the area of a square is always the square of its side length, and if the area cannot be expressed as the square of an integer, then we can say that it is not the power of 2.
A square is a quadrilateral that has four equal sides and four right angles. The area of a square is the product of its length and width, which are equal in the case of a square. So, the formula for the area of a square is:
Area = side × side
or
Area = side²
In other words, the area of a square is the square of its side length.
Now, when we say that the area of a square is "not the power of 2," it means that the area cannot be expressed as a perfect square of an integer. For example, if the area of a square is 25, then it is the square of 5, which is an integer, and so the area is the power of 2.
However, if the area of a square is, say, 12, then it cannot be expressed as the square of an integer, since the square of any integer is always a whole number. Therefore, we can say that the area of the given square is not the power of 2.
In summary, the area of a square is always the square of its side length, and if the area cannot be expressed as the square of an integer, then we can say that it is not the power of 2.
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Determining the top three winners in a Science Quiz Bee Forming lines from six given points with no three of which are
The nature of formula (Permutations or Combinations) for each scenario is the following:
1) Permutations ; 2) Combination
3) Combination ; 4) Permutations
5)Permutations ; 6)Combination
7) Combination ; 8)Combination 9)Combination ; 10)Combination.
Permutations formula: Permutation is considered an ordered combination. The general formula for this is,
P(n, r) = n! /(n-r)!
Combination formula: It is considered arrangement ways but without ordered combination. The general formula for this is C(n, r) = n!/ (n-r)! r!
Now, we have provide some situations and we have to resolve them.
1) Determining the top three winners ing Science Quiz have to Bee is an example of Permutation as here we just arrange the position for top winners.
2) Forming lines from six given points with no three of which are collinear, is an example of combination because only pair of points is needed.
3) It will be a combination as here we select 3 points to make a triangle user.
4) Four people posing for pictures is an example of Permutation as oder does not matter.
5) Assembling a jigsaw puzzle is an example of Permutations.
6) As here we choose 2 household chores so it is a combination.
7) Selecting 5 basketball players out of 10 team members for the different positions members it is a combination.
8) Choosing three friend for birthday party is combination formula.
9) Picking 6 balls from a basket by 12 balls is combination formula.
10) Forming a committe of 5 members from do people 20 combinations people.
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Complete question:
P- Permutations or C- Combinations.
1. Determining the top three winners in a Science Quiz Bee
2. Forming lines from six given points with no three of which are collinear
3. Forming triangles from 7 given points with no three of which are collinear
4. Four people posing for pictures
5. Assembling a jigsaw puzzle
6. Choosing 2 household chores to do before dinner
7. Selecting 5 basketball players out of 10 team members for the different positions
8. Choosing three of your classmates to attend your party
9. Picking 6 balls from a basket of 12 balls
10. Forming a committee of 5 members from 20 people
the number of weaving errors in a twenty-foot by ten-foot roll of carpet has a mean of 0.5 . what is the probability of observing exactly 4 errors in the carpet? round your answer to four decimal places.
The probability of observing exactly 4 errors in the carpet is 0.0165 or 1.65%.
The number of weaving errors in a twenty-foot by ten-foot roll of carpet follows a Poisson distribution with a mean of 0.5. We can use the Poisson probability distribution formula to find the probability of observing exactly 4 errors in the carpet:
[tex]P(X = 4) = (e^{-0.5} * 0.5^4) / 4![/tex]
where X is the random variable representing the number of weaving errors. Plugging in the values, we get:
[tex]P(X = 4) = (e^{-0.5} * 0.5^4) / 4! = 0.0165[/tex] (rounded to four decimal places)
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Given the function h(x), find the value of h(-2). h(x) = x² + 4x - 7
Step-by-step explanation:
[tex]{ \tt{h(x) = {x}^{2} + 4x - 7 }}[/tex]
Substitute for x as -2;
[tex]{ \tt{h( - 2) = {( - 2)}^{2} + 4( - 2) - 7}} \\ \\ { \tt{h( - 2) = 4 - 8 - 7}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ { \tt{h( - 2) = - 11}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Answer:-9
Step-by-step explanation:
h(-2)=h(x)
it symbolize that x=-2;
so, we'll replace every x with -2:
-2^2+3*(-2)-7=4-6-7=-9
(x-4)(3x+4)=0 the solution is x=
Answer:
x=4, -4/3
Step-by-step explanation:
(x-4)(3x+4)=0
Using the zero product property, we can set each factor to zero and solve.
x-4 =0 3x+4 =0
x=4 3x =-4
x=4 x = -4/3
The solutions for x are:
x=4, -4/3
Answer:
4, -4/3
Step-by-step explanation:
In ΔEFG, m ∠ � = ( 5 � + 6 ) ∘ m∠E=(5x+6) ∘ , m ∠ � = ( 4 � − 6 ) ∘ m∠F=(4x−6) ∘ , and m ∠ � = ( 5 � − 2 ) ∘ m∠G=(5x−2) ∘ . Find m ∠ � . m∠G.
