The estimated flux of f out of the small sphere is approximately 0.000021.
To estimate the flux of the vector field f out of a small sphere centered at (3, 5, 6), we need to use the divergence theorem.
According to the divergence theorem, the flux of f across the surface S enclosing a volume V is equal to the triple integral of the divergence of f over V:
flux = ∫∫S f · dS = ∭V div f dV
Since the vector field f is smooth, its divergence is continuous and we can evaluate it at the center of the sphere:
div f(3, 5, 6) = 5
Therefore, the flux of f out of the sphere can be estimated as:
flux ≈ div f(3, 5, 6) [tex]\times[/tex]volume of sphere
flux ≈ 5 [tex]\times[/tex](4/3) [tex]\times[/tex]π [tex]\times[/tex](0.0[tex]1)^3[/tex]
flux ≈ 0.000021
So the estimated flux of f out of the small sphere is approximately 0.000021.
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The question is asking for an estimate of the flux of a smooth vector field out of a small sphere of radius 0.01 centered at a specific point. Flux refers to the flow of a vector field through a surface, in this case the surface of the sphere.
The given information, div f = 5 at the center of the sphere, is used to calculate the flux through the surface using the Divergence Theorem. The result is an estimate of the total amount of vector field flowing out of the sphere. The small radius of the sphere means that the estimate will likely be very small, as the vector field has less surface area to flow through. The final answer, .000021, is rounded to six decimal places.
To estimate the flux of the vector field f out of a small sphere centered at (3, 5, 6) with a radius of 0.01, you can use the divergence theorem. The divergence theorem states that the flux through a closed surface (in this case, a sphere) is equal to the integral of the divergence of the vector field over the volume enclosed by the surface.
Since the div f(3, 5, 6) = 5, you can assume that the divergence is constant throughout the sphere. The volume of a sphere is given by the formula V = (4/3)πr^3. With a radius of 0.01, the volume is:
V = (4/3)π(0.01)^3 ≈ 4.19 x 10^-6.
Now, multiply the volume by the divergence to find the flux:
Flux = 5 × (4.19 x 10^-6) ≈ 2.095 x 10^-5.
Rounded to six decimal places, the flux is 0.000021.
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A)x=45
B)x=90
C)x=20
D)x=4.5
Answer:
x=4.5
Step-by-step explanation:
We know that if all sides are congruent then all angles must also be congruent, therefore you can solve for x with the following equation:
[tex]20x=90[/tex]
Solve
[tex]x=4.5[/tex]
Katelynn is excited about her trip to Chicago with her orchestra. She needs to raise $500 in order to go. She decides to make and sell scarves in order to fund her trip. In order to make each scarf, she will need $3 worth of yarn. If she plans on making 100 scarves, how much must she charge for each scarf in order to be able to pay for her trip?
Answer:
$8 each scarf
Explanation:
Let the selling price for each scarf be x,
Formula:
unit amount(selling price - cost price) = total profit
Stepwise:
100(x - 3) = 500
100(x) - 100(3) = 500
100x - 300 = 500
100x = 500 + 300
100x = 800
x = 8
I'm having a hard time with this question so someone help please
Answer:
7.7 km
Step-by-step explanation:
This question is asking you to find the third side of a triangle in which two sides and an angle not between them are given. The law of sines provides the necessary relationships.
Law of SinesThe Law of Sines tells you that triangle side lengths are proportional to the sine of the opposite angle. For this triangle TPJ, the relation is ...
t/sin(T) = p/sin(P) = j/sin(J)
We are given T=68°, p=5.2 km, t=7.5 km, and we are asked to find the length of j, the TP distance.
SetupWe know the sum of angles in a triangle is 180°, and the sine of an angle is equal to the sine of its supplement. This lets us fill in the Law of Sines equation like this:
7.5/sin(68°) = 5.2/sin(P) = j/sin(68°+P) . . . . . solve for j
SolutionThis can be solved in two steps. First, we find angle P, then we use that to find length j.
sin(P) = 5.2/7.5 × sin(68°) ≈ 0.642847
P = arcsin(0.642847) ≈ 40.0045°
Now, we can find j:
j = 7.5 × sin(68° +40.0045°)/sin(68°) ≈ 7.693 . . . km
The distance from the tower to the plane is about 7.7 km.
__
Additional comment
We have used T, P, and J to refer to the vertices at the tower, plane, and jet.
The triangle can also be solved using the Law of Cosines. In that case, the missing side will be the solution to a quadratic equation with irrational coefficients.
PLEASE HELP!!! THIS IS TIMED!!! PLEASE HELP ASAP!! How many solutions does this system have?
