The height of a filing cabinet is 1.5 times the width. The depth is twice the width.The volume of the cabinet is 12,288 in³. What are the cabinet's dimensions?

Answer:

the solution is d = -10.75.

Step-by-step explanation:

To solve for d in this equation, we need to first simplify it by distributing the 3 on the right side:

-115 = 20 + 12d - 6

Next, we combine like terms on the right side:

-115 = 14 + 12d

Then, we isolate the variable term by subtracting 14 from both sides:

-129 = 12d

Finally, we solve for d by dividing both sides by 12:

d = -10.75

Therefore, the solution is d = -10.75.

Answer:

[tex]d=-\frac{43}{4}[/tex]

Step-by-step explanation:

First, let's apply the distributive property and multiply 4d and -2 by 3.

We have:

[tex]-115=20+3(4d-2)=\\-115=20+3(4d)+3(-2)=\\-115=20+12d-6[/tex]

Now, let's combine like terms.

[tex]-115=20+12d-6=\\-135=12d-6=\\-129=12d=\\-\frac{129}{12} =d[/tex]

Both 129 and 12 are divisible by 3, so let's simplify the fraction:

[tex]d=-\frac{129}{12} =\\d=-\frac{43}{4}[/tex]

Answer:

No solution

Step-by-step explanation:

12(2x+11) = 12(2x+12)

24x + 132 = 24x + 144

0 + 132 = 144

0 = 12

This is not true, 0 ≠ 12, so there is no solution.

no value of x will make the equation true.

The equation [tex]12(2x+11)=12(2x+12)[/tex] 12(2x+11)=12(2x+12) is linear in one variable (x) with coefficients and constants that are real numbers. It can be simplified by performing basic algebraic operations, such as distributing and simplifying, to solve for the value of x.

To solve for x in the equation[tex]12(2x+11)=12(2x+12)[/tex] 12(2x+11)=12(2x+12), we will follow the steps of algebraic manipulation:

First, we will simplify both sides of the equation by distributing the 12 on each side:

[tex]12(2x+11)=12(2x+12)[/tex] 12(2x+11) = 12(2x+12)

[tex]24x + 132 = 24x + 144[/tex] 24x +132 = 24x + 144

Next, we will simplify further by subtracting 24x from both sides:

[tex]24x - 24x + 132 = 144[/tex] 24x - 24x + 132 = 144

[tex]132 = 144[/tex] 132 = 144

Since this is not a true statement, the equation has no solution. Therefore, no value of x will make the equation true.

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There are 7,776 different outcomes when rolling five 6-sided dice.

In the game of Yahtzee, the dice used has 6 sides. This means that each dice has 6 possible outcomes.  

Dice 1 = 6outcomes  Dice 2 = 6 outcomes  dice 3 = 6outcomes

Dice 4 = 6outcomes dice 5 = 6outcomes

We multiply all the outcomes by the total number of the 6-sided dice will be used for the game, which is 5.

We can express it as follows

6 × 6 × 6 × 6 × 6

It can also be expressed as 6⁵, the power 5 being the number of times that 6 will be multiplied

= 7776

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Answer:

We are given that 50% of the ELTs are made by Company A, 45% are made by Company B, and 5% are made by Company C. We also know the rate of defects for each company's ELTs: 4% for Company A, 6% for Company B, and 9% for Company C.

Let D be the event that an ELT is defective, and let Bi be the event that an ELT was made by Company i, where i = A, B, or C. We want to find the probability that an ELT is made by Company B given that it is defective, i.e., we want to find P(B|D).

Using Bayes' theorem, we can write:

P(B|D) = P(D|B) * P(B) / P(D)

where P(D|B) is the probability that an ELT made by Company B is defective, P(B) is the prior probability that an ELT is made by Company B, and P(D) is the overall probability of an ELT being defective.

We can calculate each of these probabilities as follows:

P(D|B) = 0.06 (given)

P(B) = 0.45 (given)

P(D) = P(D|A) * P(A) + P(D|B) * P(B) + P(D|C) * P(C)

= 0.04 * 0.5 + 0.06 * 0.45 + 0.09 * 0.05

= 0.0355

Substituting these values into Bayes' theorem, we get:

P(B|D) = P(D|B) * P(B) / P(D)

= 0.06 * 0.45 / 0.0355

≈ 0.762

Therefore, the probability that an ELT made by Company B is defective given that it is found to be defective is approximately 0.762, or 76.2%.

