please help me on this will give you brainliest

Answer:

There's no A so I'm going to assume you meant X

X = 23

Step-by-step explanation:

X is equal to 23, because 23 - 18 = 5

or 5 + 18 = 23

Because VY and XY line WT is a bisector

Answer:

angle bisector

Step-by-step explanation:

hope this helps

The answer to the integral is -1/6.

To evaluate the integral below ∫3πsin4(2πx)cos3(2πx)dx,

we can use the trigonometric identity sin2Acos2A

= 1/4sin(4A).

we have the integral∫3πsin4(2πx)cos3(2πx)dx

= 1/2∫3πsin2(2πx)cos2(2πx)sin2(2πx)cos(2πx)dx

= 1/2∫3πsin2(2πx)cos2(2πx)(1-sin2(2πx))cos(2πx)dx

= 1/2∫3πsin2(2πx)cos2(2πx)(cos(2πx)-cos3(2πx))dx

= 1/2∫3π(sin2(2πx)cos(2πx)-sin2(2πx)cos3(2πx))cos2(2πx)dx

= 1/8∫3π(2sin(4πx)-sin(6πx))cos2(2πx)dx.

Let u= 2πx and du= 2πdx,

then we have the integral as 1/8∫6π(sin2u-sin3u)cos2udu

= 1/8[∫6πsin2ucos2udu-∫6πsin3ucos2udu]

We solve the first integral as follows; using the identity sin2ucos2u= 1/4sin(4u), we have the integral as

∫6πsin2ucos2udu

= 1/4∫6πsin(4u)du

= -1/16cos(4u)]6π03π

= -1/16cos(4(6π))-(-1/16cos(4(0)))

= 0.

We solve the second integral using the identity sin3u= 3sinu-4sin3u,

we have∫6πsin3ucos2udu

= 1/3∫6πsinudu-4/3∫6πsin3udu

= 1/3[-cos(6π)+cos(0)]-4/3[-1/12cos(4(6π))+1/12cos(4(0))]

= 4/3.

To complete our solution, we substitute our values into the integral as 1/8[0-4/3]

= -1/6.

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From the data points given the linear equation in slope-intercept form is y = -1/2x + 4.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The first two data points are - (-3,5.5) and (-1,4.5)

The slope-intercept form of the equation is -

y = mx + b

m represents the slope of the linear equation.

To find the value of m use the formula -

(y2 - y1)/(x2 - x1)

Substitute the values into the equation -

(4.5 - 5.5)/[(-1) - (-3)]

Use the arithmetic operation of subtraction -

(-1)/(-1 + 3)

-1 / 2

So, the slope m is m = -1/2

Now, the equation becomes y = -1/2x + b

To find the value of b substitute the  values of x and y in the equation -

5.5 = -1/2(-3) + b

5.5 = 3/2 + b

5.5 = 1.5 + b

b = 5.5 - 1.5

b = 4

So, now the equation becomes - y = -1/2x + 4

The graph for the equation is plotted.

Therefore, the equation is y = -1/2x + 4.

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Answer:

Step-by-step explanation:

Use the Law of Sines for this. Set it up as follows:

\(\frac{sin(x)}{6}=\frac{sin(61)}{6.2}\)  Cross multiply:

6.2sin(x) = 6sin(61) and solve for the term with the unknown in it:

\(sin(x)=\frac{6sin(61)}{6.2}\)

Work on the right side first. Plug that into your calculator to get

sin(x) = .8464061682

Now the problem comes down to "what angle has a sine of .8464061682?" This requires the use of the inverse button on your calculator. Hit 2nd, then sin, and you will see on your screen:

\(sin^{-1}(\)

After that open parenthesis enter that big long decimal and hit equals. You should get an angle measure of 57.822 degrees. Not sure what you are rounding to.

Answer:

Step-by-step explanation:

x + 8 < - 28

x < - 28 - 8

x < - 36

Option A is the correct answer

Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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soy uncarack  diijrjrrrrrrrrrrrrrrrrrrrrrre

Answer:

1/x = 1/4 + 1/3

Step-by-step explanation:

In 4 hours Bethany did the whole fraction 1 of the house.

In 1 hour he would do 1/4 of it.

In 3 hours Colin did the whole fraction 1 of the house.

In 1 hour he would do 1/3 of it.

In 1 hour they would both do (1/4 + 1/3)

If it takes both of them x hours to finish 1 whole fraction of the house.

In 1 hour they will both do 1/x

That means that:

1/x = 1/4 + 1/3

That is the equation. x can be solved for.