2 x minus 3 y = 10. Negative 4 x + 6 y = negative 20.
one
two
an infinite number
no solution
Answer:
No solution
Step-by-step explanation:
The equations:
2x – 3y = 10 → equ(1)
–4x + 6y = 20 → equ(2)
Using elimination method, and solving with y, we have:
3( –4x + 6y = 20) → equ(3)
6( 2x – 3y = 10) → equ(4)
Opening the bracket, we have:
–12x + 18y = 60
+12x – 18y = 60
From the above, we can see that both x and y are now eliminated, thereby giving us: 0 = 120 which makes no sense to me as it looks incorrect.
Therefore, there is no solution to the given equation.
I hope this helps
Answer:
One
Step-by-step explanation:
Line ab passes through points a(-6,6) and b(12,3). if the equation of the line is written in slope-intercept form, y=mx+b, then m= -1/6. what is the value of b?
Answer: 5
Step-by-step explanation:
We have the equation of the line is of the form [tex]y=-\frac{1}{6}x+b[/tex].
Substituting in the coordinates (12,3), we get that:
[tex]3=-\frac{1}{6}(12)+b\\\\3=-2+b\\\\b=5[/tex]
you can afford to invest $150 per month in an annuity that earns 4% per year, compounded monthly. How long will it take before your investment is worth $6000?
The time it will take before your investment is worth $6000 = 7 years
Calculation of simple interestThe amount of money invested per month = $150
Therefore the amount principally invested yearly;
= 12 × 150 = $1,800
Simple interest = $6000
Rate = 4%
Time = ?
Using the formula for Simple interest (SI)= P×T×R/100
Make T the subject of formula,
T = SI × 100/P×R
T = $6000×100/1800×4
T = 600000/7200
T= 83 months/ 12 = 7 years
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Find the surface area of the prism. Round to the nearest tenth if necessary.
Answer:
480
Step-by-step explanation:
First, lets solve for the area of the 3 rectangles in the prism
One can be found by doing 17*9. The other, 8*9, the last 15*9
Next, lets solve for the 2 triangles. This is found with...
1/2(8)(15). This turns out to be 60, and we multiply that by 2 since there are 2 of those triangles.
Add everything up:
72+153+135+120 = 480
Which of the following is equivalent to 5 squareroot of 13 3
The exponential form of ⁵√13³ is [tex]13^{3/5}[/tex].
Hence, option D) is the correct answer.
This question is incomplete, the complete question is:
Which of the following is equivalent to 5 sqrt 13³ ?.
A) 13^2.
B)13^15.
C)13^(5/3).
D)13^(3/5)
What is equivalent to 5 sqrt 13³ ?Given the expression; 5 sqrt 13³
This can be represented as; ⁵√13³
To convert from radical form to exponential form, we use apply the radical rule;
[tex]\sqrt[n]{a^m} = a^{m/n}[/tex]
Hence,
[tex]\sqrt[5]{13^3} = 13^{3/5}[/tex]
The exponential form of ⁵√13³ is [tex]13^{3/5}[/tex].
Hence, option D) is the correct answer.
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Jeri finds a pile of money with at least $200. If she puts $80 of the pile in her left pocket, gives away 1/3 of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away $200 of the original pile and kept the rest. What are the possible values of the number of dollars in the original pile of money? (Give your answer as an interval.)
The possible values of the number of dollars in the original pile of money is on the interval (200, 440)
How to solve Inequality Word Problems?We are told that Jeri finds a pile of money with at least $200.
Now, let x be the additional amount over the original amount of $200.
The greater side of the inequality will be expressed as;
Original pile = (200 + x)
After she gives away $80 and as such she has; (120 + x)
And she gives (1/3) of this away which means she will have;
= (1/3) (120 + x)
Thus, she must have (2/3) of this left
= (2/3)(120 + x) = amount in her right pocket
The lesser side of the inequality is expressed as;
(x + 200) - 200 = x
Thus, we now have that;
2[120 + x ]/3 > x
240 + 2x > 3x
240 > 3x - 2x
240 > x
x < 240
Thus, we can conclude that the original amount could be on the interval (200, 440)
The possible values of the number of dollars in the original pile of money is on the interval (200, 440)
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If joe travels 434 miles in 7 hours, how far will he travel in 10 hours at the same speed?
He travels 620miles at the same speed.
Given that joe travels 434 miles in 7 hours.
An object's speed is determined by how quickly it moves. It is the distance a body travels in one unit of time.