The complete algebraic expression would be

Gross wages = 4.15 × hours worked + 0.21 × total food sales.

What is an algebraic expression?

The idea of expressing numbers using letters or alphabets without specifying their actual values is called Algebraic expressions . The basics of algebra taught us to express an unknown value with letters like x, y, z, etc. These letters are called variables here. It can be a combination of both constants and variables. Any value placed in front of a variable and multiplied by it is a coefficient.

Examples,

3x + 4a – 7, 4x – 10, etc.

These expressions are represented using unknown variables, constants, and coefficients. A combination of these three (as terms) is considered an expression. It should be remember that unlike an algebraic equation, an algebraic expression has no sides or an equal sign. Some examples of this include,

An algebraic expression that could be used to represent Enrique's gross salary would be:

Gross salary = hourly rate x hours worked + tip

Where Hourly rate = $4.15 per hour

Hours Worked = Number of hours worked by Enrique

Tipping = 21% of total food sales

So the complete algebraic expression would be:

Gross wages = 4.15 × hours worked + 0.21 × total food sales.

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6 bottles would hold 3 liters of water.

In general, the total capacity of x bottles would be 0.5x liters, where x represents the number of bottles.

If nine bottles have a total capacity of 4.5 liters, we can determine the capacity of each bottle by dividing the total capacity by the number of bottles.

In this case, we have:

Capacity per bottle = Total capacity / Number of bottles

= 4.5 liters / 9 bottles

= 0.5 liters per bottle.

Now, if we want to find out how much x bottles would hold, we can simply multiply the capacity per bottle by the number of bottles (x). Therefore, the formula to calculate the total capacity of x bottles would be:

Total capacity of * bottles = Capacity per bottle *  Number of bottles

= 0.5  liters per bottle *  x  bottles

= 0.5x liters.

So, x bottles would hold 0.5x liters of water.

For example, if we wanted to find out how much 6 bottles would hold, we could substitute x with 6 in the formula:

Total capacity of 6 bottles = 0.5 * 6 liters

= 3 liters.

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On solving the equations the amount of 95% mixture required is obtained as 135 mL.

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 ("=").

Let's call the amount of 95% alcohol mixture we need to add "x".

We want to end up with a 50% alcohol solution, so the amount of pure alcohol in the final solution should be 50% of the total volume.

The amount of pure alcohol in the 405 mL of 35% alcohol mixture is -

0.35 × 405 = 141.75 mL

Let's set up an equation to solve for x -

0.95x + 141.75 = 0.5(x + 405)

First, let's distribute the 0.5 on the right side -

0.95x + 141.75 = 0.5x + 202.5

Subtract 0.5x and 141.75 from both sides -

0.45x = 60.75

Divide both sides by 0.45 -

x = 135

Therefore, you need to add 135 mL of the 95% alcohol mixture to obtain the desired 50% alcohol solution.

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The amount in the account after 5 years would be $9555.42.

What is the formula for compound interest?

[tex]A = P(1 + \frac{r}{n} )^{(nt)}[/tex]

Where:

A = the amount of money in the account after t years

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $6500, r = 8% = 0.08, n = 1 (compounded annually), and t is the number of years.

If no withdrawals are made from the account, then the amount of money in the account after t years will be

[tex]A = 6500(1 + \frac{0.08}{1})^{(1t)} \\ A = 6500(1.08)^t[/tex]

Now the amount of money in the account after a specific number of years,

A = 6500(1.08)⁵

A = 6500(1.469328)

A = $9555.42

So after 5 years, the amount in the account would be $9555.42

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Correct question is "Suppose Juan places $6500 in an account that pays 8% interest compounded each year. Assume that no withdrawals are made from the account.Then find What would be the amount in the account after 5 years?"

The value of x in the right triangle is 5.6 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the side length x of the right triangle can be found using trigonometric ratios as follows:

tan 48 = opposite / adjacent

where

opposite side = x

adjacent side = 5

Hence,

tan 48 = x / 5

cross multiply

x = 5 tan 48

x = 5 × 1.11061251483

x = 5.55306257415

Therefore,

x = 5.6 units

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Answer:

x = 7

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

9x - 3 + 30 + 90 = 180

9x + 117 = 180 ( subtract 117 from both sides )

9x = 63 ( divide both sides by 9 )

x = 7

Answer:

First account: $6380.

Second account: $4251.