Therefore , the solution of the given problem of angles comes out to be m∠G= 63° is the response to the second component of the query.
What does an angle mean?The curved lines which make up the ends of a skew are divided by its highest and bottom walls using Cartesian measurements. There is a possibility who two poles will collide at an intersection. Another result of two objects interacting is an angle. They most closely mimic dihedral shapes. Two line beams can be arranged in different ways between their extremities to form a two-dimensional curve.
Here,
m∠E + m∠F + m∠G = 180°
Additionally, we are aware that mE = (5x + 6)°, mF = (4x - 6)°, and mG = (5x - 2)°. When we enter these numbers into the formula above, we obtain:
=> (5x + 6)° + (4x - 6)° + (5x - 2)° = 180°
When we simplify and find x, we obtain:
=> 14x - 2 = 180
=> 14x = 182
=> x = 13
Now that we know the three vectors' values:
=> m∠E = (5x + 6)° = (5(13) + 6)° = 71°
=> m∠F = (4x - 6)° = (4(13) - 6)° = 46°
=> m∠G = (5x - 2)° = (5(13) - 2)° = 63°
In light of this, mE = 71°, mF = 46°, and mG = 63°.
The first portion of the question has the following solution:
=> m∠EFG = m∠E + m∠F + m∠G = 71° + 46° + 63° = 180°.
m∠G= 63° is the response to the second component of the query.
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A student is building a squirrel feeder for a family member. The figure is a model of the feeder.
A rectangular prism with dimensions 2 and three fourths inches by 16 and one half inches by 4 inches.
How much feed can the container hold?
twenty-seven and one-half in3
sixty-eight and three-fourths in3
ninety and three-fourths in3
one hundred eighty-one and one-half in3
The container can hold the feed equal to volume = 181.5 cube
A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. It also goes by the name cuboid. Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism. It is referred to as a prism because of the length of its cross-section. The study of shapes and the arrangement of objects is known as Geometry. The surface area and volume of a rectangular prism are similar to those of other three-dimensional forms. The prism's net area is equal to its surface area.
To find how much feed the rectangular prism can hold you have to find its volume.
The formula to find the volume form a rectangular prism is:
Volume= Length x Width x Height
Now we must insert the values you have given:
Volume= 2.75 x 16.50 x 4
When you multiply that out it comes to:
Volume= 181.5
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in how many ways can first, second, and third prizes be awarded in a contest with 170 contestants? your answer is
There are 4,826,640 possible ways to award first, second, and third prizes in a contest with 170 contestants.
To calculate this, use the formula nP3, where n is the number of contestants (170) and P3 represents the permutation of 3 elements. This can be simplified to P(170, 3) = 170! / (170 - 3)! = 170 x 169 x 168 = 4,826,640.
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eric from exercise 3.30 continues driving. after three years, he still has no traffic accidents. now, what is the conditional probability that he is a high-risk driver?
The conditional probability that Eric is a high-risk driver, given that he has had no traffic accidents in the past three years, is very low. Generally, insurance companies use the number of traffic violations and/or the number of claims a driver has had within a certain time period as indicators of their riskiness.
As Eric has had no accidents or traffic violations, the probability that he is a high-risk driver is very low. However, this does not mean that the probability is zero. There are many other factors which can contribute to a driver's risk, such as age, gender, experience, and location.
If Eric is an experienced driver, who has been driving for many years with no traffic accidents, then the probability of him being a high-risk driver will be lower than the average driver. On the other hand, if Eric is a new driver, or is located in an area with a high rate of traffic accidents, then the probability of him being a high-risk driver may be higher than the average driver.
Overall, the conditional probability that Eric is a high-risk driver, given that he has had no traffic accidents in the past three years, is very low. However, this probability can change depending on other factors, such as his age, experience, and location.
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when conducting a logistic regression analysis, what is the problem of class imbalance in a dataset?
Class imbalance is a common problem in logistic regression analysis, where one class of data significantly outnumbers the other.
Class imbalance can be problematic because it leads to an over-representation of one class and an under-representation of the other, which can bias the model’s prediction towards the more frequently occurring class.
