a textile manufacturing process finds that on average, two flaws occur per every 50 yards of material produced. a. what is the probability of exactly two flaws in a 50-yard piece of material? b. what is the probability of no more than two flaws in a 50-yard piece of material? c. what is the probability of no flaws in a 25-yard piece of material?

Therefore, the probability of getting a prime number on one die and a composite number on the other die when rolling two dice simultaneously is 1/6 or approximately 0.1667.

Probability theory is a branch of mathematics that deals with the study of random events and the analysis of their outcomes. It is widely used in statistics, science, engineering, finance, and many other fields to model and predict the behavior of complex systems.

Here,

There are a total of 6 x 6 = 36 possible outcomes when two dice are rolled simultaneously. We need to count the number of outcomes where one die shows a prime number and the other die shows a composite number.

Prime numbers in the sample space are 2, 3, and 5. Composite numbers are 4, 6, and any number greater than 1 that is not prime.

So, there are three possible outcomes where one die shows a prime number and the other die shows a 4 or 6:

(2, 4), (2, 6), (3, 4), (3, 6), (5, 4), (5, 6)

Therefore, there are a total of 6 possible outcomes where one die shows a prime number and the other die shows a composite number.

The probability of getting one prime number and one composite number on the two dice is:

P = number of favorable outcomes / total number of possible outcomes

P = 6 / 36

P = 1/6

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The probability of winning something from the Pepsi sales promotion with winning symbols under the caps of 10% of all Pepsi bottles in a six-pack is 46.9%.

The probability of winning something from the Pepsi sales promotion depends on the total number of bottles in the six-pack and the percentage of bottles with winning symbols under the caps.

Assuming that the six-pack contains six bottles, and 10% of all Pepsi bottles have winning symbols under the cap, the probability of winning something from the promotion can be calculated using the following formula:

Probability of winning = Number of bottles with winning symbols / Total number of bottles

Since 10% of all Pepsi bottles have winning symbols, the probability of finding a winning symbol under one bottle cap is 10%. Therefore, the probability of winning from a six-pack is the same as finding at least one winning bottle cap in six bottles.

To calculate the probability of winning, we can use the complement rule, which states that the probability of an event occurring is equal to one minus the probability of the event not occurring.

So, the probability of not winning from a single bottle is 1 - 0.1 = 0.9. The probability of not winning from all six bottles is 0.9^6 = 0.531. Therefore, the probability of winning something from a six-pack is 1 - 0.531 = 0.469 or 46.9%.

In conclusion, the probability of winning something from the Pepsi sales promotion with winning symbols under the caps of 10% of all Pepsi bottles in a six-pack is 46.9%. This means that nearly half of the customers who buy a six-pack are likely to win something from the promotion.

However, it is important to note that this probability may vary depending on the total number of bottles and the percentage of winning symbols used in the promotion.

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The image of vertex C is closest to point A=(3,0).

What is transformation?

A transformation is a process or operation that changes the position, shape, or orientation of a geometric figure or an object in space.

When a point is reflected over the x-axis, its y-coordinate changes sign (positive becomes negative, and negative becomes positive), while its x-coordinate remains the same.

In this case, if point C is reflected over the x-axis, its image will be (-3, -5) because the x-coordinate remains the same (3), and the y-coordinate changes sign from positive to negative.

We can now find the closest point to the image of vertex C, which is (-3, -5), among the given options:

Distance from (-3, -5) to A=(3,0):

d = √((3 - (-3))² + (0 - (-5))²) = sqrt(6² + 5²) ≈ 7.81

Distance from (-3, -5) to B=(6,0):

d = √((6 - (-3))² + (0 - (-5))²) = √(9² + 5²) ≈ 9.43

Therefore, the image of vertex C is closest to point A=(3,0).

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The thief stole 22 oranges using algebraic equations.

To solve this problem, we need to use algebra. Let x be the number of oranges the thief stole.

According to the problem, the thief gave the guard half of the stolen oranges and two more. This means that he gave away (1/2)x + 2 oranges.

