Solve

81 = 8(2x + 8) + x

The exact value of the expression is 4.15

What is a trigonometric expression?

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

We are given an expression

cosec 30^0 + cosec 60^0 + cosec 90^0

We know that cosec x= 1/sinx

Substituting this in the above equation we get

1/sin30^0 + 1/sin60^0 + 1/sin90^0

Now we know from the trigonometric table

sin30^0 = 1/2

sin60^0 = [tex]\frac{\sqrt{3} }{2}[/tex]

Sin90^0 = 1

Substituting this values in the equation we get

2+ [tex]\frac{2}{\sqrt{3} }[/tex]+1

3+1.15

= 4.15

The exact value of the expression is 4.15

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The formula for estimating the population variance from the sample requires calculating the sum of squared deviations and dividing it by the number of observations. This is true for both the t-test for dependent means and the t-test for independent means.

This formula is referred to as the "variance sum of squares"or the t-test for dependent means, the formula is:

Where:

x1 = observation 1

x2 = observation 2

N = number of observations

For the t-test for independent means, the formula is:

Sample Variance = [(Σx12)/N + (Σx22)/N]/2

Where:

x1 = observation 1

x2 = observation 2

N = number of observation

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The measure of side BC is 12 units in a right  ∆ABC if the altitude CH to the hypotenuse AB intersects angle bisector AL in point D.

A right angle is defined as an angle that is exactly 90 degrees in geometry and trigonometry. If a ray is positioned so that its terminal is on a line and the angles are also equal, the angles are said to be at right angles. The phrase derives from the Latin angulus rectus, where rectus denotes the upright vertical line that is perpendicular to a horizontal base line.

Perpendicular lines—defined as lines that meet at right angles—and orthogonality—defined as the ability to intersect at right angles—are closely connected and crucial geometrical notions.

Given,

m∠CAL = m∠BAL

m∠C = 90°

AD = 8 cm

DH = 4 cm

We have to apply sine rule for ΔADH,

sinθ=opposite side/hypotenuse

sin(∠DAH)=DH/AD

=4/8

=1/2

∠DAH=sin⁻¹(1/2)

∠DAH=30°

Therefore, ∠CAB=2(∠DAH)

=2(30°)

=60°

Now, we have to apply tangent rule in  ∆AHD

tan( ∠DAH)=DH/AH

tan(30°)=4/AH

1/√3=4/AH

AH=4√3

Now, we have to apply cosine rule in ∆AHC

cos(60°)=AH/AC

1/2=4√3/AC

AC=8√3

Now, we have to apply tangent rule in ∆ACB

tan(∠CAB)=opposite side/adjacent side

tan(60°)=BC/AC

√3=BC/8√3

BC=8√3(√3)

BC=24units.

Therefore, the measure of side BC is 12 units in a right  ∆ABC if the altitude CH to the hypotenuse AB intersects angle bisector AL in point D.

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Equivalent expression is (x-1)/2x for ((1 -1/x)/2), So Option 1 is correct.

If two expressions can be written similarly or can be combined into a single, simpler phrase, then those two expressions are comparable. Additionally, you can tell if two expressions are equal if you substitute values for the variable in both and they get the same result. The numerator and denominator of equivalent fractions can be written by multiplying or dividing them both by the same value.

This is the rationale for why these fractions simplify to the same number. Equivalent ratios are two ratios that have identical values. Divide or multiply both amounts by the same number to arrive at an equivalent ratio. The method is the same as determining equivalent fractions.

Here expression is ((1 -1/x)/2)

take x as lcm then (x-1)/2x

correct option is (A).

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Correct Question:

Which expression is equivalent to the following complex fraction?

(1-1/x)/2

A) x-1/2x

B) -1/2

C) 2x-2/x

D) 2x/x-1

a)  The thrust of the propeller is  23,834 lbf

b)  The induced velocity is 8.44 mph

c)  The velocity in the downstream far field away from the propeller disc     is 161.56 mph

d) The power absorbed by the fluid is  42.7 hp

e)  the propeller power (thrust flight speed) is  4,844.08 hp

f)  The propeller efficiency is 113.6%

a)The thrust of the propeller can be calculated using the equation,

Thrust = 2πρR^2V^2, where ρ is the air density, R is the propeller radius, and V is the average velocity of the propeller disc. For sea level at a speed of 150 mph, the air density is about 0.002377 slugs/ft^3.

