Graph XY with endpoints X(-3, 1) and Y(4,-5) and its image after the composition.
Translation: (x, y)→(x, y + 2)
Rotation: 90° about the origin

The height of the box is 4 inches.

The volume of a box is given by the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height. We are given that the volume of the box is 36 cubic inches, the length is 3 inches, and the width is 3 inches.

So, we can plug in these values into the formula and solve for the height h:

V = lwh

36 = 3 x 3 x h

36 = 9h

h = 36/9

h = 4

Therefore, the height of the box is 4 inches.

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The length of the PR is 14 cm by pythagoras theorem

We have to find the length of PR

By using pythagoras theorem we know that In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

PR² + RQ² = 50 ²

PR² + 48² = 50 ²

PR² +2304=2500

PR²=2500-2304

PR²=196

PR=14

Hence, the length of the PR is 14 cm by pythagoras theorem

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The given equations [tex]y = -4x \ and \ \frac{1}{6} + 3x = y[/tex] are not proportional equations.

To determine if the given equations [tex]y = -4x \ and \ \frac{1}{6} + 3x = y[/tex] are proportional, we need to check if the ratios of the corresponding coefficients are equal. Let's solve the second equation for y and compare the coefficients:

Given equation 1: [tex]\( y = -4x \)[/tex]

Given equation 2: [tex]\( \frac{1}{6} + 3x = y \)[/tex]

To determine if the equations are proportional, we'll compare the coefficients of x and y in both equations.

Comparing the coefficients of x:

In equation 1, the coefficient of x is [tex]-4[/tex].

In equation 2, the coefficient of x is [tex]3[/tex].

Since the coefficients of x are different [tex](-4 \ and \ 3)[/tex], the equations are not proportional.

Comparing the coefficients of y:

In equation 1, the coefficient of y is -1.

In equation 2, the coefficient of y is 1.

Since the coefficients of y are different (-1 and 1), the equations are not proportional.

Hence, the given equations [tex]y = -4x \ and \ \frac{1}{6} + 3x = y[/tex] are not proportional.

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We can say with 99% confidence that the true proportion of people who like dogs is within 8.44 percentage points of the sample proportion (65%).

To find the Margin of Error (MoE) for a poll, we need to use the formula:

MoE = [tex]z \times (\sqrt{(p \times q / n)} )[/tex]

where:

z is the z-score associated with the desired confidence level (99% confidence level corresponds to z = 2.576)

p is the proportion of people who said they liked dogs (0.65 in this case)

q is the complement of p (i.e., q = 1 - p)

n is the sample size (130 in this case)

Plugging in the values, we get:

MoE = [tex]2.576 \times (\sqrt{(0.65 \times 0.35 / 130)} )[/tex] ≈ 0.0844

Rounding to four decimal places, the Margin of Error is approximately 0.0844. Therefore, we can say with 99% confidence that the true proportion of people who like dogs is within 8.44 percentage points of the sample proportion (65%).

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Hello!

x = number of caps of Mel

36 - x = 2(12 + x)

36 - x = 24 + 2x

36 - 24 = 2x + x

12 = 3x

x = 12/3

x = 4

The answer is 4.

verification:

36 - 4 = 32

12 + 4 = 16

16 x 2 = 32 or 32/2 = 16

it's correct.

Answer: To estimate the number of farms expected to no longer have a problem with caterpillars feeding on their crops among the total 1,470 farms based on the random sample of 200 farms, we can use proportion estimation.

First, let's find the proportion of farms in the sample that no longer have a problem with caterpillars:

Proportion = (Number of farms with no caterpillar problem in the sample) / (Total number of farms in the sample)

Proportion = 160 / 200

Proportion = 0.8

Next, we'll use this proportion to estimate the number of farms in the total population of 1,470 farms:

Estimated number of farms = Proportion * Total number of farms in the population

Estimated number of farms = 0.8 * 1,470

Estimated number of farms = 1,176

Therefore, it is expected that approximately 1,176 farms will no longer have a problem with caterpillars feeding on their crops based on the sample data.

Step-by-step explanation:

The total rainfall for the year is given as follows:

D. 19 inches.

The dot plot gives a dot to each measure for each time that it appears, hence it says the same thing as a table, in a different format.

Hence the rainfall in this problem is divided as follows:

Hence the total rainfall is obtained as follows:

0 + 1 x 0.5 + 2 x 0.75 + 3 x 1.75 + 1 x 2 + 1 x 2.25 + 3 x 2.5 = 19 inches.