We also know that the thief was left with only 9 oranges. So we can set up the equation:

x - [(1/2)x + 2] = 9

Simplifying this equation:

(1/2)x - 2 = 9
(1/2)x = 11
x = 22

Therefore, the thief stole 22 oranges.

The problem presents us with a scenario where a thief entered an orange garden and stole some oranges. However, he was caught by the guard. In order to get rid of the guard, the thief decided to give him half of the stolen oranges and two more. As a result, the thief was left with only 9 oranges.

To solve this problem, we used algebraic equations. We let x be the number of oranges the thief stole. We also knew that the thief gave away (1/2)x + 2 oranges to the guard. Using this information, we were able to set up an equation where x - [(1/2)x + 2] = 9. Simplifying the equation, we were left with (1/2)x - 2 = 9. Solving for x, we found that the thief had stolen 22 oranges.

In conclusion, algebraic equations are a useful tool in solving mathematical problems. By setting up an equation and simplifying it, we were able to determine the number of oranges that the thief had stolen.

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Each element of D8 is mapped to a permutation of {1, 2, 3, 4, 5, 6, 7, 8} by considering its action on the labeled generators 1, 2, ..., 8 under composition.

The elements of D8 are 1, r,[tex]r^2, r^3, s, sr, sr^2, sr^3,[/tex] which we can label with the integers 1, 2, 3, 4, 5, 6, 7, 8 respectively. The left regular representation of D8 into S8 is given by:

1 → (1)(2)(3)(4)(5)(6)(7)(8)

r → (1 2 3 4)(5 6 7 8)

[tex]r^2[/tex] → (1 3)(2 4)(5 7)(6 8)

[tex]r^3[/tex]→ (1 4 3 2)(5 8 7 6)

s → (1 2)(3 4)(5 6)(7 8)

sr → (1 8 3 6)(2 7 4 5)

[tex]sr^2[/tex]→ (1 4)(2 3)(5 8)(6 7)

[tex]sr^3[/tex] → (1 6 3 8)(2 5 4 7)

Here, each element of D8 is mapped to a permutation of {1, 2, 3, 4, 5, 6, 7, 8} by considering its action on the labeled generators 1, 2, ..., 8 under composition.

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We have exhibited the image of each element of D8 under the left regular representation into S8, represented as a product of disjoint cycles.

The left regular representation of D8 is a homomorphism from D8 to the symmetric group S8, where each element of D8 is represented as a permutation of the set {1, 2, ..., 8}.

Using the generators r and s, we can construct the elements of D8 as follows:

[tex]r^0[/tex] = 1

[tex]r^1[/tex]= r

[tex]r^2[/tex] = rr

[tex]r^3[/tex] = rrr

[tex]s^0[/tex]= 1

[tex]s^1[/tex] = s

[tex]s^2[/tex] = 1

[tex]s^3[/tex] = ss

Now, let's apply the left regular representation to each element of D8:

1 → (1 2 3 4 5 6 7 8)

r → (1 2 3 4 5 6 7 8)(1 2)

[tex]r^2[/tex] → (1 2 3 4 5 6 7 8)(1 3)(2 4)

[tex]r^3[/tex]→ (1 2 3 4 5 6 7 8)(1 4 3 2)

s → (1 8)(2 7)(3 6)(4 5)

sr → (1 7 3 5)(2 8 4 6)

[tex]sr^2[/tex] → (1 6 3 2)(4 7 5 8)

[tex]sr^3[/tex] → (1 5)(2 6)(3 7)(4 8)

Note that we can represent each permutation as a product of disjoint cycles, where each cycle corresponds to an orbit under the action of the permutation. For example, the permutation corresponding to r is a product of two cycles: (1 2) and (3 4 5 6 7 8). This means that r fixes the elements 1 and 2, and permutes the elements 3, 4, 5, 6, 7, and 8 cyclically. Similarly, the permutation corresponding to s is a product of four cycles: (1 8), (2 7), (3 6), and (4 5), which means that s fixes the pairs (1, 8), (2, 7), (3, 6), and (4, 5), and transposes each pair.

