Help me solve this problem

Answer:

We can start by using the identity 2 sin ϕ cos ϕ = sin 2ϕ to simplify the left-hand side of the equation:

2 sin ϕ cos ϕ + 2 sin ϕ + cos ϕ + 1 = sin 2ϕ + 2 sin ϕ + cos ϕ + 1

Next, we can use another identity, sin^2 ϕ + cos^2 ϕ = 1, to eliminate the cosine term:

sin 2ϕ + 2 sin ϕ + cos ϕ + 1 = sin 2ϕ + 2 sin ϕ + √(1 - sin^2 ϕ) + 1

Now, we can substitute u = sin ϕ to obtain a quadratic equation in u:

sin 2ϕ + 2 sin ϕ + √(1 - sin^2 ϕ) + 1 = sin^2 ϕ + 2 sin ϕ + √(1 - sin^2 ϕ) + 1

sin 2ϕ = sin^2 ϕ

2 sin ϕ cos ϕ = sin^2 ϕ - cos^2 ϕ

2 u √(1 - u^2) = u^2 - (1 - u^2)

2 u √(1 - u^2) = 2 u^2 - 1

4 u^2 (1 - u^2) = (2 u^2 - 1)^2

4 u^4 - 4 u^2 + 1 = 0

This is a quadratic equation in u^2, which can be solved using the quadratic formula:

u^2 = [4 ± √(16 - 16)] / 8 = 1/2 or u^2 = 1

Since 0 < ϕ < 2π, we have 0 < u < 1, so u^2 = 1/2. Therefore, sin ϕ = u = ±√(1/2) and cos ϕ = ±√(1 - u^2) = ±√(1/2).

We can summarize the solutions as follows:

sin ϕ = √(1/2) or sin ϕ = -√(1/2)

cos ϕ = √(1/2) or cos ϕ = -√(1/2)

Therefore

The first car consumed 15 gallons of gas

The second car consumed 30 gallons of gas during the week

Let's denote the number of gallons consumed by the first car as x, and the number of gallons consumed by the second car as y.

We know that the total gas consumption is 45 gallons, so:

x + y = 45

We also know that the total distance traveled is 1725 miles, and that the fuel efficiency (miles per gallon) of the first car is 35, and of the second car is 40. Using this information, we can write another equation:

35x + 40y = 1725

We now have two equations with two unknowns, which we can solve simultaneously to find x and y.

Multiplying the first equation by 35, we get:

35x + 35y = 1575

Subtracting this equation from the second equation, we get:

5y = 150

y = 30

Substituting y = 30 into the first equation, we get:

x + 30 = 45

x = 15

Therefore, the first car consumed 15 gallons of gas, and the second car consumed 30 gallons of gas during the week.

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The reflection line  that maps polygon ABCDE to polygon A' B' C' D' E' is the y-axis.

The image is reflected through a line known as a reflection line. A pattern is said to mirror another pattern, and then every point in the pattern is equidistant from every corresponding point in the other pattern. The reflected image must be the same shape and size, but the image is in the opposite direction.

In order to determine the line of reflection that maps  polygon ABCDE to polygon A' B' C' D' E', we must find a symmetrical line  equidistant from each corresponding pair of points. If you project the image across the x-axis, vertex A (-1, -4) is mapped to A' (13, -4) and vertex E (1, -6) is mapped to E'. (11, 6). Therefore, the reflection line must be the x-axis.

If we map the image to the cross x=6, vertex A (-1, -4) would correspond to A' (13, -4) and vertex E (1, -6) would correspond to E' (3, 6). ). Therefore, the reflection line cannot be x=6.

If we project the pattern perpendicular to y=-3, the point A (-1, -4) is opposite to the point A' (-7, -4) and the vertex E (1, -6)  to  the point E . (7, 6). Therefore, the reflection line  cannot be y=-3.

 If you project the image across the y-axis, point A (-1, -4) is mapped to point A' (-13, -4) and  vertex E (1, -6) is mapped to E. (-11 , 6). Therefore, the reflection line  must be the y-axis.

 Therefore, the reflection line  that maps  polygon ABCDE to polygon A' B' C' D' E' is the y-axis.

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he two numbers that multiply to -35 and add to get -18 are -5 and 3.

To see why, you can use the factoring method. First, find two numbers that multiply to give you -35. The factors of -35 are -1, 1, -5, and 5. So, the two numbers that multiply to -35 are either -5 and 7 or 5 and -7.

Next, find which pair of numbers adds up to -18. It's clear that 5 and -7 add up to -2, so they don't work. However, if we choose -5 and 3, we get:

-5 + 3 = -2

So, -5 and 3 are the two numbers that multiply to -35 and add to -18.

