Answer:
y-3=-1/5(x+6)
Step-by-step explanation:
The student setup 30 games booths;the teachers also setup some. If 5/6 of the game booths were set up by the students, how many game booths are there in total?
The total number of game booths is 36, with the students setting up 30 booths denoting 5/6 of the total, and teachers setting up the remaining 6 booths which corresponds to 1/6 of the total.
Explanation:The student question asks about finding the total number of game booths if 5/6 of them were set up by students, and it is known that students set up 30 booths. First, we assume the fraction 5/6 represents the portion of booths that the students were responsible for setting up. Since 5/6 equates to the 30 booths the students set up, each fraction of 1/6 represents 6 booths (30 divided by 5). As there are 6 fractions of 1/6 in a whole, to find the total (which is 6/6), you simply multiply 6 (the value of 1/6) by 6.
The calculation is as follows: 6 booths per 1/6 x 6 = 36 game booths in total. Therefore, the teachers set up the remaining sixth, which corresponds to 6 game booths, making the combined total 36. This result indicates that there is a total of 36 game booths when we include the contributions from both students and teachers.
In this case, There are 36 game booths in total.
Let's denote the total number of game booths as T.
According to the information given, 5/6 of the game booths were set up by the students.
Since the students set up 30 game booths, we can write the following equation:
[tex]\[\frac{5}{6}T = 30\][/tex]
To find the total number of game booths, T, we need to solve for T.
We can do this by multiplying both sides of the equation by the reciprocal of 5/6, which is 6/5:
[tex]\[T = 30 \times \frac{6}{5}\][/tex]
Now, we calculate the value of T:
[tex]\[T = 30 \times \frac{6}{5}\][/tex]
T = 36
Therefore, there are 36 game booths in total.
Please help me the brainliest.
Answer:
A² - B² = 0 (Proved).
Step-by-step explanation:
Given that
[tex]A = \frac{\cot \theta + \csc \theta - 1}{\cot \theta - \csc \theta + 1}[/tex]
⇒[tex]A = \frac{\csc \theta + \cot \theta - (\csc^{2} \theta - \cot^{2} \theta)}{\cot \theta - \csc \theta + 1}[/tex]
{Since, we know the identity as [tex]1 = \csc^{2} \theta - \cot^{2} \theta[/tex]}
⇒ [tex]A = \frac{\csc \theta + \cot \theta - (\csc \theta + \cot \theta)\times (\csc \theta - \cot \theta)}{\cot \theta - \csc \theta + 1}[/tex]
⇒ [tex]A = \frac{(\csc \theta + \cot \theta) (\cot \theta - \csc \theta + 1)}{\cot \theta - \csc \theta + 1}[/tex]
⇒ [tex]A = \csc \theta + \cot \theta[/tex]
Again, given that [tex]B = \csc \theta + \cot \theta[/tex]
So, A = B . ⇒ (A - B) = 0.
Hence, A² - B² = (A + B)(A - B) = 0 (Proved)
change 0.03 to mixed number
Answer: 3/100
Step-by-step explanation: Using the place value chart, we can see that 0.03 means 3 hundredths so 0.03 can be written as the fraction 3/100.
3/100 is a proper fraction so it can't be changed to a mixed number.
the dimensions of a blackboard are 9/10 of a meter by 7/10 of a meter. In drawing of the blackboard given below, 1/2 of a inch represents 2 meters. What is unit rate of area in square meters of the blackboard per square inch of area in the drawing?
Answer:
16 square meters per square inch
Step-by-step explanation:
we know that
The scale drawing is
[tex]\frac{(1/2)}{2}=\frac{1}{4}\ \frac{in}{m}[/tex]
That means ---> 1 in in the drawing represent 4 meters in the actual
Find the dimensions of the blackboard in the drawing
Divide by 4
[tex]\frac{9}{10}\ m=\frac{9}{10}/4=\frac{9}{40}\ in[/tex]
[tex]\frac{7}{10}\ m=\frac{7}{10}/4=\frac{7}{40}\ in[/tex]
Find the area of the blackboard
[tex](\frac{9}{10})(\frac{7}{10})=\frac{63}{100}\ m^2[/tex]
Find the area in the drawing
[tex](\frac{9}{40})(\frac{7}{40})=\frac{63}{1,600}\ in^2[/tex]
Find out the unit rate of area in square meters of the blackboard per square inch of area in the drawing
[tex](\frac{63}{100})/(\frac{63}{1,600})=\frac{1,600}{100}=16\ \frac{m^2}{in^2} [/tex]
10. Which of the following functions is the inverse of the function {(1,2).(3,4).(6,8)) ? (1 point)
A. {(6,8).(3,4),(1,2))
B. {(2,1),(4,3).(6,8)}
C. {(2,1),(4,3), (8,6)
D. {(2,1),(3,4).(8.6)]
Answer:
C
Step-by-step explanation:
Inverse of function(x,y) is equal to (y,x)
A dairy needs 332 gallons of milk containing 6% butterfat. How many gallons each of milk containing 7% butterfat and milk containing 3% butterfat must be used to obtain the desired 332 gallons?