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Answer:

y=x+5;1

Step-by-step explanation:

Hope this helps! =D

Six and forty-seven thousandths.

or six point zero four seven.

the answer depends on what you have to write.

Hope this helps!

The measure of the angle m∠HLK subtended by the arc HK is derived to be equal to 45°.

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference.

Given that the arc HK = 90°

arc measure and the angle it subtends at the center of the circle are directly proportional.

so arc HK = m∠HJK = 90°

m∠HJK = 2(m∠HLK)

2(m∠HLK) = 90°

m∠HLK = 90°/2 {divide through by 2}

m∠HLK = 45°

Therefore, the measure of the angle m∠HLK subtended by the arc HK is derived to be equal to 45°.

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Answer:

25 units²

Step-by-step explanation:

Area of a triangle = (1/2)b*h

After graphing the triangle you can see that the two legs are at points

(4,3) and (-2,11) and (4,3) and (0,0). Using the distance formula:

[tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}[/tex]

then plug in the first line

[tex]\sqrt{(-2-4)^{2} + (11-3})^{2}}[/tex]

simplify

[tex]\sqrt{(-6)^{2} + (8})^{2}}[/tex]

[tex]\sqrt{36 +64}[/tex]

[tex]\sqrt{100}[/tex]

10

then the second line

[tex]\sqrt{(4-0)^{2} + (3-0)^{2}}[/tex]

[tex]\sqrt{(4)^{2} + (3)^{2}}[/tex]

[tex]\sqrt{16 + 9}[/tex]

[tex]\sqrt{25\\}[/tex]

=5

5*10=50

50*0.5 =25

so the area is equal to 25 units²

Answer:

(-13.82, ∞)

Step-by-step explanation:

To solve this inequality, we need to isolate the variable X on one side of the equation. First, we can subtract 3.8 from both sides of the inequality, which gives us:

X > -10.02 - 3.8

Simplifying this expression, we get:

X > -13.82

Therefore, the solution set for this inequality is all the values of X that are greater than -13.82. In interval notation, we can write the solution set as (-13.82, ∞).

The probability that a randomly selected man is shorter than 65 inches can be determined using the concepts of normal distribution and z-scores.

Step 1: Determine the average height and standard deviation :

Assuming the average height (μ) for men is 69 inches and the standard deviation (σ) is 3 inches. These values are commonly used in such problems and can vary based on the specific population being considered.

Step 2: Calculate the z-score :

We want to find the probability of a man being shorter than 65 inches. The formula for the z-score is: Z = (X - μ) / σ Here, X is the target height (65 inches), μ is the average height (69 inches), and σ is the standard deviation (3 inches).

Substituting values to calculate the z-score: Z = (65 - 69) / 3 Z = -4 / 3 Z ≈ -1.33

Step 3: Determine the probability :

Using a z-score table or a calculator with a normal distribution function, we can find the probability that corresponds to the calculated z-score of -1.33. The table will show a value of 0.092 (approximately) for the z-score of -1.33.

Thus, the probability that a randomly selected man is shorter than 65 inches is approximately 9.2%.

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The required location on the gird is:

[tex](x + y + 3)(x + y - 4) = x^{2}+y^2 +2xy-x-y-12[/tex]

Consider the provided expression.

We need to place the indicated product in the proper location on the grid.