Step-by-step explanation:

let the first account have $x at the start of the first year

So at the end of 1 year it had x + 0.1x = $1.1x

In the same we we calculate the amount in the second account

= $1.09(9700 - x)

So we have the following equation

1.1x + 1.09(9700 - x) = 9700 + 931

1.1x + 10573 - 1.09x = 10631

0.01x = 10631 - 10573 = 58

x = 58/0.01

   =$5800

So at the end of the year there was

5800 * 1.1 = $6380 in first account

and

the second account had

1.09 (9700 - 5800) = $4251.

Answer:-1/6

Step-by-step explanation:

Draw a line out in the 2nd quadrant.

Your y=[tex]\sqrt{35}[/tex]    hypotenuse=6  use pythagorean theorem to solve for x

6² = 35 + x²

x=1

so

cosΘ = -1/6

We can see that for one who doesn't fall ill frequently, the PPO Plan will be the best. This is as a result of its lower premium and broader network of healthcare providers.

A PPO (Preferred Provider Organization) plan is known to be a type of health insurance plan which allows individuals to actually choose their healthcare providers. It allows them to choose from a network of preferred providers who have agreed to provide services at a discounted rate.

We can see here that in the PPO Plan, the PPO (Preferred Provider Organization) plan actually has a lower premium, but the coverage is only 80%, and you need to pay 20% of the cost-sharing or co-insurance.

Also, the PPO plan has a higher deductible of $1,000, which means that the insurance coverage starts later.

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The value of x that satisfies this equation 4(2.5)2^x= 4 is x = -1.32

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

4(2.5)2^x= 4

This gives

(10)2^x= 4

Divide the equation by 10

So, we have the following

2^x = 0.4

Take the logarithm of both sides and evaluate

x = -1.32

Hence, the solution is x = -1.32

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The dimensions of the wooden platform are 24 feet long by 60 feet wide, making the area 1440 square feet and the perimeter 168 feet.

Area is a two-dimensional measurement of a surface, usually measured in square units, such as square feet or square meters. It is used to measure the size of a room, a piece of land, an object, or any other two-dimensional shape. Area is also used to calculate the perimeter, or distance around an object, or the volume of a three-dimensional object. It is an important concept in mathematics and helps us understand the world around us.

The wooden platform built by Mr Burns has a rectangular shape with a length of 24 feet and a width of 60 feet. This yields an area of 1440 square feet (24 x 60 = 1440). The perimeter of the platform is 168 feet (2 x 24 + 2 x 60 = 168).

The platform is large enough to accommodate the entire drama club. It is also big enough to accommodate other activities, allowing the drama club to have a larger space for their performances. The platform also provides a secure base for the club to perform on.

The dimensions of the wooden platform are 24 feet long by 60 feet wide, making the area 1440 square feet and the perimeter 168 feet. The size of the platform is suitable for the size of the drama club, and its sturdy construction will give them a secure and safe place to perform.

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The median, mean, range and mode will be 6, 5.4, 9 and 7.

What is median?

The median is the middle number in the data set when the data set is written from least to greatest.

The median is the number in the middle when arranged in an ascending order. The numbers will be:

0, 3, 4, 6, 6, 7, 7, 7, 9.

The median is 6.

The range is the difference between the highest and lowest number which is: = 9 - 0 = 9

The mode is the number that appears most which is 7.

The mean will be the average which will be:

= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.

= 49/9

= 5.4

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Answer:

15 = m

Step-by-step explanation:

10 − 3(m − 5) = 2(5 − m)

10 - 3m + 15 = 10 - 2m

25 - 3m = 10 - 2m

25 - 10 = - 2m + 3m

15 = m

__________

hope it helps!

Answer:

m=15

Step-by-step explanation:

10 − 3(m − 5) = 2(5 − m)

-3m+25=10-2m

-3m= -2m -15

-m=-15

m=15

The equation of the line of best fit is y = x + 16 and the money spent on entertainment for a student who works 8 hours is $24

Drawing the line of best fit, we have the following points

(0, 6) and (16, 22)

The equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 6

Using the points, we have

16m + 6 = 22

So, we have

m =1

So, the equation is

y = x + 6

This means that

x = 8

So, we have

y = 8 + 16

y = 24

Hence, the amount is $24

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For the given normal distribution a. We expect approximately 954 chicks to hatch between 25 and 33 days. b. We expect approximately 683 chicks to hatch between 27 and 31 days.