Class imbalance can cause the model to focus on optimizing accuracy by predicting the majority class more often than the minority class, leading to an underestimation of the minority class. It can also reduce the model’s ability to capture the nuances of the data that can be associated with the minority class. To address this, techniques such as oversampling, undersampling, and cost-sensitive learning can be employed to balance the data and improve model performance.
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Find the value of x. Round to the nearest degree. Did you find it with sin, cos−1, sin-1, or cos.
The value of x is 61° ( nearest degree)
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. If side opposite the acute angle is the opposite side and the longest side is hypotenuse.
Sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan( tetha) = opp/ adj
In this case,
the hypotenuse = 8
opposite = 7
therefore sin x = 7/8
sin x = 0.875
x = sin^-1 ( 0.875)
x = 61° ( nearest degree)
therefore the value of x is 61°
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If $4,323 was withheld during the year and taxes owed were $4,576:
a. Would the person owe an additional amount or receive a refund?
b. What is the amount? [Make sure to show your work]
Answer:
a. Since taxes owed ($4,576) are greater than the amount withheld ($4,323), the person would owe an additional amount.
b. The additional amount owed can be calculated by subtracting the amount withheld from the taxes owed:
Additional amount owed = Taxes owed - Amount withheld
= $4,576 - $4,323
= $253
Therefore, the person would owe an additional $253.
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Ali and ben and clare each played a game
clares score was seven times alis score
ben score was half of alis score
write down the ratio of alis score to bens score to clares score
give your answer in its simplest form
The ratio of Ali's score to Ben's score to Clare's score in its simplest form is 1 : 3.5 : 7
Given data:
Claire's score = 7 * Ali's score
Ben's score = 0.5 * Claire's score
How to solve for the ratio of Ali's score to Ben's score to Clare's score
let Ali's score = x
let Ben's score = y
let Claire's score = z
z = 7 * x = 7x
z = 7x
y = 0.5 * z = 1/2 * z = z / 2
plugging the value of z gives
y = 7x / 2
writing the ratios in terms of x gives
Ali : Ben : Claire
x : y : z
x : 7x/2 : 7x
Reducing the terms by dividing through by x
1 : 7/2 : 7
OR
1 : 3.5 : 7
clearing the fraction gives
2 : 7 : 14
Therefore, the ratio of Ali's score to Ben's score to Clare's score in its simplest form is 1 : 3.5 : 7
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Find the missing of dimension of the cone. Round you answer to the nearest tenth. Volume=13. 4m³
Radius=3. 2m
Height=h
The missing dimension of the cone is its height, which is approximately 2.5 m when rounded to the nearest tenth.
We can use the formula for the volume of a cone, which is:
Volume = (1/3)πr²h
where r is the radius of the base and h is the height of the cone.
We are given the volume of the cone as 13.4 m³ and the radius as 3.2 m. Substituting these values into the formula, we get:
13.4 = (1/3)π(3.2)²h
Multiplying both sides by 3 and dividing by π(3.2)², we get:
h = 3 × 13.4 / π(3.2)²
h ≈ 2.5 m
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Given the right triangle in the diagram below, what is the value of x, to the nearest foot
Therefore, the value of x, to the nearest foot, is A. 11 in the right triangle in the diagram below.
What is triangle?A triangle is a two-dimensional geometrical shape with three sides and three angles. It is a polygon with the least number of sides. Triangles are classified based on the length of their sides and the measure of their angles. The three sides of a triangle can be classified as equal, two equal sides, or three unequal sides. Triangles can also be classified based on their angles as acute (all angles less than 90 degrees), right (one angle is equal to 90 degrees), obtuse (one angle greater than 90 degrees), or equiangular (all angles are equal). The interior angles of a triangle always add up to 180 degrees. The longest side of a right triangle is called the hypotenuse, and it is opposite to the right angle. The Pythagorean theorem is used to find the missing side of a right triangle. Triangles are widely used in mathematics, physics, engineering, and other fields. They form the basic building block of more complex geometrical shapes and structures.
Here,
Using trigonometry, we can find that:
tan(40°) = x/14
Multiplying both sides by 14, we get:
x = 14 * tan(40°)
Using a calculator, we get:
x ≈ 11.0
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Complete question:
Given the right triangle in the diagram below. what is the value of x, to the nearest foot?