Answer:

y = -0.5x + 1

Step-by-step explanation:

The slope intercept form of a line is given by:

y = mx + b

where m is the slope of the line and b is the y-intercept (i.e. the point at which the line crosses the y-axis). To find the equation of a line using two points, we can use the slope formula to calculate the slope, then use one of the points to find the y-intercept.

The slope of a line is given by:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates of the two given points into this formula, we get:

m = (-1 - 1) / (4 - 0) = -2 / 4 = -1/2

Now that we know the slope of the line, we can use one of the points to find the y-intercept. Let's use the point (4,-1):

y = mx + b

-1 = (-1/2) * 4 + b

-1 = -2 + b

b = 1

Therefore, the equation of the line that passes through the points (4,-1) and (0,1) in slope intercept form is:

y = (-1/2)x + 1

Note that the equation can also be written as:

y = -0.5x + 1

For a random sample of beverage cans, the test statistic or t-test value is equals to 8.1308 and null hypothesis should be rejected. So, the samples mean volume differs by 10.

We have a machine fills beverage cans. The amount of beverage in each can = 10 ounces. Consider a simple random sample of cans with Sample size, n = 8

Sample is approximately normal. We have to check the sample differ from 10 ounces and determine the test statistic value. Let the null and alternative hypothesis are defined, \(H_0 : \mu = 10 \\ H_a: \mu ≠ 10\)

Using the table data, determine the mean and standard deviations. So, Sample mean, \(\bar X = \frac{ 10.11 + 10.11 + 10.12 + 10.14 + 10.05 + 10.16 + 10.06 + 10.14}{8} \\ \)

\( = \frac{80.89}{8} \)

= 10.11125

Now, standard deviations, \(s = \sqrt {\frac{\sum_{i}(X_i -\bar X)²}{n-1}}\)

= 0.03870

degree of freedom, df = n - 1 = 7

Level of significance= 0.10

Test statistic for mean : \(t = \frac{\bar X - \mu}{\frac{s}{\sqrt{n}}}\)

\( = \frac{10.11 - 10}{\frac{0.03871} {\sqrt{8}}}\)

= \( \frac{0.11 }{\frac{0.03871}{\sqrt{8}}}\)

= 8.1308

The p-value for t = 8.1308 and degree of freedom 7 is equals 0.0001. As we see, p-value = 0.0001 < 0.1, so null hypothesis should be rejected. So, the sample mean volume differs from 10 ounces.

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Complete question:

a machine that fills beverage cans is supposed to put 10 ounces of beverage in each can. The below table contains are the amounts measured in a simple random sample of eight cans. assume that the sample is approximately normal. can you conclude that sample mean volume differs from 10 ounces? compute the value of the test statistic at 0.05 level of significance.

The height of the pillar is 14 feet.

We can use the ratio of the building's height to the length of its shadow to solve for the pillar's height and apply it to the pillar as well. This is because similar-shaped objects will produce shadows that are proportional to their size.

Let h represent the pillar's height, and let's establish a proportion:

height of building / length of building's shadow = height of pillar / length of pillar's shadow

Substituting the given values:

70 / 50 = h / 10

We can simplify this proportion by cross-multiplying:

70 x 10 = 50h

700 = 50h

And solving for h:

h = 700 / 50 = 14

Therefore, the height of the pillar is 14 feet.

In conclusion, we can solve for the pillar's height by establishing a ratio between the building's height and the length of its shadow and applying that ratio to the pillar.

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Maximize Z = -2x1 + x2 - 4x3 + 3x4 subject to the following constraints:

x1 + x2 + x3 + 2x4 + s1 = 4,

-x1 + x3 + x4 - s2 = -1,

2x1 + x2 + s3 = 2,

and x1 + 2x2 + x3 + 2x4 = 2, where x1, x2, x3, x4, s1, s2, s3 ≥ 0.

To reformulate the given problem in the standard form of a linear programming model, we need to convert all the inequalities into equations and express all variables as non-negative.