Answer:
249 gallons of 7% butterfat milk and 83 gallons of 3% butterfat milk
Step-by-step explanation:
If x is the gallons of 7% butterfat milk, and y is the gallons of 3% butterfat milk, then:
x + y = 332
0.07x + 0.03y = 0.06(332)
Solve the system of equations using substitution:
0.07x + 0.03(332 − x) = 0.06(332)
0.07x + 9.96 − 0.03x = 19.92
0.04x = 9.96
x = 249
y = 332 − x
y = 83
You need 249 gallons of 7% butterfat milk and 83 gallons of 3% butterfat milk.
a rectangles width is 4 less than its area and its length is 19. what is it’s width?
The width of the rectangle is [tex]\frac{2}{9}[/tex] unit
Step-by-step explanation:
The given is:
A rectangles width is 4 less than its areaIts length is 19 unitsWe need to find the width of the rectangle
Assume that the width of the rectangle is x units
∵ The area of the rectangle = length × width
∵ The width of the rectangle = x units
∵ The length of the rectangle = 19 units
∴ The area of the square = 19 × x = 19 x units²
∵ The width of the rectangle is 4 less than its area
- That means subtract 4 from the area to find the width
∴ x = 19 x - 4
- Subtract 19 x from both sides
∴ -18 x = -4
- Divide both sides by -18
∴ x = [tex]\frac{-4}{-18}[/tex]
- Reduce the fraction by dividing up and down by -2
∴ x = [tex]\frac{2}{9}[/tex]
The width of the rectangle is [tex]\frac{2}{9}[/tex] unit
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Height is proportional to foot length. A person whose foot length is 10 inches is 67 inches tall. A human-like creature has a foot length of 35 inches. Use a proportion to find the height of the creature.
Answer:
the creature 268 inches tall
Step-by-step explanation:
set it up and cross multiply!
10 = 40
67 X
67*40=10*X
2680=10X
then divide 10 from both sides:
so X=268
A cylinder and a cone have the same volume. the cylinder has a radius of 2 inches and a height of 3 inches. the cone has a radius of 3 inches. What is the height of the come?
Answer:h = y^2 / 27
Step-by-step explanation:
Volume of a cylinder = pi*(xx)^2*yy
= x^4*pi*yy
Volume of a cone = 1/3*pi*(9x^2)^2*h
= 27pi*x^4*h
x^4*pi*y^2 = 27pi*x^4*h
h = y^2 / 27
Answer:
4 inches
Step-by-step explanation:
The volume of the cylinder is:
V = π r² h
V = π (2)² (3)
V = 12π
The cone has the same volume, so its height is:
V = ⅓ π r² h
12π = ⅓ π (3)² h
12π = 3π h
h = 4
The height of the cone is 4 inches.
dis
You roll a fair 6-sided die.
What is P(not 5)?
If necessary, round your answer to 2 decimal places.
ro
Answer:
There would be an 83.3% chance (0.83 chance) that the die would not land on 5.
Step-by-step explanation:
Use the probability formula: [tex]\frac{desired}{total}[/tex] (desired events over total events)
There are 5 desired events. (The events that the die would not land on five)There are 6 total events.[tex]\frac{desired}{total} =\frac{5}{6}= 0.8333333[/tex]
Rounded to two decimal places, there would be a 0.83 chance that the die would not land on 5.
10. Write an equation in point-slope form and slope-intercept form for the line.
Passes through (2,-2) and (4,-1)
We can use the points (2, -2) and (4, -1) to solve.
Slope formula: y2-y1/x2-x1
= -1-2/4-(-2)
= -3/6
= -1/2
Point slope form: y - y1 = m(x - x1)
y - 2 = -1/2(x + 2)
Solve for y-intercept.