First open the parenthesis as shown:

(x + y + 3)(x + y - 4) = x(x + y - 4) + y(x + y - 4) + 3(x + y - 4)

[tex](x + y + 3)(x + y - 4) =[/tex] [tex]x^{2} +xy-4x+yx+y^2-4y+3x+3y-12[/tex]

Now add the like terms as shown:

[tex](x + y + 3)(x + y - 4) = x^{2}+y^2 +2xy-x-y-12[/tex]

Hence, the required location on the gird is:

[tex](x + y + 3)(x + y - 4) = x^{2}+y^2 +2xy-x-y-12[/tex]

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Answer:

the answer of the sequence is a

If  circumference of a circle is 7π cm then area of circle is 38.465 square centimeter

The circumference of a circle is 7π cm

We have to find the area of the circle

To find area we have to know the radius

Circumference = 2πr

7π= 2πr

r=7/2

= 3.5 cm

Area of circle = πr²

=3.14×(3.5)²

=3.14×3.5×3.5

=38.465 square centimeter

Hence, if  circumference of a circle is 7π cm then area of circle is 38.465 square centimeter

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Answer:

Step-by-step explanation:
<ABC is 72 degrees.

1) This triangle is isosceles because two sides are equivalent. Thus, <C and <B are the same.
2) We know that <A + <B + <C = 180 in total
3. x + 2x + 2x = 5x
5x = 180
x = 36
4. <ABC = 2x = 2(36) = 72

The Unit-Price for first-bag is $1.72/kg and for second-bag is $1.86/kg, then the first-bag is cheaper compared to the second-bag with a unit-price.

The "Unit-Price" refers to the cost of dog food per kilogram. It is calculated by dividing the "total-cost" of the bag of dog-food by its weight in kilograms.

⇒ For the first bag of dog food:

The Cost is = $10.47,

The Weight is = 6.08 kg,

So, the Unit-Price is = Cost/Weight = $10.47/6.08 kg ≈ $1.72/kg,

⇒ For the second bag of dog food:

The Cost is = $13.88,

The Weight is = 7.48 kg,

So, the Unit Price will be = Cost/Weight = $13.88/7.48 kg ≈ $1.86/kg,

Based on the "unit-prices" calculated, the first bag of dog food has a unit price of $1.72 per kilogram, and the second bag has a unit price of $1.86 per kilogram.

Therefore, the first bag of dog food is the better-buy as it is cheaper compared to the second bag.

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The given question is incomplete, the complete question is

Justin paid $10.47 for a 6.08-Kg bag of dog food.  A few weeks later, he paid $13.88 for a 7.48-kg bag at a different store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price.

The statement "the average height of an adult male is 5'10''" is an example of a statistical estimate.

An estimate is an approximation or prediction of a value based on limited information or data. In this case, the estimate is based on data collected from a sample of adult males, and it represents the expected height of an average adult male in the population.

Statistical estimates are commonly used in many fields like business, finance, economics, and social sciences. They are used to make predictions and decisions based on uncertain information.

For example, a company might use statistical estimates to predict future sales. It is important to note that estimates are not exact or precise measurements, but rather are based on assumptions and limitations. They are subject to errors and uncertainties, and can be affected by factors such as sample size, sampling method, and measurement errors. Therefore, it is important to understand the limitations of statistical estimates and to interpret them with caution.

In summary, the statement "the average height of an adult male is 5'10''" is an example of a statistical estimate, which represents an approximation of a value based on limited information and assumptions.

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Answer:

32 degrees

Step-by-step explanation:

Recall the three main trig functions: sine, cosine, and tangent.

When using sine, we divide the opposite side from the angle by the hypothenuse.

When using cosine, we divide the adjacent side of the angle by the hypothenuse.

When using tangent, we divide the opposite side from the angle by the adjacent side to the angle.

Since we are given the opposite and adjacent sides, we'll use tangent.

We set up the equation like normal:

tan x [tex]= \frac{13}{21}[/tex]

Now, when finding the angle measurement using trig, we must use the opposing trig function, arcsine, arccosine, and arctangent. The opposing trig function is arctangent. We have to move arctangent to the other side, so that it can be used with the fraction, so:

[tex]x = arctan(\frac{13}{21} )[/tex]

(You would also write arctan, as tan with an exponent of -1) Now, just punch the right side of the equation into a calculator. The nearest degree is 32.

Therefore, the answer is 32 degrees. If you got something different, make sure your calculator is in degrees, not radians! (They are usually abbreviated as DEG and RAD.)