A. 11
B. 17
c. 18
D. 22
2 and 1 half divided by 5
Answer: 0.5
Step-by-step explanation:
Answer:
As a decimal 0.5, as a fraction 1/2
Mariah has an after school babysitting job, This is a record of the number of hours she worked last week on Monday 2 1//2 on Tuesday it was 3 1/2 Wednesday 2 1/4 and Thursday 3 2/3 and she gets paid 6$ per hour how much money would she make? And also this is improper fractions as well
Answer: 71 1/2$
Step-by-step explanation:
1 1/3 + 2 1/4. 8 5/8-7 1/2 =
Answer:
9/8
Step-by-step explanation:
1 1/3 + 2 1/4 = (4/3 + 9/4) = (16/12 + 27/12) = 43/12
8 5/8 - 7 1/2 = (69/8 - 15/2) = (69/8 - 60/8) = 9/8
Therefore, 1 1/3 + 2 1/4 = 43/12 and 8 5/8 - 7 1/2 = 9/8.
7. The expression below is evaluated as shown. In which step does the first
mistake appear?
The mistake in the solution of the expression is in step 3, where the product should be solved first.
In which step is the first mistake?Here we have the expression:
0.5*(3*5 + 1) - 2
And we also have the solution in steps, and we want to find in which step we have a mistake.
The first step gives:
0.5*(15 + 1) - 2
Where the first product is solved.
The second step is
0.5*16 - 2
Where we solved the parentheses.
The third step gives:
0.5*14
Here they subtracted the 2 from the 16, but this is incorrect, the first thing that needs to be solved here is the product between 0.5 and 16, we should get:
0.5*16 - 2
8 - 2
6
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Please help me this is due after class (20 mins) (I-Ready Math)
YOU GET 20 POINTS!!!!
Here's the picture
The value of h in the given parallelogram is 6 units, which can be found by using the formula for the area of a parallelogram.
In the given parallelogram, we can see that the base is 12 units long and the distance between the base and the opposite side is 6 units.
To find the value of h (the height or distance between the base and the opposite side), we can use the formula for the area of a parallelogram which is:
Area = base x height
Since we know the area of the parallelogram is 72 square units (given in the diagram), we can plug in the values we know and solve for h:
72 = 12 x h
h = 72/12
h = 6
Therefore, the value of h in the parallelogram is 6 units.
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Help please, it’s simple I’m just slow
10 v^5 w^10
CHEESEburgeCheeseburger
find the surface area of this figure
The Surface area of the given cuboid is found to be 872 sq, in.
Explain about the cuboid?Three-dimensional shapes with length, breadth, and height are called cuboids. Six of the cuboid's sides are referred to as faces.
Every corner of a cuboid's faces, which usually refer to as vertices, are at a 90-degree angle. Hence, a cuboid is any object that has the shape of a box.The only thing that cuboids have are straight angles. It is not a cuboid if it has additional kinds of angles. The same is true for cubes. A cube and even a cuboid have the same number of edges, faces, and vertices: 12 edges, 8 vertices, and 6 faces.Surface area of a cuboid is = 2(lw + 2lh + hw0
l= lengthw= width.h = heightS.A = 2[(17)*(8) + (8)*(12) +(12)*(17)]
S.A = 2*436
S.A = 872
Thus, the Surface area of the given cuboid is found to be 872 sq, in.
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A pavement 4m wide is constructed along the outer side of the boundary of a square shaped ground having it's side of 13m length. Find the cost of levelling the pavement at the rate of RS 1. 25 per square meter
A pavement 4m wide is constructed along the outer side of the boundary of a square shaped ground having it's side of 13m length. The cost of levelling the pavement at the rate of Rs 1.25 per square meter is Rs 340.
As per given information,
Side of a square shaped ground = 13 m
Width of pavement constructed = 4 m
We need to find the cost of levelling the pavement at the rate of Rs 1.25 per square meter.
Area of the square shaped ground = Side × Side= 13 × 13= 169 sq.m
Area of the square shaped ground along with pavement constructed
= (13 + 8) × (13 + 8)
= 21 × 21
= 441 sq.m
Area of the pavement constructed
= Area of the square-shaped ground along with pavement constructed - Area of the square shaped ground
= 441 - 169
= 272 sq.m
Cost of levelling 1 sq.m of pavement = Rs 1.25
Cost of levelling 272 sq.m of pavement = 272 × Rs 1.25 = Rs 340
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Which system has exactly one solution?
A.(y + 4x = -2
y = -4x + 5
B. (6x + 3y = -1
2x + y = 4
C. y = 4x - 5
{ y = -x-5
D.3x - = 2
{y-4 = 3(x-2)
The system of equations that has only one solution is the one where the equations have different slopes, it is the one in option C.
y = 4x - 5
y = -x - 5
Which system of equations has only one solution?A system of linear equations will have only one solution always that the lines are neither parallel nor the same line.