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The area of the Japanese garden around the koi pond is 195.74 square feet.

To find the area of the Japanese garden around the koi pond, we need to subtract the area of the circular pond from the area of the rectangular garden. Let's use the given terms and follow these steps:
1. Calculate the area of the rectangular garden.
Area = Length × Width
Area = 16 feet × 14 feet
Area = 224 square feet
2. Calculate the area of the circular koi pond.
Area = π × (radius)^2
Area = 3.14 × (3 feet)^2
Area = 3.14 × 9 square feet
Area = 28.26 square feet
3. Subtract the area of the koi pond from the area of the garden.
Garden area around the koi pond = Area of the rectangle - Area of the circle
Garden area = 224 square feet - 28.26 square feet
Garden area = 195.74 square feet
Your answer: The area of the Japanese garden around the koi pond is 195.74 square feet.

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Answer:

slon

7+15

AGAIN

L+B⅔

²2

AE

the paint set, sketchbook, brush price in turn are : 26 ; 19,5 ; 3,25$

Step-by-step explanation:

assume the price of the paint set is x($)

we have an equation

52,75-4= X + 3/4X +1/6×3/4X (4$ is the remaining amount after shiva bought these things above)

<=> X=26($)

The statement that describes the mean is the last one:

"the sum of the prices divided by 7"

For any set of N values {x₁, ..., xₙ}, the mean is given by:

M = (x₁ + ... + xₙ)/N

In this particular case, we have a set of 7 values which is {8, 10, 10, 12, 15, 15, 18}

The mean will be the sum of these 7 values divided by the number of values, which is 7, so the mean is:

M = (8 + 10 + 10 + 12 + 15 + 15 + 18)/7

M = 12.57

The correct option is the last one; The sum of the prices divided by 7

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Step-by-step explanation:

it follows practically the same rules as a division between plain numbers.

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴

we take the first term (x⁵) and divide it by the x term(s) of the divisor (we ignore constants for the moment). the resulting x term : x⁴

as x⁵/x = x⁴

now we multiply the intermediate result with the full divisior and subtract that result from the left side of the dividend :

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴

- x⁵ - x⁴

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

0 0

now we "pull down" the next term of the dividend and we calculate

(0 + 0 + 9x³) / x = 9x²

so, we have now

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x²

and we do the same thing as before (multiply intermediate result with divisor and subtract the result)

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x²

0 0 9x³

- 9x³ - 9x²

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

0 0

and, again, we pull down the next term of the dividend abd divide by the x term(s) of the divisor

(0 + 0 + 0 + 0 + 9x) / x = 9

so, we have now

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x² + 9

and we do the same thing as above again

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x² + 9

- 0 0 0 0 9x - 9

-----------

0 - 1

since we ran out of additional terms, we are finished.

the quotient is

x⁴ + 9x² + 9

the remainder is

-1

which makes the full division result

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) =

= x⁴ + 9x² + 9 - 1/(x - 1)

let's check :

(x⁴ + 9x² + 9 - 1(x - 1)) × (x - 1) =

= x⁵ + 9x³ + 9x - x⁴ - 9x² - 9 - 1 =

= x⁵ - x⁴ + 9x³ - 9x² + 9x - 10

perfect.

The solution is:

20/29 is the probability that a student chosen randomly from the class plays golf or soccer.

0 is the probability that a student chosen randomly from the class plays golf and soccer.

Here, we have,

given that,

In a certain Integrated Math II class of 29 students, 6 of them play golf and 14 of them play soccer.

There are 9 students who play neither.

Number of students that play = 20

let, students play golf = A

students play soccer = B

so, given that,

n ( A) = 6 and, n ( B) = 14

so, total sample space = 29

now, P(A) = 6/29

P(B) = 14/29

and, P(students who play neither) = 9/29

we get, 6/29 + 14/ 29 + 9/29 = 29/29 = 1

i.e. there are no students who play both golf and soccer = 0

all the events are independent.

so, we have,

the probability that a student chosen randomly from the class plays golf or soccer = P(A) + P(B)

               = 6/29 + 14/ 29

               = 20/29

and, the probability that a student chosen randomly from the class plays golf and soccer = 0.

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(a). The ratio of blue marbles to all marbles as 5/14.

(b). The number of blue marbles by the number of red marbles: 5/9

(a) The ratio of blue marbles to all marbles in the bag is 5/14.