The standard form of a linear programming problem is as follows:

Maximize (Z) = c1x1 + c2x2 + c3x3 + c4x4

Subject to:

a11x1 + a12x2 + a13x3 + a14x4 = b1

a21x1 + a22x2 + a23x3 + a24x4 = b2

a31x1 + a32x2 + a33x3 + a34x4 = b3

an1x1 + an2x2 + an3x3 + an4x4 = bn

x1, x2, x3, x4 >= 0

Now let's reformulate the given problem:

Maximize (Z) = -2x1 + x2 - 4x3 + 3x4

Subject to:

x1 + x2 + x3 + 2x4 <= 4

-x1 + 0x2 + x3 + x4 >= -1

2x1 + x2 + 0x3 + 0x4 <= 2

x1 + 2x2 + x3 + 2x4 = 2

x1, x2, x3, x4 >= 0

The reformulated linear programming problem in standard form is as follows:

Maximize (Z) = -2x1 + x2 - 4x3 + 3x4

Subject to:

x1 + x2 + x3 + 2x4 + s1 = 4

-x1 + x3 + x4 - s2 = -1

2x1 + x2 + s3 = 2

x1 + 2x2 + x3 + 2x4 = 2

x1, x2, x3, x4, s1, s2, s3 >= 0

Note: The reformulated problem includes slack variables s1, s2, and s3 to convert the inequalities into equations, and all variables are non-negative.

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The recursive formula is f(n+1)= f(n)-5.

Given sequence :

f(1)= 6, n≥1.

Let f(n) denote the nth term of the given sequence.

f(1)= 6

f(2)= 1 = f(1)-5

f(3)= -4 = 1-5= f(2) -5

f(4)= -9 = 1-10 = f(2)-10

and so on

Hence, the recursive formula is f(n+1)= f(n)-5.

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Answer:

24%

Step-by-step explanation:

we subtract to see how much it increased

62-50=12

Now divide 12 by 50 to get percent

12/50

0.24

0.24x100

24%

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The Measure of ∠BOC is 50 degrees.

The Angle Addition Postulate states that if point B lies in the interior of angle AOC, then the measure of angle AOB plus the measure of angle BOC is equal to the measure of angle AOC. Mathematically, it can be expressed as:

m∠AOB + m∠BOC = m∠AOC

Here are a few examples to illustrate how to use the Angle Addition Postulate:

Example 1:

Given that m∠AOB = 60 degrees and m∠BOC = 30 degrees, find the measure of ∠AOC.

Using the Angle Addition Postulate:

m∠AOB + m∠BOC = m∠AOC

60 + 30 = m∠AOC

90 = m∠AOC

Therefore, the measure of ∠AOC is 90 degrees.

Example 2:

If m∠AOB = 100 degrees and m∠AOC = 150 degrees, find the measure of ∠BOC.

Using the Angle Addition Postulate:

m∠AOB + m∠BOC = m∠AOC

100 + m∠BOC = 150

m∠BOC = 150 - 100

m∠BOC = 50 degrees

Therefore, the measure of ∠BOC is 50 degrees.

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The volume of the cone, to the nearest whole number, is: 50 cm³.

The volume of a cone is defined as the amount of space it contains. The volume can be calculated using the formula:

Volume of cone = 1/3 × π × r² × h, where h is the height of the cone, and r is the radius of the cone.

Given the parameters:

Plug in the values:

Volume of the cone = 1/3 × π × 4² × 3

Volume of the cone = 1/3 × π × 16 × 3

Volume of the cone = 16π

Volume of the cone = 50 cm³

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Step-by-step explanation:

Answer:

Step-by-step explanation:

13824 = 2a*3b

13824= 6ab

Ab = 13824/6

A= 13824/b

B= 13824/a

At the production level of 40 units, profit is maximized and the profit at this production level is $64,000.

Revenue is given by R(q) = 600q and cost is given by C(q) = 10,000 + 5q2. Profit is given by P(q) = R(q) - C(q).Therefore, P(q) = 600q - (10,000 + 5q2) or P(q) = -5q2 + 600q - 10,000. The profit is maximized at the production level where the derivative of P(q) is equal to zero.The derivative of P(q) is given by P'(q) = -10q + 600. Setting this to zero, we get -10q + 600 = 0 or q = 60. However, this is the maximum point of the revenue function R(q) and not the profit function P(q).To determine the maximum point of P(q), we need to find the second derivative of P(q) which is given by P''(q) = -10. Since P''(q) is negative, the maximum point of P(q) occurs at the production level q = 40. At q = 40, P(q) = -5(40)2 + 600(40) - 10,000 = $64,000.

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The paths of two particles are described by parametric equations. The first particle follows a circular path, while the second particle follows a path with both circular and linear components.

We need to graph the paths and determine the number of points of intersection.

Additionally, we need to find the collision point where the particles occupy the same position at the same time.

Lastly, we need to determine if there is a collision when the x-coordinate of the second particle is modified.

(a) To graph the paths of both particles, we plot the parametric equations x1 = 3sin(t), y1 = 2cos(t) and x2 = -3 + cos(t), y2 = 1 + sin(t) on a coordinate plane for 0 ≤ t ≤ 2π. The paths of the particles will be represented by curves. By analyzing the graph, we can count the number of points of intersection.