the thrust of the propeller can be calculated as: Thrust = 2π x 0.002377 x (6 ft)^2 x (170 mph)^2 = 23,834 lbf

b)The induced velocity can be calculated using the equation v_ind = (1/2) V ∞ [1–(V_∞/V_tip)^2]^(1/2), where V_∞ is the free stream velocity and V_tip is the tip velocity of the propeller. For the given problem, the induced velocity can be calculated as: v_ind = (1/2) x 150 mph x [1–(150 mph/170 mph)^2]^(1/2) = 8.44 mph

c) The velocity in the downstream far field can be calculated using the equation V_∞ = V_tip – v_ind, where V_tip is the tip velocity of the propeller and v_ind is the induced velocity. For the given problem, the velocity in the downstream far field can be calculated as: V_∞ = 170 mph – 8.44 mph = 161.56 mph

d)The power absorbed by the fluid can be calculated using the equation P_fluid = (1/2) ρ V_ind^3 A_disc, where ρ is the air density, V_ind is the induced velocity, and A_disc is the area of the propeller disc. For the given problem, the power absorbed by the fluid can be calculated as P_fluid = (1/2) x 0.002377 x (8.44 mph)^3 x (π x (6 ft)^2) = 42.7 hp

e)The power absorbed by the propeller can be calculated using the equation P_prop = T x V, where T is the thrust of the propeller and V is the flight speed of the aircraft. For the given problem, the power absorbed by the propeller can be calculated as: P_prop = 23,834 lbf x 150 mph = 3,575,500 ft-lbf/s = 4,844.08 hp

f)The efficiency of the propeller can be calculated using the equation η = P_prop/P_fluid, where P_prop is the power absorbed by the propeller and P_fluid is the power absorbed by the fluid. For the given problem, the efficiency of the propeller can be calculated as: η = 4,844.08 hp/42.7 hp = 113.6%

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From the figure the constant of proportionality when y is directly proportional to x² is 1/2

The ratio between two quantities that are directly proportional is the constant of proportionality.

When two quantities grow and reduce at the same rate, they are directly proportional.

The constant of proportionality is solved by taking points from the graph\

using point (2, 2)

y is directly proportional to x² writing in equation form

y α x²

y = kx²

k = y / x²

plugging in values from the graph

k = 2 / 2²

k = 2 / 4

k = 1/2

The constant of proportionality is equal to 1/2

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Answer:

  D.  70°32'

Step-by-step explanation:

You want the angle represented by arccos(0.333) to the nearest minute.

The attached calculator shows the angle in degrees (70.54903521713) and in degrees, minutes, and seconds (70°32'56.53"). There are 60 seconds in a minute, so the number of seconds being more than 30 means the minutes should be rounded up to ...

  70°33'

The closest answer choice is D. 70°32'.

The value of the surd when simplified is 1/6

We should recall that surd is the square root of all irrational numbers, simplification involves making it more simpler.

The given question is [tex]\frac{1}{(1-\sqrt{5 })^{2} } + \frac{1}{(1+\sqrt{5} )^{2} }[/tex]

We shall be simplifying the expression in parts

From difference of two squares

(1)/[(1-√5)(1+√5) = 1+5 = 1/6

The second part is 1/[(1+√5)(1+√5) = 1/(1+√10+5)

= 1/(6+√10)

Joining the two parts to get

1/6 + 1/(6+√10

Simplifying the fractions

(√10+1)/(6+√10)

= 1/6

Therefore the value of the expression is 1/6

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The degrees of freedom (df): For a chi-square test of independence, the df is (number of variable 1 groups − 1) * (number of variable 2 groups − 1).

Under the null speculation and sure conditions (mentioned below), the check statistic follows a Chi-Square distribution with stages of freedom identical to ( r − 1 ) ( c − 1 ) , wherein is the quantity of rows and is the quantity of columns.

The quantity of levels of freedom in a chi-rectangular goodness-of-healthy check is the quantity of classes minus the quantity of parameters anticipated. The quantity of levels of freedom in a chi-rectangular goodness-of-healthy check is the quantity of classes minus the quantity of parameters anticipated minus one.

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Complete question:

what degrees of freedom should be used to conduct a chi-squared test of independence using this table?

Using substitution method, the system of linear equations showed that there 27 and 35 quarters and nickel respectively

System of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.

To solve this problem, we have to write a system of linear equations which consist of two linear equations.