To see this, we add the number of blue marbles and the number of red marbles to get the total number of marbles, which is 5 + 9 = 14.

Then we can express the ratio of blue marbles to all marbles as 5/14.

(b) The ratio of blue marbles to red marbles is 5/9. To see this, we divide the number of blue marbles by the number of red marbles: 5 ÷ 9 = 0.55555..., which we can simplify to 5/9.

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After considering all the given data we conclude that the binomial that is a factor of the polynomial P(x) is (x-4), which is Option C

As it is seen in the context of the remainder theorem of polynomials, in the event that a  polynomial function f(x) is divisible by a factor (x-a), the remaining reminder is zero, now the generated value of f(a) will be also zero. As it is given that the value of the polynomial function P(4)+2=2,
therefore, the value can be restructured as,
P(4) + 2 = 2
P(4) = 0
Therefore, (x-4) is a factor of P(x).
A  polynomial that is the summation of two monomial  is considered a binomial.
For instance , x + 2 is a binomial, here x and 2 are two separate terms.
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The correct answer for the statement is,

⇒  Alternative Hypothesis

Hence, Option D is true.

We have to given that;

To complete the sentence,

A statement is,

That is referred to as ___ and is accepted if the sample data provide enough evidence to refute the null hypothesis.

Now, We know that;

Definition of Alternative Hypothesis,  

When the sample data support the null hypothesis sufficiently, a statement is taken as true, yet it is untrue.

Hence, Complete sentence is,

A correct statement which is accepted for the sample data provided sufficient evidence that the null hypothesis is false, is called Alternative Hypothesis.

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The upper quartile line of the box plot be placed at D

The left and right sides of the box are the lower and upper quartiles.

In the given figure the A represents the minimum value

The point E represents the maximum value

The point B is the lower quartile of the data

The point C is median of the data

The point D is the upper quartile which is 56

Hence, the upper quartile line of the box plot be placed at D

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The L.C.M of c, 3c , 3 is 3c.

The L.C.M of c, 3c, and 3, we first need to factor each term:
c cannot be factored any further.
3c can be factored as 3 x c.
3 cannot be factored any further.
Next, we look for the highest common factors among the factors of these terms.

The only common factor is 3, which is included in both 3c and 3.
Therefore, the L.C.M of c, 3c, and 3 is 3c.
The L.C.M (Least Common Multiple) of c, 3c, and 3 can be found by analyzing the factors of each term.
For c, the only factor is c itself.
For 3c, the factors are 3 and c.
For 3, the only factor is 3.
Now, find the LCM by taking the highest power of each unique factor:
LCM(c, 3c, 3) = 3 * c = 3c

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Answer:

Refer to the step-by-step.

Step-by-step explanation:

Verify the given identity.

[tex]E_0\cos^4(\theta)=E_0(\frac{1}{2} +\frac{\cos(2\theta)}{2} )^2[/tex]

Pick the more complex side to manipulate, in this case it is the R.H.S.

(1) - Apply the following double-angle identity

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Double-Angle Identity:}}\\\\\cos(2A)=1-2\sin^2(A)\end{array}\right}[/tex]

[tex]E_0(\frac{1}{2} +\frac{\cos(2\theta)}{2} )^2\\\\\Longrightarrow \boxed{ E_0\Big(\frac{1}{2} +\frac{1-2\sin^2(\theta)}{2}\Big )^2}[/tex]

(2) - Split of the right fraction

[tex]E_0(\frac{1}{2} +\frac{1-2\sin^2(\theta)}{2} )^2\\\\\Longrightarrow E_0(\frac{1}{2} +\frac{1}{2} -\frac{2\sin^2(\theta)}{2})^2\\\\\Longrightarrow \boxed{E_0(1 -sin^2(\theta))^2}[/tex]

Apply the following Pythagorean identity

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Pythagorean Identity:}}\\\\1-\sin^2(A)=\cos^2(A)\end{array}\right}[/tex]

[tex]E_0(1 -sin^2(\theta))^2\\ \\\Longrightarrow E_0(\cos^2(\theta))^2\\\\\therefore \boxed{E_0\cos^4(\theta)=E_0\cos^4(\theta)}[/tex]

Thus, the identity is verified.

It has been proven and verified that [tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{cos2 \theta}{2} )^2[/tex] below.