(b) To find the collision point, we need to find the values of t where x1 = x2 and y1 = y2 simultaneously. By setting 3sin(t) = -3 + cos(t) and 2cos(t) = 1 + sin(t), we can solve for t. The obtained value(s) of t will give us the collision point (x, y) where the particles occupy the same position at the same time.

(c) If the x-coordinate of the second particle is modified to x2 = 3 + cos(t), we need to repeat the process of finding the collision point. By setting 3sin(t) = 3 + cos(t) and 2cos(t) = 1 + sin(t), we solve for t. Depending on the solution(s) of t, we can determine if there is still a collision or not.

Please note that since this question involves graphing and solving equations, it is best to draw the graphs and solve the equations visually or using numerical methods to obtain specific values.

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The dimension of the rectangular model shows that the length is 9 inches and the width is 8 inches

The area of a rectangle is the multiplication of the length and the width of the rectangle.

The area of the rectangle is expressed as:

Area (A) = length (L) × width (w)

A = l × w

Given that:

72 = (2x - 7) × (x)

72 = 2x² - 7x

2x² - 7x - 72 = 0

Using the quadratic calculator

x = 8 or x = -9/2

However, since our length/width distance can't be negative, then:

x = 8

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Answer: 3/7 (Smallest), 0.43, 7/16, 43.8% (largest)

Step-by-step explanation:

0.43

3/7 = 0.4286

43.8% = 0.438

7/16 = 0.4375

The volume of the slice = π(64 - x²) cm³, and the exact volume of the cylinder = 128π cm³.

Explanation:

Given values: Radius of the cylinder = 8 cm height of the cylinder = 6 cmWidth of slice = 1 cmLet us find the expression for the volume of the slice used in the Riemann sum representing the total volume of the cylinder:

Volume of slice = (Area of the slice) × (Width of the slice)

Area of slice = πr² where, r is the radius of the circular slice.

The volume of slice = πr² × (Width of the slice)For a general rectangular slice of the cylinder with a width of 1 cm and radius r, we get:r = 8 - x (since the slice is taken at a distance of x from the end of the cylinder)

Width of slice = Δx = 1 cmArea of slice = π(8 - x)²Volume of slice = π(8 - x)² × (1) = π(64 - 16x + x²) cm³Let us write a definite integral that represents the exact volume of the cylinder:

To evaluate the definite integral, we will use the Riemann sum, with Δx = 0.001.Number of slices, n = (8 - 0)/0.001 = 8000Interval [a, b] = [0, 8]Height of each slice, f(xi) = π(64 - 16xi + x²)Definite integral = \(\large\int\)f(x)dx = \(\lim_{n\to\infty}\sum_{i=1}^n f(xi)Δx\)= \(\lim_{n\to\infty}\sum_{i=1}^n π(64 - 16xi + x²)Δx\)= \(\lim_{n\to\infty}\) π\(\sum_{i=1}^n\) (64 - 16xi + x²)Δx= π\(\large\int\)[64 - 16x + x²]dx= π[(64x - 8x² + (1/3)x³)]8 to 0= π[(64 × 8 - 8 × 8² + (1/3) × 8³) - (64 × 0 - 8 × 0² + (1/3) × 0³)]= 128π cm³

Hence, the volume of the slice = π(64 - x²) cm³, and the exact volume of the cylinder = 128π cm³.

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Answer:

4v^2 + 6v + 3

Step-by-step explanation:

The derivatives of the functions are:

A) y = 93x is dy/dx = 93.

B) y = ln(3x² + 2x + 1) is dy/dx = (6x + 2)/(3x² + 2x + 1).

C)  y = x²e⁽⁴ˣ⁾ is dy/dx = 2xe⁽⁴ˣ⁾ + 4x²e⁽⁴ˣ⁾

D) y = e(sin(3x)) is dy/dx = 3e(sin(3x))cos(3x).

E) y = 8 + 3x is dy/dx = 3.

A) For the function y = 93x, we use the power rule to find the derivative:

The power rule states that if we have a function of the form y = cxⁿ, where c and n are constants, the derivative is given by dy/dx = cnx⁽ⁿ⁻¹⁾.

So, c = 93 and n = 1.

Applying the power rule:

dy/dx = 1 * 93 * x⁽¹⁻¹⁾ = 93 * x⁰ = 93.

Therefore, the derivative of y = 93x is dy/dx = 93.

B) Function y = ln(3x² + 2x + 1):

Here, use the chain rule. The chain rule states that for a composition of functions, y = f(g(x)), the derivative is dy/dx = f'(g(x)) * g'(x).

f(u) = ln(u) and g(x) = 3x² + 2x + 1.