Thus, the number of volume read by both Eva and Maria in total 2 weeks is 8.

Slope is a crucial topic in economics because it's used to gauge how quickly things are changing.

The slope expresses how quickly the dependent variable changes when the independent variable changes. The line becomes steeper as the slope increases.

Given data:

Now,

Let the number of weeks at which both read the equal number of volume be x.

Total number of volume be y

So,

For Eva: y = 4 + 2x

For Maria: 0 + 4x

Equating both equations:

4 + 2x = 4x

4x - 2x = 4

2x = 4

x = 4/2

x = 2

Number of volumes read by each girl:

For Eva: y = 4 + 2(2)= 8

For Maria: 0 + 4(2) = 8

Thus, the number of volume read by both Eva and Maria in total 2 weeks is 8.

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According to the information, We can continue drawing more triangles by varying the angles in different ways.

Since the given triangle has one side with a fixed length of 4 cm, we can draw an infinite number of triangles by varying the other two angles.

To draw the second triangle, we can keep the 50 degree angle fixed and change the 40 degree angle. For example, we could draw a triangle with a 50 degree angle, a 60 degree angle, and a side of length 4 cm.

To draw the third triangle, we can keep the 40 degree angle fixed and change the 50 degree angle. For example, we could draw a triangle with a 30 degree angle, a 40 degree angle, and a side of length 4 cm.

We can continue drawing more triangles by varying the angles in different ways.

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The Cartesian Coordinate System is a method used to represent points in a plane by using two numerical values called coordinates

a.) . These coordinates represent the distances of the point from a fixed reference point called the origin, along two perpendicular axes called the x-axis (horizontal) and y-axis (vertical).

b.) The system is used for various purposes, such as plotting points and lines in geometry, graphing functions in mathematics, analyzing data in statistics, designing objects in computer-aided design, and representing locations in geography and mapping.

c.) The system was developed by the French mathematician and philosopher René Descartes in the 17th century.

d.) Historically, the system is unique because it introduced a method of visualizing and analyzing geometric shapes and algebraic equations using a common framework, which enabled the development of analytic geometry and the fusion of algebra and geometry.

a.) x-coordinate

b.) y-coordinate

c.) quadrant

d.) intersection

e.) coordinates

f.) origin

g.) axes (of a graph)

h.) y-axis

i.) x-axis

j.) number line

k.) ordered pair

l.) coordinate grid

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The length of wire per unit length is 8.168 cm.

Its function is to produce a regulated magnetic field through a coil twisted into a compact helix. The solenoid is a sort of electromagnet.

The magnetic field inside a solenoid is given by:

B = u*n*I

where B is the magnetic field, u is the permeability of free space, n is the number of turns per unit length, and I is the current.

The number of turns in a solenoid is given by:

N = n*L

where N is the total number of turns, L is the length of the solenoid, and n is the number of turns per unit length.

Therefore, the magnetic field can be written as:

B = u*N*I/L

Rearranging this equation, we get:

L = u*N*I/B

Substituting the given values, we get:

L = (4*pi*10⁻⁷)*(N=?) * (I=18.0 A) / (B=23.0 mT)

The number of turns per unit length is not given, so we cannot determine the total number of turns N. However, we can calculate the length of wire per unit length by using the formula for the circumference of a circle:

C = 2*pi*r

where r is the radius of the solenoid.

Substituting the given values, we get:

C = 2*pi*(d/2) = pi*d = 8.168 cm

Therefore, the length of wire per unit length is 8.168 cm.

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option 1 is correct , trigonometric ratio to solve for the missing side is sine.

we have an angle of 54 degrees and a hypotenuse of 12 units. We can use trigonometric ratios to solve for the missing side, which is the perpendicular side.

In a right triangle, the three primary trigonometric ratios are:

Sine (sin): the ratio of the length of the side opposite the angle to the hypotenuse.