A probability distribution that is frequently used in statistics is the normal distribution, usually referred to as the Gaussian distribution. The majority of the data are within one standard deviation of the mean, resulting in a bell-shaped curve that is symmetrical around the mean.

In a normal distribution, the mean, median, and mode are all equal, and the mean and standard deviation serve as the two parameters that define the curve. While the standard deviation reflects the distribution's spread, the mean represents the distribution's centre.

The z-score is given by the formula:

z = (x - mu) / sigma

a. For 25 to 33 days:

z = (25 - 29) / 2

z = -2

and

z = (33 - 29) / 2

z = 2

Thus, P(z < 2) = 0.9772.

Now, we have:

P(25 < x < 33) = P(z < 2) - P(z < -2)

P(25 < x < 33) = 0.9772 - 0.0228

P(25 < x < 33) = 0.9544

Expected number of chicks = 0.9544 x 1000 = 954.4

Hence, we expect approximately 954 chicks to hatch between 25 and 33 days.

b. For 27 to 31 days:

P(27 < x < 31) = P(z < 1) - P(z < -1)

P(27 < x < 31) = 0.8413 - 0.1587

P(27 < x < 31) = 0.6826

Expected number of chicks = 0.6826 x 1000 = 682.6

Therefore, we expect approximately 683 chicks to hatch between 27 and 31 days.

c. For 29 days or fewer:

P(x <= 29) = P(z <= 0) = 0.5

Expected number of chicks = 0.5 x 1000 = 500

d. In 23 to 35 days:

P(23 < x < 35) = P(z < 3) - P(z < -3)

P(23 < x < 35) = 0.9987 - 0.0013

P(23 < x < 35) = 0.9974

Expected number of chicks = 0.9974 x 1000 = 997.4

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Based on the calculations given below, the value of the marginal product is option A: $37.50.

The value of marginal product (VMP) is one that can be calculated as the additional revenue generated by hiring an additional worker.

So to o calculate the VMP of the first worker, it will be:

Hence:

VMP of the first worker = (output with one worker - output with zero workers) x price per unit

VMP of the first worker = (25 - 0) x $2

                                            = $50

Note that the ingredients needed to make each cup of coffee cost 50 cents, so the total cost of making 25 cups of coffee with one worker will be:

Total cost = ingredients cost x output

                = $0.50 x 25

                   = $12.50

So, the value of the marginal product of the first worker can be obtained by:

VMP of the first worker = additional revenue - additional cost

                                  = $50 - $12.50

                                    = $37.50

So the value of the marginal product is: $37.50.

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The graph will bounce like a polynomial of degree equal to the multiplicity minus 1.

What is polynomial?

A polynomial is a mathematical expression that consists of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and non-negative integer exponents.

The power of the factor that causes the graph to bounce at the corresponding zero depends on the multiplicity of the zero.

If the zero has odd multiplicity, the graph will cross the x-axis at the zero, meaning there will be no bounce.

If the zero has even multiplicity, the graph will bounce at the zero. Specifically, if the multiplicity is 2, the graph will bounce like a parabola; if the multiplicity is 4, the graph will bounce like a quartic; and so on. In general, the graph will bounce like a polynomial of degree equal to the multiplicity minus 1.

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Answer:

1499.06 cm³

Step-by-step explanation:

volume = length × width × height

length = 22.5 cm

width = 10.25 cm

height = 6.5 cm

volume = 22.5 cm × 10.25 cm × 6.5 cm

volume = 1499.0625 cm³

Answer: 1499.06 cm³

The correct answer is: B. They have the same y-intercept, but the graph of g(x) gets faster over time.

Exponents and powers are ways of representing very large  or very small numbers in a simplified way. For example, if we need to represent 3 x 3 x 3 x 3 in a simple way,  we can write it as 34, where 4 is the exponent and 3 is the base. The whole expression 34 is said to be a force.

The  functions provided are:

[tex]f(x) = 500(1.015)^x[/tex]

[tex]g(x) = 500(1.021)^x[/tex]

Both functions have an initial value of $500 (when x = 0). Therefore, they share the same y-intercept, which is (0, 500).  

To compare the graphs of f(x) and g(x), we can look at their growth rates. Note that the exponent of f(x) has a base of  1.015, while the exponent of g(x) has a base of  1.021. Since both bases are greater than 1, both functions grow exponentially with time.  

However, since 1.021 is greater than 1.015, the function g(x) increases with time faster than f(x). This means that the graph of g(x) is steeper than the graph of f(x).  