Required Answers :

1. 2x + 4 = 10

[tex]\: :\implies [/tex] 2x = 10 - 4

[tex]\: :\implies [/tex] 2x = 6

[tex]\: :\implies [/tex] x = 6/2

[tex]\: :\implies [/tex] x = 3.

Hence, Option (A) x = 3 is the answer.

2. 25/5 × 7 = ?

[tex]\: :\implies [/tex] 5 × 7

[tex]\: :\implies [/tex] 175/5

[tex]\: :\implies [/tex] 35

Hence, The required answer is 35.

3. 100 - 50 + 10 - 5 = ?

[tex]\: :\implies [/tex] 50 + 5

[tex]\: :\implies [/tex] 55

Hence, Option (A) 55 is the answer.

4. 24 / 6 = ?

[tex]\: :\implies [/tex] 24 ÷ 6

[tex]\: :\implies [/tex] 4

Hence, Option (A) 4 is the answer.

5. A triangle has base 6 inches and height 8 inches. What is the area?

Area of triangle = ½ × Base × Height

[tex]\: :\implies [/tex] 1/2 × 6 × 8

[tex]\: :\implies [/tex] 1/2 × 48

[tex]\: :\implies [/tex] 48/2

[tex]\: :\implies [/tex] 24 sq. in

Hence, Option (A) 24 sq in is the answer.

6. What is the greatest common factor of 36 and 56?

36 = 1,2,3,4,6,9,12, 18 and 36.

56 = 1,2,4,7,8,14,28 and 56.

Hence, Option (A) 4 is the answer.

7. What is the square root of 121?

[tex]\: :\implies [/tex] 11 × 11

[tex]\: :\implies [/tex] 121

Hence, (A) 11 is the answer

8. If 2x + 4 = 14, what is x?

[tex]\: :\implies [/tex] 2x + 4 = 14

[tex]\: :\implies [/tex] 2x = 14 - 4

[tex]\: :\implies [/tex] 2x = 10

[tex]\: :\implies [/tex] x = 10/2

[tex]\: :\implies [/tex] x = 5

Hence, Option (A) 5 is the answer

9. (3x - 5) + (7x + 1) = ?

[tex]\: :\implies [/tex] 3x - 5 + 7x + 1

[tex]\: :\implies [/tex] 10x - 5 + 1

[tex]\: :\implies [/tex] 10x - 4

Hence, Option (A) 10x - 4 is the answer.

10. What fraction is 5/12?

[tex]\: :\implies [/tex] 1/2 (approximately)

Hence, Option (A) 1/2 is the answer.

The average velocity is given by the displacement during the time thus,[3, 4]: Average Velocity = 40 m/s. [3, 3.5]: Average Velocity = 40 m/s. [3, 3.1]: Average Velocity = 40 m/s. [3,3.01]: Average Velocity = 40 m/s.

Unaffected by direction, speed is a scalar quantity that describes how quickly an object is travelling. The speed and direction of an object's motion are both described by its velocity, which is a vector quantity. In other terms, velocity is the rate of positional change of an object in a specific direction. Therefore, if two objects are travelling in separate directions or if one is accelerating while the other is not, they can have the same speed but distinct velocities.

The average velocity is given by the displacement during the time, thus we have:

Displacement = h(t2) - h(t1) = (40t2 - 0.8312) - (40t1 - 0.8312) = 40(t2 - t1)

Now, the average velocity between t2 - t1 is:

Average Velocity = Displacement / Duration = 40(t2 - t1) / (t2 - t1) = 40 m/s

Using the different values of t2 and t1 we see that:

[3, 4]:

Average Velocity = 40 m/s

[3, 3.5]:

Average Velocity = 40 m/s

[3, 3.1]:

Average Velocity = 40 m/s

[3,3.01]:

Average Velocity = 40 m/s

[3, 3.001]:

Average Velocity = 40 m/s

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Answer:

2

Step-by-step explanation:

just did it on end 2022 test quiz

120 × 5 ÷ 20

= 120 × 5/20

= 6 × 15

= 90 Answer.

The number of dahlias should the florist expect to sell on a day with 120 customers is 90 bouquets.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that;

Sold bouquets=15

Total customers=120

Now,

In this case, the number of successful outcomes is 15, and the number of total outcomes is 20.

So the experimental probability is:

2015​=43​

To find the expected number of bouquets of dahlias to sell on a day with 120 customers, you need to multiply the experimental probability by the number of customers.