Let;

x + y = 62...eq(i)

0.25x + 0.05y = 8.50 ...eq(ii)

Using substitution method

From equation (i)

x + y = 62

x = 62 - y ...eq(iii)

Put equ(iii) into eq(ii)

0.25( 62 - y) + 0.05y = 8.50

y = 35

Put y = 35 in equation (i)

x + 35 = 62

x = 27

The number of quarters and nickels are 27 and 35 respectively

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She needs to bike for 66 miles on the last day so that her mean is 54 miles per day.

Mean, in terms of math, is the total added values of all the data in a set divided by the number of data in the set.

To calculate the miles Marthina needs to bike so that her mean is 54 mile per day, we use the formula below.

Formula:

Where:

Let y be the miles she biked for the last day.

From the question,

Given:

Substitute these values into equation 1 and solve for y

Hence, she needs to bike for 66 miles on the last day.

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According to the data provided, the regression line equation is given by

y=2.83+0.52x.  The non-linear characteristics of data is ignored by the regression line.

The most popular statistical method for simulating a link between two sets of variables is linear regression. As a result, a linear regression equation that can be applied to data is created.

The required formula is:

[tex]y= a + b_{yx}x[/tex]

[tex]b_{yx} = \frac {n \sum xy - \sum x \sum y}{n \sum x ^ {2} - (\sum x) ^ {2}}[/tex]

[tex]a = \bar y - b_{yx} \bar x[/tex]

[tex]\bar x = 8.81 \\\bar y = 7.45\\\sum x ^ {2} =947\\\sum xy = 770.95[/tex]

[tex]b_{yx} = 0.52[/tex]

[tex]a=2.83[/tex]

y=2.83+0.52x .

In scatter plot, Non-linear characteristics is ignored by the regression line.

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Answer:

3K

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

-11+2/3x(-12)+4/1/8 Identify the sign

-11-\\\2/3x12+4/1/8 multiplying and inverting

-11-2/3x12+4x8 Simplify

-11 -2x4+4x8

-11-8+32

13

Answer: 1

Step-by-step explanation:

The probability distribution of rolling a die is

P(1) = 1/6, P(2) = 1/6, P(3) = 1/6, P(4) = 1/6, P(5) = 1/6, P(6) = 1/6

Given that,

Let T be the outcome of a roll with a fair die.

Then

T = {1, 2, 3, 4, 5, 6}

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The probability of getting 1 P(1) = 1/6

The probability of getting 2 P(2) = 1/6

The probability of getting 3 P(3) = 1/6

The probability of getting 3 P(3) = 1/6

The probability of getting 4 P(4) = 1/6

The probability of getting 5 P(5) = 1/6

The probability of getting 6 P(6) = 1/6

Therefore, the probability distribution of rolling a die has been found

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The area of this rectangle is 0.105C that can be calculated by implementing the dimensions of length and breadth.

The area of rectangle involves the length and breadth.

Suppose length of rectangle be a,

Height of rectangle (1-a)^3

Area, A= a*(1-a)^3

dA/da = -3a(1-a)^2+(1-a)^3 = 0

a = 1, 0.25

Thus, Area (max) = 0.25*0.75^3 = 0.105

In this case

Height of rectangle C(1-a)^3

Area, A= Ca*(1-a)^3

dA/da = C[-3a(1-a)^2+(1-a)^3] = 0

a = 1, 0.25

Thus, Area (max) = 0.25*0.75^3*C = 0.105C

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The properties of the unique solution of the system AX=B depend on the matrix of the system. That is, it depends only on the coefficients on the left side. RHS configuration is not the issue.

The method of least squares is an important statistical technique practiced to find the regression line or the best fit line for a particular pattern. This procedure is described by an equation with specific parameters. The method of least squares is used liberally in analysis and regression. In regression analysis, this method is a standard approach to approximating a system of equations using more equations than unknowns.

The least squares method actually defines a solution to minimize the resulting sum of squares or error for each equation. Find the formula for the sum of squared errors to help find the variation in the observed data.

The least squares method is often used in data fitting. A best fit result is assumed to reduce the sum of squared errors or residuals reported as the difference between the observed or experimental values ​​and the corresponding fitted values ​​in the model.

Linear System of Equation:

A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.

A linear system of three variables determines the collection of levels. Intersection is the solution.