The derivative of f(u) = ln(u) with respect to u is 1/u.

To find g'(x), we differentiate each term separately:

g'(x) = d/dx (3x²) + d/dx (2x) + d/dx (1) = 6x + 2 + 0 = 6x + 2.

Next, we apply the chain rule:

dy/dx = f'(g(x)) * g'(x) = (1/(3x² + 2x + 1)) * (6x + 2).

Therefore, the derivative of y = ln(3x² + 2x + 1) is dy/dx = (6x + 2)/(3x² + 2x + 1).

C) function y = x²e⁽⁴ˣ⁾:

We use the product rule to find its derivative.

The product rule says for a function of the form y = f(x)g(x), the derivative is given by dy/dx = f'(x)g(x) + f(x)g'(x).

Here, f(x) = x² and g(x) = e⁽⁴ˣ⁾. The derivative of f(x) = x² with respect to x is 2x.

To find g'(x), we differentiate e⁽⁴ˣ⁾ using the chain rule.

The derivative of \(e^{u}\) with respect to u is \(e^{u}\).

g'(x) = d/dx (e⁽⁴ˣ⁾) = e⁽⁴ˣ⁾) * d/dx (4x) = 4e⁽⁴ˣ⁾.

Apply the product rule:

dy/dx = f'(x)g(x) + f(x)g'(x) = 2x * e⁽⁴ˣ⁾ + x² * 4e⁽⁴ˣ⁾.

Thus, the derivative of y = x²e⁽⁴ˣ⁾ is dy/dx = 2xe⁽⁴ˣ⁾ + 4x²e⁽⁴ˣ⁾.

D) Function y = e(sin(3x)):

We use the chain rule here: It states that for a function y = f(g(x)), the derivative is dy/dx = f'(g(x)) * g'(x).

So, f(u) = \(e^{u}\) and g(x) = sin(3x).

The derivative of f(u) = \(e^{u}\) with respect to u is \(e^{u}\).

To find g'(x), we differentiate sin(3x:.

The derivative of sin(u) with respect to u is cos(u), and the derivative of 3x with respect to x is 3.

g'(x) = d/dx (sin(3x)) = cos(3x) * d/dx (3x) = 3cos(3x).

Let's, apply the chain rule:

dy/dx = f'(g(x)) * g'(x) = e(sin(3x)) * 3cos(3x).

So, the derivative of y = e(sin(3x)) is dy/dx = 3e(sin(3x))cos(3x).

E) y = 8 + 3x:

We use the power rule to find the derivative:

y = cxⁿ, where c and n are constants, and the derivative is dy/dx = cnx⁽ⁿ⁻¹⁾.

In this case, c = 3 and n = 1.

Apply the power rule:

dy/dx = 1 * 3 * x⁽¹⁻¹⁾ = 3 * x⁰ = 3.

Therefore, the derivative of y = 8 + 3x is dy/dx = 3.

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Answer:

x = 68

Step-by-step explanation:

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Answer:

x = -7

Step-by-step explanation:

f(x) = -x - 1

when f(x) = 6:

- x - 1 = 6

-x = 7                   [Add 1 to both sides]

x = -7                   [Divide both sides by -1]

The equation of the line passing through (9,11) and perpendicular to the line passing through (6,1) and (2,1) is x = 6

Find the slope of the line passing through (6,1) and (2,1):

The slope of a line passing through two points (x1,y1) and (x2,y2) is given by:

slope = (y2 - y1) / (x2 - x1)

Substituting the given coordinates, we get:

slope = (1 - 1) / (2 - 6) = 0

Therefore, the slope of the line passing through (6,1) and (2,1) is 0.

Find the slope of the line perpendicular to the line passing through (6,1) and (2,1):

The slope of a line perpendicular to a line with slope m is given by:

perpendicular slope = -1/m

Substituting the slope of the line passing through (6,1) and (2,1), we get:

perpendicular slope = -1/0 (which is undefined)

This means that the line perpendicular to the line passing through (6,1) and (2,1) is a vertical line passing through the point (6,1) and (2,1).

Write the equation of the line passing through (9,11) and perpendicular to the line passing through (6,1) and (2,1):

Since the line passing through (6,1) and (2,1) is a horizontal line with equation y = 1, the line perpendicular to it is a vertical line passing through the point (6,1) and (2,1). The equation of a vertical line passing through a point (a,b) is given by:

x = a

Substituting the value of x = 6 (since the vertical line passes through (6,1) and (2,1)), we get:

x = 6

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