In this case, you need to multiply 3/4 by 120:

3/4​×120=3×120​/4

=360/4​

=90

Therefore, by the unitary method the answer will be 90 bouquets

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If Fred books a certain number of nights, If Fred books 30 nights at either hotel, he will earn 1,661 points.

What are the points?

Let's assume that Fred books "n" nights at the hotel.

For Hotel Elegance, the total number of points that Fred will earn is:

881 + 22n

For Hotel Paradiso, the total number of points that Fred will earn is:

851 + 23n

According to the problem, Fred will earn the same number of points at both hotels if:

881 + 22n = 851 + 23n

Solving for "n", we get:

n = 30

Therefore, if Fred books 30 nights at either hotel, he will earn the same number of points. To find out how many points he will earn, we can substitute "n=30" into either equation:

For Hotel Elegance:

881 + 22n = 881 + 22(30) = 1,661 points

For Hotel Paradiso:

851 + 23n = 851 + 23(30) = 1,621 points

Therefore, if Fred books 30 nights at either hotel, he will earn 1,661 points.

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The volume of the figure is 1795.5 m³.

The volume of the figure can be found as follows:

volume of the figure = base area × height

Therefore, the base of the figure is a trapezium.

Hence,

base area  = 1 / 2 (a + b)h

where

Therefore,

base area  = 1 / 2 (11 + 16)9.5

base area = 1 / 2 (27)9.5

base area = 256.5 / 2

base area = 128.25

Hence,

volume of the figure = 128.25 × 14

volume of the figure = 1795.5 m³

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So, the length of WZ is 24 in kite WXYZ with diagonals WY and XZ.

A triangle is a closed, two-dimensional geometric shape that is formed by three line segments, called sides, that intersect at three points, called vertices. Triangles are one of the most basic shapes in geometry and are studied extensively in mathematics. The properties of triangles depend on the length of their sides and the size of their angles. Triangles can be classified based on the length of their sides as equilateral, isosceles, or scalene, and based on the size of their angles as acute, right, or obtuse. In an equilateral triangle, all three sides are of equal length. In an isosceles triangle, two sides are of equal length, while the third side is of a different length. In a scalene triangle, all three sides are of different lengths.

Here,

Since WXYZ is a kite, we know that its diagonals, WY and XZ, intersect at a right angle and bisect each other. Let M be the point of intersection of the diagonals, so that MW = MY and MX = MZ.

We can use the Pythagorean theorem to find MW and MX, and then use the fact that they are equal to find WZ.

Using the Pythagorean theorem in right triangles WMX and WMY, we have:

MW² = WX² - MX²

= 17² - 5²

= 264

MY² = WY² - MW²

= 13² - 264

= 25

MX² = XZ² - MZ²

= 17² - 13²

= 144

Since MW = MY, we have MW = √(25)

= 5

Therefore, WZ = 2MX

= 2√(144)

= 2*12

= 24

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Answer:

0.0625

Step-by-step explanation:

hope this helps :)

Answer:

Step-by-step explanation:

I can cover this, so a math book is a rectangle, I hope you knew that, there is the front, back, and sides of a math book, given 2 faces and 4 sides of a book, there will be 6 faces, now for the vertices, there are 6 faces, so the edges will make 8 vertices, a vertex is where 2 or more edges meet, so now we will count the edges, given the 6 faces, we can count all of the edges and end up with 8 edges, I hope this helped you

a. The absolute value of a number is the distance of the number from zero on a number line. It is always a non-negative value, meaning that it is either zero or a positive number. It is denoted by two vertical bars surrounding the number, like |x|.

b. The absolute value of -109 is the distance of -109 from zero on a number line. Since -109 is 109 units away from zero, the absolute value of -109 is 109. Therefore, |-109| = 109.

c. First, we need to evaluate |-7|, which is the absolute value of -7. The distance of -7 from zero on a number line is 7 units, so |-7| = 7. Therefore, the expression |-7| - 2 is equivalent to 7 - 2, which is equal to 5. Therefore, |-7| - 2 = 5.

Answer:

B.

Step-by-step explanation:

x + 3x + 6 = 6 + 4x

4x + 6 = 6 + 4x

4x - 4x = 6 - 6

This means, whatever value we pick in place of x, there will always be a solution therefore, the equation in option B has infinitely many solutions.

The height of the plane above the ocean is approximately 15,000 meters to the nearest meter.

The angle of depression is an angle formed between a horizontal line (such as the ground, ocean surface, or any other reference plane) and a line of sight from an observer looking downward towards an object or point of interest that is located below the observer's line of sight.

According to the given information:

The angle of depression is the angle formed between the horizontal line (such as the ocean's surface) and the line of sight from an observer looking downward to an object (such as the island). In this case, the angle of depression is given as 45 degrees.