Firstly, we will find the speed when the distance is 434 miles and the time is 7 hours by using the formula
Speed=Distance/Time
Substitute the values in the formula, we get
Speed=434miles/7 hours
Speed=62 miles/hour
Now, we will find the distance when time is 10 hours, we get
62=distance/10
Multiply both sides by 10, and we get
62×10=(distance/10)×10
620miles=distance.
Hence, in 10 hours at the same speed, he travels when joe travels 434 miles in 7 hours is 620miles.
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A kite is made up of two isosceles triangles, KIT and KET, with the lengths shown. The top triangle of the kite, ΔKIT, is made from approximately 17 square inches of material.
Isosceles triangles K I T and K E T are connected at side K T. The length of K T is 10 inches. The length of sides K E and E T are 8 inches. The lengths of sides K I and I T are 6 inches.
Heron’s formula: Area = StartRoot s (s minus a) (s minus b) (s minus c) EndRoot
How much material is used for the entire kite, quadrilateral KITE? Round to the nearest square inch.
31 square inches
34 square inches
48 square inches
62 square inches
The amount of material needed for the entire kite is 48 square inches
How to determine the amount of material?The given parameters:
KI =6 inches
ET = 8 inches
KT=10 inches
Area of ΔKIT = 17 square inches
Start by calculating the area of the bottom triangle using:
A = 0.5 * Base * Height
This gives
A = 0.5 * 10 * 6
Evaluate
A = 30
The amount of material is
A = 30 + 17
A = 47
Hence, 48 square inches of material is used for the entire kite, quadrilateral KITE
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Corresponding Parts Of Congruent Figures Are Congruent
Please Help !!
In Mathematics, two geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.
Since we know that rigid motions preserve both the side length and angle measure, this ultimately implies that congruent segments have the same (equal) length.
Thus, line segment UV ≅ line segment XY i.e UV = XY and as such the side lengths are as follows:
SU = VX = 43 feet.
For the congruent angles, we have:
<J ≅ <K i.e m<J = m<K
m<S = m<V = 38°.
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FIRST PERSON TO ANSWER GETS BRAINLIEST OR FIVE STARS Define the domain and range of the function.
Domain:
Range:
Answer:
Domain: (-∞, ∞)
Range: (-∞, ∞)
Step-by-step explanation:
The domain are the x-values included in the function (the horizontal axis).
The range are the y-values included in the function (the vertical axis).
The two arrows on the ends of the line (pointing upwards and downwards respectively) indicate that the function goes in those direction for infinity. Therefore, if there are an infinite amount of y-values, the range is (-∞, ∞).
While the slope is quite steep, there is still a slope and slowly "expands" the line on the horizontal axis. Because there is no limit to the y-values, the domain will also expand infinitely. Therefore, the domain is also (-∞, ∞).
Answer:
Domain: All real numbers (interval notation: [tex](-[/tex]∞, ∞[tex])[/tex]
Range: All real numbers (interval notation: [tex](-[/tex]∞, ∞[tex])[/tex].
Step-by-step explanation: The domain of a graph is all the x-values where the line touches or will eventually touch.
The range of a graph is like the domain, but it is all the y-values where the line touches or will touch.
In a linear function in the form y = mx + b or ax + by = c, the domain and range will always be "all real numbers" and the interval will always be (-∞, ∞). This makes sense since a line always goes on forever (unless it's piecewise or an inequality.) So the line will eventually meet every single x and y value on the xy graph.
Help me please 10 pts for you mark you brainliest
Answer 1: A and C
Step-by-step explanation:
Use distribution law to see which answer match the equation at the top.
Answer 2: 16q + 4
10q and 6q are like terms
10q + 6q = 16q
+
5 - 1
Answer:
Hello,
Step-by-step explanation:
page 1:
60-36j=12(5-3j) answer C
=6(10-6j) answer A
page 2:
10q+5+6q-1=16q+4=4(4q+1)
page 3:
24j-16=8(3j-2)
page 4:
10h+30+50j=10*(h+3+5j) answer B
=2*(5h+15+25j) answer C
=5(2h+6+10j) not A nor D
Help me please
6. Find the LCM of 22a³b³c4 and 55abc.
O 110abc
O 77a³b³c¹
O 110a³b³c4
O 11a³b³c4
Your team decides to erect 8 tent frames that can each hold a tarp to provide shade and cover if needed. The area under each tarp is 25 feet wide and 40 feet long, and the top of the tarp will run the length of your seating area. Your tarp needs a slope of to allow runoff in case of rain. The frame will be 10 feet high around the outside. 5. How high does the center of the frame need to be?
The height of the center of the frame has to be 15ft.