In Mathematics and Geometry, the standard equation of a cosine function is represented or modeled by the following mathematical equation (formula):

y = Acos(Bx - C) + D

Where:

In this exercise, you are required to prove that the right-hand side of the cosine function is equal to left-hand side of the cosine function;

[tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{cos2 \theta}{2} )^2[/tex]

From the double-angle formulas, we have:

2sin²θ = 1 - cos2θ

cos2θ = 1 - 2sin²θ

Next, we would evaluate the right-hand side of the cosine function by substituting "1 - 2sin²θ" for cos2θ as follows;

[tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{1-2sin^2 \theta}{2} )^2\\\\E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{1}{2} -\frac{2sin^2 \theta}{2})^2\\\\E_0cos^4 \theta = E_0(1 -\frac{2sin^2 \theta}{2})^2\\\\E_0cos^4 \theta = E_0(1 -sin^2 \theta)^2\\\\[/tex]

E₀cos⁴θ = E₀(1² - (sin²θ)²)

E₀cos⁴θ = E₀(1 - sin⁴θ)  ⇒ (Verified).

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Answer:

  8

Step-by-step explanation:

You want to know the measure of segment XY if ∆XYZ ≅ ∆MNL and MN = 8.

Segment XY is named using the first two vertices listed in the name of ∆XYZ. That means the segment is the same length as the one named by the first two vertices listed in the name of congruent ∆MNL, segment MN.

Segment MN is given as 8 units long. Segment XY is congruent, so is also 8 units long.

  XY = 8 units

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The solution is: the interest rate and principal is 6% and Rs 65,000

The interest rate, r = 6% and the principal, P = Rs 65,000

Here, we want to find the interest rate and principal

Compound interest:

A = P(1 + r/n)^t

Simple interest :

I = P * r * t

Simple interest for 2 years = Rs 7800

Simple interest for 1 year = Rs 7800 / 2

= Rs 3900

Compound interest for 2 years = Rs 8034

Compound interest for the second year = Rs 8034 - Rs 3900

= Rs 4134

Interest on Rs 3900 = Rs 4134 - Rs 3900

= Rs 234

Therefore,

Interest rate, r = 234/3900 × 100

= 0.06 × 100

r = 6%

Recall,

Simple interest :

I = P * r * t

Then,

P = I / r * t

= 3900 / 6% * 1

= 3900 / 0.06

= 65,000

P = Rs 65,000

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complete question:

compound interest on a sum of money for 2 years compounded annually is Rs 8034 simple interest on the same sum for the same period and at the same rate is Rs 7800 find the sum and the rate of interest​

A transformation that would take Figure A to Figure B include the following: D. A counterclockwise rotation of 90° about the origin.

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise around the origin to vertices, the coordinates of the vertices of the image are as follows:

(x, y)                               →                (-y, x)

Ordered pair (-4, 9)        →           Ordered pair (-9, -4)

In conclusion, we can logically deduce that a rotation of 90° counterclockwise around the origin is a type of transformation that would take Figure A to Figure B.

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The maximum rate of change of f(x, y, z) = e³ˣ × sin(y + 2z) at (3, -1, 1) is |∇f(3, -1, 1)| = √(10e¹⁸ × sin²(1) + 5e¹⁸ × cos²(1)), and the direction in which this maximum rate of change occurs is given by the unit vector u = (∇f(3, -1, 1) / |∇f(3, -1, 1)|).

To find the maximum rate of change of the function f(x, y, z) = e³ˣ × sin(y + 2z) at the point (3, -1, 1) and the direction in which this maximum rate of change occurs, we can use the gradient vector.

The gradient vector of a function represents the direction of the maximum rate of change, and its magnitude represents the maximum rate of change itself. The gradient vector is given by:

∇f(x, y, z) = (∂f/∂x, ∂f/∂y, ∂f/∂z)

Let's calculate the partial derivatives of f(x, y, z) with respect to each variable:

∂f/∂x = 3e³ˣ × sin(y + 2z)

∂f/∂y = e³ˣ × cos(y + 2z)

∂f/∂z = 2e³ˣ × cos(y + 2z)

Now, we can evaluate these partial derivatives at the point (3, -1, 1):

∂f/∂x = 3e³ ˣ ³ × sin(-1 + 2 × 1) = 3e⁹ × sin(1)

∂f/∂y = e³ ˣ ³ × cos(-1 + 2 × 1) = e⁹ × cos(1)

∂f/∂z = 2e³ ˣ ³ × cos(-1 + 2 × 1) = 2e⁹ × cos(1)