Cosine (cos): the ratio of the length of the side adjacent to the angle to the hypotenuse.

Tangent (tan): the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Given that we know the hypotenuse (12 units) and the angle (54 degrees), we can use the sine ratio to solve for the length of the perpendicular side. The sine ratio is defined as:

sin(x) = opposite/hypotenuse

Plugging in the given values:

sin(54 degrees) = opposite/12

To solve for the length of the perpendicular side (opposite), we can rearrange the equation:

opposite = sin(54 degrees) * 12

Using a calculator, we can find the value of sin(54 degrees) and multiply it by 12 to find the length of the perpendicular side.

therefore, option 1 is correct , trigonometric ratio to solve for the missing side is sine.

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Answer:

A

Step-by-step explanation:

[tex]\frac{9x+7}{2}[/tex] - [ x - [ [tex]\frac{-2}{7}[/tex] ]] = 36← distribute bracket by - 1

[tex]\frac{9x+7}{2}[/tex] - x +[tex]\frac{x-2}{7}[/tex] = 36

multiply through by 14 ( the LCM of 2 and 7 ) to clear the fractions

7(9x + 7) - 14x + 2(x - 2) = 504 ← distribute parenthesis on left side

63x + 49 - 14x +2x - 4 = 504 ← simplify left side

51x + 45 = 504 ( subtract 45 from both sides )

51x = 459 ( divide both sides by 51 )

x = 9

Answer:

4 hexagons * 6 equilateral triangles per hexagon = 24 equilateral triangles

Step-by-step explanation:

Pattern blocks are a set of geometric shapes commonly used in math education. The set typically includes six different shapes: triangle, rhombus, trapezoid, hexagon, square, and equilateral triangle. Each hexagon in a pattern block set is made up of six equilateral triangles.

To make 4 hexagons using pattern blocks, we would need to calculate the total number of equilateral triangles required. Since each hexagon is made up of 6 equilateral triangles, we can multiply the number of hexagons by 6 to get the total number of equilateral triangles needed.

4 hexagons * 6 equilateral triangles per hexagon = 24 equilateral triangles

So, you would need 24 pattern block triangles to make 4 hexagons using pattern blocks.

Answer:

Let's use pattern blocks to visualize the situation and say that a hexagon is 1 whole. Since 3 rhombuses make a hexagon, 1 rhombus represents and 2 rhombuses represent . We can see that 6 pairs of rhombuses make 4 hexagons, so there are 6 groups of in 4.

Thus, the new coordinates of the image of ΔEFG after the given translations is found as:  E'(-2, 3), F'(-4, 0), G'(-1, -2).

A translation is represented as a column vector. Using a column vector, the translation is divided into:

Given that-

Now,

translation of 3 units left and 1 unit down - subtract 3 from the x coordinates and 1 from the y coordinates.

E(1,4)  = E' (1 - 3, 4 - 1) = E'(-2, 3)

F(-1 , 1) = F'(-1 - 3, 1 - 1) = F'(-4, 0)

G(2, -1) = G'(2 - 3, -1- 1) = G'(-1, -2)

Thus, the new coordinates of the image of ΔEFG after the given translations is found as:  E'(-2, 3), F'(-4, 0), G'(-1, -2).

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The correct answer is,

Debt is usually expected in any of the following cases EXCEPT ''purchase of car.''

We have to given that;

Debt is usually expected in any of the following cases EXCEPT ....

Now, We know that;

it's important to note that there may be individual situations where debt is expected when buying a car.

Hence, The correct answer is,

Debt is usually expected in any of the following cases EXCEPT ''purchase of car.''

Thus, Option C is true.

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The linear function that represent the situation is as follows:

f(x) = 27x + 254

A function relates input and output values.

Julia has 254 dollars. Each week she saves an additional 27 dollars .

Therefore, the function that models the amount of money Julia has  after x week can be represented as follows:

The function is a linear function. A linear function can be represented in the form as follows:

y = mx + b

where

Therefore,

f(x) = 27x + 254

where

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