How to solve for the height of the frameSlope of the tarp is given as 2/5
The height is said to be 10 feet
The width is given as 25
25/2 = 12.5
AB/BC = 2/5
AB/12.5 = 2/5
cross multiply to find AB
5AB = 25
AB = 5
The height = 10 feet + 5 feet
= 15 feet
Hence the center of the frame has to be 15 feet.
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which of the following can be used to support the idea that the set of polynomials is closed under multiplication?
A) (5x-1)(3x^2+4x)
B) (9x^-3-5)(2x-17)
C) (10x^0.5)(5x^0.5+4)
D) (2x^-1-5x^4)(7x-2^-5)
The polynomial which can be used to support the idea that the set of polynomials is closed under multiplication is: A. (5x - 1)(3x² + 4x).
What is a polynomial?A polynomial can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations such as:
AdditionSubtractionMultiplicationIn Mathematics, a set is considered as closed under a multiplication operation, if the multiplication performed on two (2) elements of the set produces an element of the same set.
Note: The exponents of the variables are added when multiplying polynomials in accordance to the rules of exponents.
For option A, we have:
P = (5x - 1)(3x² + 4x)
P = 15x³ - 3x² + 20x² - 4x
P = 15x³ - 23x² - 4x.
For option B, we have:
P = (9x⁻³ - 5)(3x - 17)
P = 27x⁻² - 15x - 153x⁻³ + 85.
In conclusion, we can infer and logically deduce that the polynomial (5x - 1)(3x² + 4x) can be used to support the idea that the set of polynomials is closed under multiplication.
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Find the area of the figure
Answer:
100
Step-by-step explanation:
Lets first find the area of the greater square:
[tex]8*14=112[/tex]
And now the area of the cut inside of the square:
[tex]3*4=12[/tex]
Now subtract the area cut from the area of the greater square:
[tex]112-12=100[/tex]
Arnold paid R2 599,99 for a car sound system in 1997 Assuming an average inflation rate of 7% per annum what did he pay for a sound system with the equivalent value in 2014
The value of the car in 2014 is 154709
How to determine the value?The given parameters are:
Initial, a = 599,99
Rate, r = 7%
The value of the car in t years is
Value = a * (1 + r)^t
This gives
Value = 59999 * (1 + 7%)^t
2014 is 17 years from 1997.
So, we have:
Value = 59999 * (1 + 7%)^14
Evaluate
Value = 154709
Hence, the value of the car in 2014 is 154709
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What is the factored form of 27 - 530?
(2 - 10 ) ( - 590) (9 - 510)
( 20 + 1820م + 18 ) ( 10 - 2) -
O
O
0
(2 - 10) ( 9 + 9 10 + 510)
(2 - 10 ) ( 18 + 2 510 + 20 )
All of the following are suggestions of things to do if you have time left after completing the test except:
The correct option is B. Reread the directions for each section.
If you have time left after completing the test don't reread the directions for each section.
What is meant previewing a test?In order to find the various problem kinds and their point values during the test preview, you must read the complete test. Mark the questions that you can answer quickly and easily.
The benefits of previewing the test are-
You will probably be given credit for the answers even if you accidentally copied them from the scratch paper.Your effort on the scratch paper can earn you some points if a thoughtless mistake causes you to get the answer wrong.If you do make a mistake, it will be simpler to find it when the instructor goes through the test. By doing this, you can avoid making the same errors on your next exam.Therefore, resolve each issue by re-entering the solution into the equation or performing the opposing operation needed to provide the appropriate response. Do not leave the testing room until the bell has rung or after you have gone over each problem twice.
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The complete question is-
All of the following are suggestions of things to do if you have time left after completing the test except
A. Look at your answer sheet to make sure its filled properly
B. Reread the directions for each section
C. Return to the questioms you were unsure of
D. Make sure your answers correspond to the correct questions
The probability of correctly rejecting the null hypothesis when the null hypothesis is false is the _____.
The probability of correctly rejecting the null hypothesis when the null hypothesis is false is the power
How to complete statement?From the question, we have the following highlights
Null hypothesis is falseNull hypothesis is correctly rejectedThe statement that represents the probability of the above highlights is power
Hence, the statement that completes the blank is power
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Starting at its rightmost position, it takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right. Write a cosine function, d
The cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds) is d(t) = 6cos([tex]\pi[/tex]t).
What is the principle of pendulum?As long as its length is constant, a pendulum completes each swing (or oscillation) in precisely the same amount of time. Any particular pendulum oscillates for a fixed amount of time.