-2 = -1/2(2) + b
-2 = -1 + b
-2 + 1 = -1 + 1 + b
-1 = b
Slope Intercept Form: y = mx + b
y = -1/2x - 1
______
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a cylindrical well has a radius of 10 feet and a height of 15 feet what volume of water will it take to fill in the well
Volume of water will it take to fill in the well is 4710 cubic feet
Solution:Given that a cylindrical well has a radius of 10 feet
Height of cylindrical well = 15 feet
To find: volume of water will it take to fill in the well
Since, the well is in the form of cylinder, This means that we need to find the volume of cylindrical well
The volume of cylinder is given as:
[tex]\text { Volume of water in the well }=\pi r^{2} h[/tex]
Where "r" is the radius and "h" is the height of cylinder
Substituting the given values we get,
[tex]\begin{array}{l}{\text { Volume of water in the well }=(3.14) \times(10)^{2} \times(15)} \\\\ {=(3.14) \times(1500)=4710}\end{array}[/tex]
[tex]\text { Volume of water in the well }=4710 \text { feet }^{3}[/tex]
Hence, the amount of water that can be stored in the well is 4710 cubic feet
Final answer:
The volume of water that will fill the cylindrical well with a radius of 10 feet and height of 15 feet is 1500π cubic feet.
Explanation:
To calculate the volume of water that will fill the cylindrical well, we need to use the formula: V = πr²h. Given that the radius is 10 feet and the height is 15 feet, we can substitute these values into the formula as follows:
V = π(10)^2(15) = 1500π cubic feet.
Therefore, it will take 1500π cubic feet of water to fill the well.
Rosa brought d drawings to an art show. After selling 15 of them, she had 38 left. Identify the equation that represents the situation and the correct solution.
The Answer:
D
Step-by-step explanation:
d=53
When 4 is subtracted from the square of a number, the result is 3 times the number. Find the positive solution.
Answer:
4
Step-by-step explanation:
The square of 4 is 16, or 4 times 4.
When you subtract 4 from it, it becomes 3 times 4.
Therefore, 4 is the answer.
Answer:
The positive solution is 4.
Step-by-step explanation:
x^2-4=3x
x^2-3x-4=0
factor out the trinomial
(x-4)(x+1)=0
zero property,
x-4=0, x+1=0
x=0+4=4
x=0-1=-1
-------------
x=4, -1
Place the indicated product in the proper location on the grid.
(4ya - 6xb)(4ya + 6xb)
Answer:
Simplify the expression.
16y^2a - 36x^2b
Step-by-step explanation: hope this helps!
Two quantities are related, as shown in the table:
x y
2 3
4 4
6 5
8 6
Which equation best represents the relationship?
y = 1 over 2 x + 2
y = 1 over 2 x + 1
y = x + 2
y = 2x + 1
Answer:
[tex]y = \frac{1}{2} x + 2[/tex].
Step-by-step explanation:
From the given table it is clear that x and y are linearly related.
Now, any two points that satisfy the relation between x and y are sufficient to express the equation.
The first two given points are (2,3), and (4,4).
Therefore, the equation is [tex]\frac{y - 4}{4 - 3} = \frac{x - 4}{4 - 2}[/tex]
⇒ [tex]y - 4 = \frac{1}{2} (x - 4)[/tex]
⇒ [tex]y - 4 = \frac{1}{2} x - 2[/tex]
⇒ [tex]y = \frac{1}{2} x + 2[/tex]. (Answer)
Answer:
A
Step-by-step explanation:
bc i said so
There are 325 rows of 9 chairs in the theater. There are 102 chairs in the the balcony. About how many chairs are there?
The total number of chairs there are in the theater and balcony is; 3027 chairs.
According to the question;
There are 325 rows in the theater.Each row contains 9 chairs.Additionally, there are 102 chairs in the balcony.In essence, The number of chairs in the theater is;
= 325 × 9= 2925 chairs.Additionally, there are 102 chairs in the balcony;
In essence, the total number of chairs is;
= 2925 + 102= 3027 chairs.Read more:
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Final answer:
To find the total number of chairs in the theater, multiply the number of rows by chairs per row and add the chairs in the balcony, resulting in approximately 3027 chairs.
Explanation:
To calculate how many chairs there are in total, we need to add the number of chairs in the rows to the number of chairs in the balcony.
First, multiply the number of rows by the number of chairs per row to find the total number of chairs in the rows: 325 rows × 9 chairs per row = 2925 chairs.
Then, add the number of chairs in the balcony to this total: 2925 chairs + 102 chairs in the balcony = 3027 chairs. So, there are approximately 3027 chairs in the theater.
Step by step I need
The circumference of a circle with a 6 in diameter using pi
[tex]\bf \textit{circumference of a circle}\\\\ C=\pi d~~ \begin{cases} d=diameter\\[-0.5em] \hrulefill\\ d = 6 \end{cases}\implies C=6\pi \implies C\approx 18.85[/tex]
The next model of a sports car will cost more than the current model. The current model costs . How much will the price increase in dollars? What will be the price of the next model?
Answer:
$1677
$40677
Step-by-step explanation:
Compared to the price of the current model sports can the next model price will be 4.3% higher.
The cost of the current model sports car is $39000.