Therefore, the gradient vector ∇f(3, -1, 1) is:

∇f(3, -1, 1) = (3e⁹ × sin(1), e⁹ × cos(1), 2e⁹ × cos(1))

The magnitude of the gradient vector represents the maximum rate of change of the function at the given point. Let's calculate the magnitude:

|∇f(3, -1, 1)| = √((3e⁹ × sin(1))² + (e⁹ × cos(1))² + (2e⁹ × cos(1))²)

= √(9e¹⁸ × sin²(1) + e¹⁸ × cos²(1) + 4e¹⁸ × cos²(1))

= √(10e¹⁸ × sin²(1) + 5e¹⁸ × cos²(1))

To find the direction in which the maximum rate of change occurs, normalize the gradient vector by dividing it by its magnitude:

u = ∇f(3, -1, 1) / |∇f(3, -1, 1)|

The direction vector u represents the unit vector pointing in the direction of the maximum rate of change.

Therefore, the maximum rate of change of f(x, y, z) = e³ˣ × sin(y + 2z) at (3, -1, 1) is |∇f(3, -1, 1)| = √(10e¹⁸ × sin²(1) + 5e¹⁸ × cos²(1)), and the direction in which this maximum rate of change occurs is given by the unit vector u = (∇f(3, -1, 1) / |∇f(3, -1, 1)|).

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Answer:

25 sheets

Step-by-step explanation:

=42-17 = 25 sheets

Answer:

25 sheets of paper

Step-by-step explanation:

42-17=25

Descriptive Statistics for Variables in the Study

Variable Mean Standard Deviation Skewness Kurtosis

Variable1 10.2 2.1 -0.15 2.8

Variable2 15.3 3.2 0.10 3.2

Variable3 20.1 4.5 -0.05 2.9

Variable4 8.9 1.8 0.30 3.5

Based on Table 1, we can see that all variables have skewness and kurtosis values within the acceptable range of -2 to +2. This suggests that the assumption of normality is not violated, and the variables are normally distributed.

The results of the normality test indicate that the assumption of normality is not violated, and the variables are normally distributed. Therefore, we can proceed with the correlation analysis.

Skewness measures the degree of asymmetry of the distribution, with positive values indicating a right-skewed distribution, negative values indicating a left-skewed distribution, and a value of zero indicating a symmetrical distribution.

Kurtosis measures the degree of peakedness of the distribution, with positive values indicating a more peaked distribution than a normal distribution, negative values indicating a less peaked distribution than a normal distribution, and a value of zero indicating a normal distribution.

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The procedure step that the student could follow to accomplish the goal of increasing the force of the electromagnet would be C. Add more batteries in series at location 3.

Adding batteries in a series has the effect of increasing the electromagnet's force by augmenting the voltage applied to the wire coil.

The intensity of the magnetic field produced by an electromagnet corresponds directly to the magnitude of current coursing through the wire coil and the number of wire coils present in the magnet respectively. Meanwhile, the amount of current that travels through said coil is intrinsically related to the resistance of the coil itself and the applied voltage across it.

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Step-by-step explanation:

To find the expected value of the number of bids won, E(X), we need to multiply each value of X with its corresponding probability and then sum these products.

E(X) = (X1 * P1) + (X2 * P2) + (X3 * P3)

Here, X1 = 0, X2 = 1, X3 = 2, and their corresponding probabilities are P1 = 0.81, P2 = 0.18, and P3 = 0.01.

E(X) = (0 * 0.81) + (1 * 0.18) + (2 * 0.01)

E(X) = (0) + (0.18) + (0.02)

E(X) = 0.20

The expected value of the number of bids won is 0.20.

The length of the pool is 5 meters

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

The length of the pool is calculated as

Length = Surface area / Width

substitute the known values in the above equation, so, we have the following representation

Length = 20/ 4

EValuate

Length = 5

Hence, the length is 5 meters

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The length of wire is 82.78 foot.

After guiding wire,

It form a right angle triangle which have

One angle is of 65 degree

perpendicular = 75 foot

And we have to find hypotenuse of the triangle which is length of wire.

Since we know that,

The trigonometric ratio sin is the ratio of opposite side of angle and

hypotenuse.

Therefore,

⇒ Sin65 = 75/hypotenuse

⇒ 0.906 = 75/hypotenuse

⇒  hypotenuse = 82.7 foot

Since hypotenuse of triangle represents  length of wire

So, required length of wire is 82.7 foot.

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