Calculation for the cosine function-
The given function is: cosine function, d = acos(bt).
As, the pendulum takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right.
The total time 't' by the pendulum is 2 sec.
Calculate the angular speed of the pendulum by-
ω = 2[tex]\pi[/tex]f
= 2[tex]\pi[/tex]×(1/2)
ω = [tex]\pi[/tex] which is 'b' value of the given function.
As given, the distance of the pendulum from the centre is half of the total distance.
a = 12/2
a = 6
Substitute the obtained values in the cosine function, d = acos(bt),
d(t) = 6cos([tex]\pi[/tex]t)
Therefore, the cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds) is d(t) = 6cos([tex]\pi[/tex]t).
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The complete question is -
Starting at its rightmost position, it takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right. Write a cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds).
Answer:
a=6
The period is 2 seconds.
b=pi
t=0.5
d=4.243
Step-by-step explanation:
Which of the following is an arithmetic sequence where a₁ = 9 and d= 7?
A) 9, 16, 23, 30, 37, ...
B) 0, 9, 18, 27, 36,...
C) 7, 16, 25, 34, 43,...
D) 0, 7, 14, 21, 28, ...
Answer:
Option A
Step-by-step explanation:
Arithmetic sequence:In a arithmetic sequence, difference between any two consecutive term is constant.
a₁ = 9 & d = 7
t₁ = 9
t₂ = a₁ + d
= 9 + 7
= 16
t₃ = t₂ + d = 16+ 7
= 23
t₄ = t₃ + d
= 23 + 7
= 30
t₅ = t₄ + d
= 30 + 7
= 37
9,16,23,30,37,.......
What is the
y-intercept
of this line?
Answer: (0, 3)
Step-by-step explanation:
The y-intercept of the line is where the line intercepts the y-axis. In other words, the coordinate value of the line when x is 0.
Answer: (3, 0)
Step-by-step explanation:
y-intercept = y=a number and x=0
So, y=3, x=0.
(3, 0)
1. The perimeter of a rectangle is 16cm, and the area of the same rectangle is 8cm^2. What is the diagonal length of the rectangle?
2. Kendrick rides his bike x miles per hour to school and it takes him x + 15 minutes to get there. If Kendrick lives 5.4 miles from school, how many minutes does it take for Kendrick to ride to school?
Answer:
Step-by-step explanation:
What are the ratios for sin A and cos A? The diagram is not drawn to scale.
Answer:
C
Step-by-step explanation:
Sin represents opposite/hypotenuse. Thus, when A is the reference angle, 21 is the measure of the opposite side (CB) and 29 is the measure of the hypotenuse (AB).
Cos represents adjacent/hypotenuse. Therefore, when A is the reference angle, 20 is the measure of the adjacent side (AC) and 29 is the measure of the hypotenuse (AB).
Our company parking lot has cars, trucks, and motorcycles. The ratio of cars, trucks, and motorcycles is $4:3:2.$ If there are a total of $42$ cars and trucks, then how many motorcycles are there
There are 12 motorcycles in a company.
According to the statement
The ratio of cars, trucks, and motorcycles is 4:3:2.
The total number of cars and trucks is 42.
then
4x + 3x =42
7x = 42
x = 6.
now put these values in the ratio of vehicles.
Number of cars = 4*6 = 24
Number of truck = 3*6 = 18
Number of motorcycle = 2*6 = 12
So, There are 12 motorcycles in a company.
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There is a number that if you subtract 9 from it first, and then divide that total by 6, you get 7. What's the number?
Answer:
51
Step-by-step explanation:
Translate the problem into an equation and solve the equation.
(x - 9)/6 = 7
x - 9 = 42
x = 51
Answer: 51
Answer:
51
Step-by-step explanation:
Create an equation.
[tex]\frac{(x-9)}{6} = 7[/tex]
Multiply 6 to both sides.
x-9 = 42
Add 9 to both sides.
x=51
To check if this is correct follow the steps given in the question.
51-9=42
42÷6=7
It is correct.
Hope this helps!
Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown: A coordinate grid is shown from negative 5 to 0 to 5 on both x -and y-axes. A polygon ABCD has A at ordered pair 1, 3, B at ordered pair 3, 4, C at ordered pair 2, 1, D at ordered pair 1, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 3, 3, B prime at ordered pair negative 5, 4, C prime at ordered pair negative 4, 1, D prime at ordered pair negative 3, 1. Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD?
Figure ABCD was translated 2 units to the right so as to obtain figure A'B'C'D'
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.
Figure ABCD was translated 2 units to the right so as to obtain figure A'B'C'D'
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