Given:

Angle of depression = 45 degrees.

Distance from airplane to island = 15,000 meters.

To find the height of the plane, we can use trigonometry. The tangent function is commonly used to relate angles of depression to the height of an object above the horizontal.

In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the side opposite the angle of depression is the height of the plane, and the side adjacent to the angle is the distance from the airplane to the island.

Using the tangent function:

tan(angle of depression) = height of plane/distance to the island

Plugging in the given values:

tan(45 degrees) = height of plane / 15,000 meters

We can now solve for the height of the plane:

height of plane = tan(45 degrees) * 15,000 meters

Using a calculator, we find:

height of plane = 15000 * tan(45 degrees) ≈ 15000 meters (rounded to the nearest meter)

So, the height of the plane above the ocean is approximately 15,000 meters to the nearest meter.

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The subtraction expression for each length is given as follows:

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Hence the distance OB is given as follows:

OB = sqrt((3 - (-3))² + (4 - 4)²)

OB = 3 - (-3).

The distance AB is given as follows:

AB = sqrt((-2 - (-2))² + (4 - (-2))²)

AB = 4 - (-2)

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(a) This study is observational because the consultant is not manipulating any variables or imposing treatments on the machines.

(b) The factors are:

Machine (experimental factor): There are six machines, labeled A through F.

Carton (observational factor): There are 20 cartons selected randomly from each machine.

Deviation from 32 ounces (response variable): This is the weight difference between the actual fill amount and the target fill amount of 32 ounces.

The factor levels are:

Machine: A, B, C, D, E, F

Carton: 1, 2, 3, ..., 20

The factor-level combinations are all possible pairs of machine and carton, such as A-1, A-2, ..., F-20.

(c) This is a nested design because the 20 cartons selected from each machine are not interchangeable between machines.

(d) Here's an example code snippet in R to import the data and display the structure of the dataframe:

data <- read.csv("filling_machine_data.csv")

data$Machine <- factor(data$Machine)

levels(data$Machine)

Assuming the data is stored in a CSV file called "filling_machine_data.csv", the code reads in the data, coerces the Machine variable to a factor, and displays the factor levels of Machine

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The equation of the circle in standard form with a center at (-6, 5) and passing through the point (-11, 3) is (x + 6)² + (y - 5)² = 29.

The equation of a circle in standard form with a center at (h, k) and a radius r is:

(x - h)² + (y - k)² = r²

Center: (h, k) = (-6, 5)

Point on circle: (-11, 3)

Substituting these values into the standard form equation:

(x - (-6))² + (y - 5)² = r²

(x + 6)² + (y - 5)² = r²

Now we need to find the value of r, which is the radius of the circle.

The distance between the center (-6, 5) and the point (-11, 3) is equal to the radius of the circle.

Using the distance formula:

r = √((x₂ - x₁)² + (y₂ - y₁)²)

r = √((-11 - (-6))² + (3 - 5)²)

r = √((-5)² + (-2)²)

r = √(25 + 4)

r = √29

r² = 29

The equation of the circle:

(x - h)² + (y - k)² = r²

(x + 6)² + (y - 5)² = 29

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The answer of the given question based on the probability is , the probability that at least 6 adults watch the news is approximately 0.755.

Probability is  measure of likelihood or chance of  event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain. Probability is used to analyze random experiments and events, and it is an essential concept in statistics, mathematics, and many other fields.

This is a binomial probability problem, where X follows a binomial distribution with n = 8 and p = 0.60. We want to find the probability that at least 6 adults watch the news, which can be written as:

P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + ...

To solve , we use  binomial probability formula:

P(X = k) =(n choose k) *p^k *(1 - p)^(n - k)

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

Using this formula, we can find the probabilities for each value of k:

P(X = 6) = (8 choose 6) * 0.60⁶ * 0.40² = 0.311

P(X = 7) = (8 choose 7) * 0.60⁷ * 0.40¹ = 0.276

P(X = 8) = (8 choose 8) * 0.60⁸ * 0.40⁰ = 0.168

Note that we can also use  binomial probability table or  calculator with  binomial probability function to find the probabilities.

Then, we can add these probabilities to get the probability that at least 6 adults watch the news:

P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + ... = 0.311 + 0.276 + 0.168 + ...

This is a infinite series, but we can stop at P(X = 8) since the probabilities become very small after that.

P(X ≥ 6) = 0.755

Therefore, the probability that at least 6 adults watch the news is approximately 0.755.