Therefore, the correct answer is:

B. They have the same y-intercept, but the graph of g(x) gets faster over time.

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According to given fraction values, Harry used 4 gallons of paint in total.

What is fraction?

A fraction is a way of representing a part of a whole or a ratio of two numbers. It consists of a numerator (top number) and a denominator (bottom number) separated by a horizontal line.

To find the total amount of paint Harry used, we need to add the amount of paint he used for the living room and the amount of paint he used for his bedroom. We have:

2 1/4 gallons + 1 3/4 gallons

To add these two mixed numbers, we need to find a common denominator. The smallest common denominator of 4 and 4 is 4. So we can rewrite the mixed numbers as improper fractions:

2 1/4 = 9/4

1 3/4 = 7/4

Now we can add the two fractions:

9/4 + 7/4 = 16/4

Simplifying the fraction, we get:

16/4 = 4

Therefore, Harry used 4 gallons of paint in total.

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The solutions to the equation [tex]x^{2} + x[/tex]  = 11/4 are x = -1/2 + [tex]\sqrt{3}[/tex] and x = -1/2 - [tex]\sqrt{3}[/tex]

What is the equation?

An equation is a mathematical statement that indicates that two expressions are equivalent. It has two sides, one on each side, divided by an equals sign (=). An equation's left and right sides can contain numbers, variables, and mathematical operations, including addition, subtraction, multiplication, and division.

The left side of the equation should be rewritten in the form (x + a)2, where an is a constant, in order to complete the square and find the solution to the equation [tex]x^{2}+x[/tex] = 11/4.

To accomplish this, add and remove [tex](1/2)^{2}[/tex](which is equivalent to 1/4) inside of the brackets, as seen in the example below:

[tex]x^{2} +x[/tex]= 11/4

[tex]x^{2} +x[/tex]+ 1/4 - 1/4 = 11/4

[tex](x+1/2)^{2}[/tex] - 1/4 = 11/4

[tex](x+1/2)^{2}[/tex] = 3

Next, we take the square root of both sides:

x + 1/2 = ±[tex]\sqrt{3}[/tex]

Finally, we solve for x by subtracting 1/2 from both sides:

x = -1/2 ± [tex]\sqrt{3}[/tex]

So the solutions to the equation [tex]x^{2} +x[/tex]  = 11/4 are x = -1/2 + [tex]\sqrt{3}[/tex] and x = -1/2 - [tex]\sqrt{3}[/tex].

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The percdentile is 69.15 for z=0.5.Next, take the two percentiles apart.

The normal distribution is an illustration of a continuous distribution of probabilities in which most data points are grouped in the middle of the range and the remaining ones taper off equally to either extreme. The middle of the range is sometimes referred to as the distribution's mean.

The mean, median, and mode are all equal in normal distributions, which are symmetric, unimodal, and asymptotically distributed. A normal distribution is perfectly symmetrical on both sides.

Percentage of data points with z=a and b between two supplied data points

Add the a% sign and subtract the table percentile for z=a from the table percentile for z=b.

The percentile for the data table for z=-0.5 is 30.85.

the percdentile is 69.15 for z=0.5.Next, take the two percentiles apart.

69.15-30.85= 38.3%

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Approximately 38.30% of data points in a normal distribution fall between z = -0.5 and z = 0.5.

A special kind of normal distribution called a "standard normal distribution" has a mean () of 0 and a standard deviation () of 1.

When comparing alternative normal distributions with arbitrary mean and standard deviation, the standard normal distribution is frequently used as a reference distribution in statistics and probability theory.

We employ a procedure called standardisation, which entails dividing by the standard deviation and removing the mean from any normal distribution to get a standard normal distribution.

The percentage of data items in a normal distribution that lie between z = -0.5 and z = 0.5 can be found using a standard normal distribution table or a calculator with normal distribution capabilities.

Using a standard normal distribution table, the value for z = -0.5 is 0.3085, and the value for z = 0.5 is 0.6915. Subtracting these values gives:

0.6915 - 0.3085 = 0.3830

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The temperature at 8:00 A.M. was 15°C.

Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.

We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C

3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.

Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C

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The inequality with the given solution set is given as follows:

D. -2 ≤ x + 5 < 6.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

The solution to the compound inequality in this problem is given as follows:

-7 ≤ x < 1.

Hence the inequality can be obtained adding 5 to each term, as follows:

-7 + 5 ≤ x + 5 < 1 + 5 = -2 ≤ x + 5 < 6.

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