less than or greater than, different inequalities are used. For example 5<7 , 8>4.

The following problem is to model an inequality situation.

Given that ,

Najid is taller than Emily and shorter than Daniel.

 Let, height of Najid is h₁

         height of Emily is h₂

  and height of Daniel is h₃

By the condition h₁>h₂ and h₁< h₃

Combining both the statement we have the inequality

              h₂< h₁<h₃

From this inequality we have the person having h₃ height is tallest.

Hence, Daniel is tallest.

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The percentage of the cakes containing nuts using the ratio of different types of cakes is equal to 4.76%.

Let M represents the number of milk chocolate cakes

Let D represents the number of dark chocolate cakes

Let W represents the number of white chocolate cakes

From the given ratios, we have,

Ratio of the number of milk chocolate cakes to dark chocolate cakes

= 10:3

⇒D = M/(10 / 3)

⇒D = 3M/10

Ratio of the number of white chocolate cakes to milk chocolate cakes

= 1:6

⇒ W = M/6

Let N be the total number of cakes containing nuts.

Then the number of cakes not containing nuts is,

For milk chocolate cakes,

Ratio of the number of cakes containing nuts to not containing nuts = 1:8

⇒ 8N for every N containing nuts.

⇒M - N= 8N

⇒M = 9N

For dark chocolate cakes,

Ratio of the number of cakes containing nuts to not containing nuts = 3:2

⇒ 2N for every 3 containing nuts.

⇒ (D - 3N) = 2N

⇒ D = 5N

For white chocolate cakes,

Ratio of the number of cakes containing nuts to not containing nuts = 2:5

⇒5N for every 2 containing nuts

⇒ (W - 2N) = 5N

⇒ W = 7N

The total number of cakes is,

M + D + W

= 9N + 5N + 7N

= 21N

Percentage of cakes containing nuts is equal to,

=N/(21N) × 100

= 100/21

= 4.76%

Therefore, percentage of the cakes containing nuts using given ratio is equal to 4.76%.

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In response to the student question about registering multiple accounts on AliExpress for discounts, it is not recommended to create more than one account to apply coupons or discounts. This is because it goes against the platform's terms of service and may result in penalties, such as account suspension or termination.

To enjoy discounts on AliExpress without violating the platform's rules, follow these steps:
Register for an account: Sign up for a single account on AliExpress, providing your personal information and email address.
Subscribe to newsletters and promotions: Opt-in for promotional emails and newsletters from AliExpress. This way, you will be informed of any available discounts, deals, and special offers.
Shop during sales events: AliExpress regularly hosts sales events, such as the annual 11.11 sale, where a wide range of products are offered at discounted prices. Make sure to shop during these events to maximize your savings.
Collect coupons: Browse the website or use the AliExpress mobile app to collect various types of coupons, such as select coupons, store coupons, and AliExpress coupons. These can be applied at checkout to reduce the cost of your purchases.
Use cashback services: Some cashback services partner with AliExpress, offering a percentage of your purchase back as a refund or credit. Register with a cashback service, and make sure to use their links when shopping on
By following these steps, you can enjoy discounts on AliExpress without resorting to creating multiple accounts, which is not suggested and could lead to penalties.

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The frequency table shows that there is a relationship between buying a hot dog and buying a drink at a baseball game. The huge 70.2% is evidence of this.

The frequency table is meant to show the relationship between variables. Of all the values provided, the relationship with the highest percentage is 70.2%.

This shows that the number of people who purchased a hot dog while also purchasing a drink constituted the highest number. None of the figures come close to this one. So, there is a strong relationship between the variables.

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Numeric (continuous) variable: the amount of zantac in milliliters that the nurse will administer.A millilitre is a unit of capacity measurement. It is one thousandth of a litre in size. In other words, a one-liter container may hold  [tex]1,000[/tex] millilitres.

A millilitre is a more manageable unit of measurement for liquid volume or capacity in the metric system. It is used to measure smaller amounts of liquid and is equal to one thousandth of a litre (1 litre = 1000 millilitres).

To calculate how many millilitres of Zantac will the nurse administer to the patient, you need to know the concentration of Zantac in the dosage form and the prescribed dose for the patient.

For example, if the patient is prescribed 150 mg of oral Zantac twice daily and has a bottle of syrup that contains 15 mg/mL of ranitidine, then the nurse will administer [tex]10 mL (150 mg / 15 mg/mL)[/tex]  of syrup per dose.

Therefore, If the patient is prescribed 50 mg of intravenous Zantac every 8 hours and has a vial of solution that contains 25 mg/mL of ranitidine, then the nurse will administer 2 mL (50 mg / 25 mg/mL) of solution per dose.

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Answer:

꧁. ꧂

Step-by-step explanation:

꧁. ꧂꧁. ꧂

If we see the scatter plot we can conclude that the possible relation between x and y is linear and with a positive correlation since when the values of x increase the values for y increases as well.

[tex]Cov(x,y) =\frac{\sum_1^n(x_i-X')(y_i-Y')}{n-1}[/tex]

 [tex]\sum_1^5(6-16)(6-10)+(11-16)(9-10)....(27-16)(12-10)=106\\\\and\\Cov(x,y)=\frac{106}{4}=26.5\\\\r=0.693[/tex]

For this part we use excel in order to create the scatterplot and we got the result on the figure attached

If we see the scatter plot we can conclude that the possible relation between x and y is linear and with a positive correlation since when the values of x increase the values of y increase as well

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this

[tex]Cov(x,y) =\frac{\sum_1^n(x_i-X')(y_i-Y')}{n-1}[/tex]

:  

[tex]Cov(x,y) =\frac{\sum_1^n(x_i-X')(y_i-Y')}{n-1}[/tex]

 [tex]\sum_1^5(6-16)(6-10)+(11-16)(9-10)....(27-16)(12-10)=106\\\\and\\Cov(x,y)=\frac{106}{4}=26.5\\\\r=0.693[/tex]

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Answer: 2.8%

Step-by-step explanation: 2.8%

£80 :))