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Answer:

Step-by-step explanation:

minute= 250 per minute

mph = 1500/5280

Answer:

width = 3x

Step-by-step explanation:

Area of a rectangle = Length × width

Length = 5x + 4

Breadth = y

15x² + 12x = 5x + 4 × y

y = 15x² + 12x

---------------

5x + 4

y = 3x

Answer:

Using order of operations:

[tex] \frac{12a}{2} - 3a \times 5[/tex]

[tex]6a - 3a(5)[/tex]

[tex]6a - 15a = - 9a[/tex]

[tex] - 9 \times 4 = - 36[/tex]

The expression 0.20×0.30 could be modeled by the given decimal grid option (A) is correct.

What is a mathematical expression?

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: Expression: (Math Operator, Number/Variable, Math Operator).

We have a total of 10 columns and 10 rows.

Total boxes = 10×10 ⇒ 100

Number of shaded boxes = 3×10 ⇒ 30

Each box contains X's out of 100 that is:

              = 30/100

                 = 0.30

We can represent a number of columns in decimal such that:

            = 20/100  = 0.20

The expression becomes 0.20×0.30.

Thus, the expression 0.20×0.30 could be modeled by the given decimal grid option (A) is correct.

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The probability of success for given number of trials is 0.4751.

What is probability?

Probability can be used to determine the likelihood of an event. The likelihood that an event will happen is the only useful outcome. a scale where 0 indicates impossibility and 1 indicates a specific occurrence.

We know that the probability is given by:

P = nCx * [tex]p^{x}[/tex] * [tex]q^{n-x}[/tex]

P (x ≤ 3) = P(0) + P(1) + P(2) + P(3)

Now,

⇒ P(0) = 7C0 * [tex]0.4^{0}[/tex] * [tex]0.6^{7}[/tex]

⇒ P(0) = 1 * 1 * 0.0279936

⇒ P(0) = 0.02799

Similarly,

⇒ P(1) = 7C1 * [tex]0.4^{1}[/tex] * [tex]0.6^{6}[/tex]

⇒ P(1) = 7 * 0.4 * 0.046656

⇒ P(1) = 0.13064

Similarly,

⇒ P(2) = 7C2 * [tex]0.4^{2}[/tex] * [tex]0.6^{5}[/tex]

⇒ P(2) = 21 * 0.16 * 0.07776

⇒ P(2) = 0.02613

Similarly,

⇒ P(3) = 7C3 * [tex]0.4^{3}[/tex] * [tex]0.6^{4}[/tex]

⇒ P(3) = 35 * 0.064 * 0.1296

⇒ P(3) = 0.2903

So, now we get

⇒ P (x ≤ 3) = P(0) + P(1) + P(2) + P(3)

⇒ P (x ≤ 3) = 0.02799 + 0.13064 + 0.02613 + 0.2903

⇒ P (x ≤ 3) = 0.4751

Hence, the probability of success for given number of trials is 0.4751.

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Answer:

R = 3

Step-by-step explanation:

V = 4 π r³/3 = 36

Multiply both of the sides by 3

4π · r³ =108 πcm³

Now your going to divide by 4π

r³ = 27cm³

Square off the ³

r = 3

The function N for d days of both rumors are N(d) = 2 + 5d and N(d) = 2(3)^d

Here, the number of students are the students that start the rumor i.e. Susanna and Liz

So, we have

For the Justin Beiber rumor, the rumor spreads at a linear rate of 5 per day

So, we have

JB day 2 = 2 + 5(2) = 7

For the Rihanna rumor, the rumor spreads at an exponential rate of 3

So, we have

Rihanna day 2 = 2 * (3)^2 = 18

Using the functions, we have

JB

2 + 5x = 32 students

5x = 30

x = 6 days

Rihanna

2(3)^x = 162 students

3^x = 81

x = ln(81)/ln(3)

x = 4 days

JB

N(d) = 2 + 5d

Rihanna

N(d) = 2(3)^d

So, we have

d          JB          Rihanna

0           2           2

1           7           6

2          12           18

3           17           54

4           22           162

5           27           486          

6           32           1458

7           37           4374

8           42           13122

9           47           39366

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The length of the arc is approximately 7.5 inches.

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point.

I'm sorry, but the answer you provided is not correct.

To find the length of the arc, you first need to determine what fraction of the circle the sector represents. The central angle is 36 degrees, which is 36/360 or 1/10 of the full circle.

To find the length of the arc, you can then use the formula:

arc length = (central angle/360) x 2πr

where r is the radius of the circle.

Plugging in the values you provided, we get:

arc length = (36/360) x 2π(12) = 2.4π inches

Rounding to the nearest tenth gives:

arc length ≈ 7.5 inches

Therefore, the length of the arc is approximately 7.5 inches.

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