So, one way to check this, is to write both lines in the slope intercept form, and check that the two lines have different slopes.
For example, the first option will give.
y = -4x - 2
y = -4x + 5
These are parallel (same slope different intercept), then this systm has no solutions.
The correct option will be C, where the system is:
y = 4x - 5
y = -x - 5
The slopes are different.
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a data set has a range of 22, a median of 40, and a mode of 52. if there six values in the data set, what could they be?
One possible set of values could be:
29, 30, 31, 52, 53, 54
Given:
Range = 22
Median = 40
Mode = 52
Number of values in the data set = 6
Since the median is 40, it indicates that two values in the data set are below 40, and three values are above 40.
The mode is given as 52, which means that at least one value in the data set is equal to 52.
There are six values in the data set, we can construct a possible set of values:
Min Value + 2 values below median + Mode + 3 values above median + Max Value = 6 values
Let's try one possible combination:
Min Value = 40 - 11 = 29
Max Value = Min Value + Range = 29 + 22 = 51
One possible set of values could be:
29, 30, 31, 52, 53, 54
Here, the range is 51 - 29 = 22, the median is 52, and the mode is also 52.
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Find x
Find y
Need explanation
Step-by-step explanation:
Well, since this is a 45, 45, 90 triangle, it means that the given side and y have the same length.
Y = 1.5sqrt(2)
this means that X, the hypotenuse is equal to 1.5sqrt(2)^2 + 1.5sqrt(2)^2 = X^2
X is equal to 2.44948974278
PLEASE HELP ME & FAST !!!
The percentage of 65 out of 140 will be 46.428%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
[tex]\text{Percentage (P) = [Final value - Initial value] / Initial value x 100}[/tex]
The whole numbers are 65 and 140.
Then the percentage is written as,
[tex]P = (65 \div 140) \times 100[/tex]
[tex]P=0.46428 \times 100[/tex]
[tex]P=46.428\%[/tex]
The percentage of 65 out of 140 will be 46.428%.
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suppose the mean income of firms in the industry for a year is 45 million dollars with a standard deviation of 13 million dollars. if incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than 73 million dollars? round your answer to four decimal places.
The probability that a randomly selected firm will earn less than 73 million dollars is 0.9842.
The mean income of firms in the industry for a year is 45 million dollars with a standard deviation of 13 million dollars, we need to find the probability that a randomly selected firm will earn less than 73 million dollars.
We can assume that the income distribution of firms is normal. Therefore, we can use the z-score formula to find the required probability.
We have, z = (X - μ) / σ, where X is the income of the firm, μ is the mean income, and σ is the standard deviation.
z = (73 - 45) / 13
z = 2.15
Using the z-table, we can find the area under the standard normal curve to the left of z = 2.15.
The area to the left of Z-score of 2.15 is 0.984, the probability that a randomly selected firm will earn less than 73 million dollars is 0.9842
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Which statement is true?
A. 6 > 6
B. –8 < –3
C. 5 < –6
D. –12 > –6
Answer:
B is a true statement.
[tex] - 8 < - 3[/tex]
Ella is using paint to make a blackboard on her wall. The blackboard will cover a rectangular area of 44 square feet. The equation below can be used to determine w, the width of the blackboard. (w -2 ) ( w + 2 ) = 12 Create a diagram and determine the width and the length of the blackboard.
The width of the blackboard is 4 feet and the length is 11 feet.
How to find the width of the blackboard?To solve the equation[tex](w - 2) (w + 2) = 12[/tex]for the width of the blackboard, we can use the distributive property to simplify the left-hand side:
[tex]w^2 - 4 = 12[/tex]
Then we can add four to both sides:
[tex]w^2 = 16[/tex]
When we take the square root of both sides, we get:
w = ±4
We choose the positive solution because the width of the blackboard cannot be negative:
w = 4
We can calculate the length of the blackboard by dividing the area by the width:
l = 44 square feet / 4 feet = 11 feet
As a result, the blackboard's width is 4 feet and its length is 11 feet.
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4. what is the probability of choosing a red card (i.e. heart or diamond) out of a standard deck of 52 playing cards? a. 26/52 b. 13/26 c. 1/2 d. all of the above
52.
The probability of choosing a red card (heart or diamond) out of a standard deck of 52 playing cards is 26/52. This is because there are 26 red cards in a standard deck, so the probability of choosing one is 26 divided by the total number of cards in the deck
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