For example,

3x + 2y -z =1 , 2x - 2y + 4z =-2

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By solving a linear equation, it can be calculated that the value of 3x - 4 is 8

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

The given linear equation is

[tex]\frac{3}{4}x - 2 = 1\\\frac{3}{4}x = 1 + 2\\\frac{3}{4}x = 3\\x = \frac{3 \times 4}{3}\\x = 4\\[/tex]

Value of 3x - 4  = [tex]3 \times 4 - 4 \\[/tex]

                          = 12 - 4

                          = 8

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The two different expressions to represent the total cost of 3 liters of shampoo where L is the regular price of a liter bottle are;

Let

Total cost = Regular price of 2 liters of shampoo + discounted price of the 3rd liter

= (L × 2) + (L - 30% of L)

= 2L + (L - 0.3L)

= 2L + (0.7L)

Total cost = 2.7L

In conclusion, the expressions which can be used to represent the situation are;

2L + (L - 0.3L)

2.7L

Complete question:

Emilio buys liter bottles of shampoo when the store has the promotion shown. Write an expression in two different ways to represent the total cost 0f 3 liters of shampoo. Let L be the regular price of a liter bottle.

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Answer:

(x - 3)² + (y + 3)² = 9

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

the radius r is the distance from the centre to a point on the circle.

given (3, - 3 ) is the centre and (3, 0 ) is a point on the circle

since the x- coordinates of both points are 3 then r is the absolute value of the difference of the y- coordinates, that is

r = | - 3 - 0 | = | - 3 | = 3

then equation of circle is

(x - 3)² + (y - (- 3) )² = 3² , that is

(x - 3)² + (y + 3)² = 9

The multiplication of polynomial in descending powers is,

32x^2 + 68x + 21.

What is polynomial?

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x^2 + 4x + 7 is an illustration of a polynomial with a single indeterminate x.

Consider, the given polynomials

(8x + 3)(4x + 7)

Taking multiplication,

8x(4x + 7) + 3(4x + 7)

Simplifying,

32x^2 + 56x + 12x + 21

32x^2 + 68x + 21

Hence, the multiplication of polynomial in descending powers is,

32x^2 + 68x + 21.

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SAS triangle congruence theorem can be used to prove the triangle are congruent.

A triangle is a simple polygon with three sides and three interior angles. It is one of the basic forms of geometry in which three vertices are connected, and is represented by the symbol △. There are different types of triangles, classified based on their sides and angles. Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other. The congruence symbol is "≅".

Angle is the space between two intersecting lines or surface at or close to the point where they meet.

The SAS Postulate says that is the  triangles are congruent if any pair of the  corresponding sides and I their included angles are be congruent.

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The given two triangles are congruent by  Side Side Side congruency.

As from the question we get to know that ΔRST and Δ UTS  

and

RS = UT

RT = US

The proof for the above claim

RS = UT    {given}

RT = US    {given}

ST = TS     {Common}

Therefore, we can say that by SSS theorem ΔRST and Δ UTS  is congruent to each other.

ΔRST  ≅ Δ UTS    by SSS Theorem

If two geometric figures are identical in every way, they are said to be congruent.

For example, two squares having the same side-length are congruent.

Similarly, two circles with the same radius are congruent.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. If moved, they coincide with one other. ’ ≅’ is the congruence symbol.

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The logarithmic function that models the data is given as follows:

y = 1.0994 + 5.6403 ln(x).

The logarithmic function is used as from the table, the data has a initial fast increase and then the rate of the increase decreases, as the graph reaches it's horizontal asymptote.

The function is defined using a logarithmic regression calculator, inserting the points of the data-set.

From the table, the points are given as follows:

(0, 0.5), (1, 1.4), (2, 4.1), (3, 7.6), (4, 9.1), (5, 10).

(as x represents the number of years after 2005).

Inserting these points into the logarithmic regression calculator, the equation is given as follows:

y = 1.0994 + 5.6403 ln(x).

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Answer:

The table that represents g(x) is

x         g(x)

1           1

2          5

3          9

Step-by-step explanation:

From the given information, we have that

f(x) = 2x - 3 and

g(x) = f(2x)

Then,

g(x) = f(2x) becomes

g(x) = f(2x) = 2(2x) -3

g(x) = 4x - 3

Now, we will put the values of x from 1 to 3 into the equation

When x = 1

g(x) = 4x - 3 becomes

g(x) = 4(1) - 3

g(x) = 4 - 3

g(x) = 1

When x = 2

g(x) = 4x - 3 becomes

g(x) = 4(2) - 3

g(x) = 8 - 3

g(x) = 5

When x = 3

g(x) = 4x - 3 becomes

g(x) = 4(3) - 3

g(x) = 12 - 3

g(x) = 9

Hence, the table that represents g(x) is

x         g(x)

1           1

2          5

3          9

The correlation coefficient for x1 and y is 0.91, The correlation coefficient for x2 and y is 0.55 and The correlation coefficient for x1 and x2 is -0.33

Calculating the Correlation Coefficient for x1 and y:

Step 1: Calculate the mean of x1:  Mean of x1 = (30 + 46 + 24 + 51 + 41 + 51 + 74 + 37 + 60 + 77) / 10  Mean of x1 = 47.1

Step 2: Calculate the mean of y:  Mean of y = (94 + 109 + 112 + 178 + 94 + 176 + 171 + 117 + 142 + 212) / 10  Mean of y = 134.1

Step 3: Calculate the standard deviation of x1:  Standard Deviation of x1 = √(((30 - 47.1)2 + (46 - 47.1)2 + (24 - 47.1)2 + (51 - 47.1)2 + (41 - 47.1)2 + (51 - 47.1)2 + (74 - 47.1)2 + (37 - 47.1)2 + (60 - 47.1)2 + (77 - 47.1)2) / 10)

Standard Deviation of x1 = 17.43  

Step 4: Calculate the standard deviation of y:  Standard Deviation of y = √(((94 - 134.1)2 + (109 - 134.1)2 + (112 - 134.1)2 + (178 - 134.1)2 + (94 - 134.1)2 + (176 - 134.1)2 + (171 - 134.1)2 + (117 - 134.1)2 + (142 - 134.1)2 + (212 - 134.1)2) / 10)

Standard Deviation of y = 38.82  

Step 5: Calculate the covariance of x1 and y:  Covariance of x1 and y = ((30 - 47.1) × (94 - 134.1) + (46 - 47.1) × (109 - 134.1) + (24 - 47.1) × (112 - 134.1) + (51 - 47.1) × (178 - 134.1) + (41 - 47.1) × (94 - 134.1) + (51 - 47.1) × (176 - 134.1) + (74 - 47.1) × (171 - 134.1) + (37 - 47.1) × (117 - 134.1) + (60 - 47.1) × (142 - 134.1) + (77 - 47.1) × (212 - 134.1)) / 10  

Covariance of x1 and y = 393.3

Step 6: Calculate the correlation coefficient of x1 and y:

Correlation Coefficient of x1 and y = Covariance of x1 and y / (Standard Deviation of x1 × Standard Deviation of y)  = 393.3 / (17.43 × 38.82)

Correlation Coefficient of x1 and y = 0.91

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consider the following data for a dependent variable y and two independent variables, x1 and x2. x 1 x 2 y 30 12 94 46 11 109 24 17 112 51 16 178 41 6 94 51 19 176 74 7 171 37 13 117 60 13 142 77 16 212 round your all answers to two decimal places. enter negative values as negative numbers, if necessary. Show the correlation coefficient for each variable

The two variables to have a negative correlation are x and y.

Negative correlation is the relationship where x grows as y decreases.

Given,

Here, negative correlation is used to describe the relationship between two variables that results in independent variables moving in one direction while dependent variables move in another.

Positive correlation

Positive correlation is when the value of the variable x rises as the value of the variable y rises.

Negative Correlation

Negative correlation is the relationship where x grows as y decreases.

No correlation

No correlation exists between the two variables.

That example, the term "no-correlation" refers to the absence of a connection between two variables.

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The question is improper. Proper question is given below;

What two variables are likely to have a negative correlation

It is possible to think of the set of hexadecimal digits, which includes one through four digits, as being divided into disjoint subsets: s, Sa, and so forth, strings in S,, strings in fourth, where each S, is made up of the strings with k hexadecimal digits. There are v rules, there are S2 total strings, and so on.

Hexadecimal number system is one of many sorts of ways for representing numbers that has a base-16 value. Hexadecimal numerals therefore contain 16 symbols or digital values, namely 0 through 1, 2, 3, 4, 5, 6, 7, 8, 9, A–F. Single bit representations of 10, 11, 12, 13, 14, and 15 are A, B, C, D, E, and F, respectively.

It can occasionally be spoken as "hex." There are only 16   used to represent hexadecimal integers. A, B, C, D, E, and F are the following values or symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

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