Therefore, the price will increase in the next model by [tex]\frac{39000 \times 4.3}{100} = 1677[/tex] dollars. (Answer)
Now, the price of the next model will be $(39000 + 1677) = $40677 (Answer)
The price increase in dollars for the next sports car model, priced at 4.3% more than the current value, is $1,677. So, the next model of the sports car will cost $40,677.
Explanation:The subject of this question is about the calculation of a price increase in mathematical terms. If the next model of a sports car is going to cost 4.3% more than the current model, which costs $39,000, then first we need to find out how much exactly 4.3% of $39,000 is. The calculation involves multiplying 39,000 by 4.3%, which comes out to $1,677.
Therefore, the price of the next model of a sports car will be the current price which is $39,000 plus the price increase in dollars i.e., $1,677. Hence, adding the two amounts gives us a total cost of $40,677 which is the price of the upcoming model.
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solve 2cos^2x+sinx-1=0, if 0<=x<=2pi
The equation 2cos²x + sinx - 1 = 0 can be solved by converting terms involving cosine to sine, simplifying the equation, and then solving the resulting quadratic equation for sinx and consequently solving for x.
Explanation:To solve the trigonometric equation 2cos²x + sinx - 1 = 0, we can first convert the terms in the equation involving cosine to terms involving sine.
We know that cos²x= 1 - sin²x. Substituting this into the equation, we will have 2(1 - sin^2x) + sinx - 1 = 0.
This simplifies to 2 - 2sin²x + sinx - 1 = 0. Reordering terms, we get 2sin²x - sinx + 1 = 0. If we solve this quadratic equation for sinx, we can then solve for x. Assuming the domain 0<=x<=2pi, this will give us the possible values of x that satisfy the original equation.
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The three-dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. Find the volume of the solid in cubic centimeters.
A solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it is shown. The rectangular prism is 20 centimeters long, 5 centimeters wide, and 5 centimeters high. The rectangular prism-shaped-hole is 20 centimeters long, 2 centimeters wide, and 2 centimeters high.
The volume of the solid is 420 cm³
Step-by-step explanation:
The volume a rectangular prism is calculated as the product of its length, width and height.
Mathematically, V=l*w*h where l is length of the prism, w is width and h is the height
Given that the dimensions of the rectangular prism as;
Length=20 cm
Width= 5 cm
Height = 5 cm
V=20*5*5= 500 cm³
The rectangular prism shaped hole dimensions are;
Length= 20 cm
width= 2 cm
Height= 2 cm
Volume= 20*2*2=80 cm³
The volume of the solid will be: volume of rectangular prism-volume of the hole
Volume= 500-80=420 cm³
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The volume of the solid rectangular prism with a hole is 420 cm³.
To find the volume of the solid rectangular prism with a hole, we follow these steps:
Volume of the Outer Rectangular Prism:
Using the formula V = l * w * h, where l is the length, w is the width, and h is the height of the outer rectangular prism:
Volume of the outer prism (V_outer) = 20 cm * 5 cm * 5 cm = 500 cm³.
Volume of the Rectangular Prism-shaped Hole:
Using the same formula for the inner rectangular prism:
Volume of the hole (V_hole) = 20 cm * 2 cm * 2 cm = 80 cm³.
Volume of the Solid:
Subtracting the volume of the hole from the volume of the outer prism:
Volume of the solid (V_solid) = V_outer - V_hole = 500 cm³ - 80 cm³ = 420 cm³.
Therefore, the volume of the solid rectangular prism with a hole is 420 cm³.
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14. Luis placed $4500 in a certificate of deposit. He earns $20 each month
for the next 36 months. Find the annual simple interest rate for the
certificate of deposit.
To find the annual simple interest rate for the certificate of deposit, divide the total interest earned by the principal amount. In this case, the annual interest rate is 16%.
Explanation:The amount of simple interest Luis earns each month is $20, and he earns this for the next 36 months. We can find the total interest earned by multiplying the monthly interest by the number of months: $20 x 36 = $720.
To find the annual simple interest rate for the certificate of deposit, we need to divide the total interest earned by the principal amount. In this case, the principal amount is $4500. So, the annual interest rate is calculated as: $720 / $4500 = 0.16 or 16%.
Therefore, the annual simple interest rate for the certificate of deposit is 16%.
Alex bought a new truck for $42,935. According to the dealer, the truck will depreciate approximately $4,200 per year. Write and solve a linear equation to find how many years until the car is worth $5,135
Answer:
The truck is worth $5,135 when 9 years have passed
Step-by-step explanation:
Initial value of Alex's new truck: $42,935
Loss of value per year: $4,200
If n years passed, the truck would have lost
[tex]4,200n\ dollars[/tex]
The current value of the truck will be
[tex]V(n)=42,935-4,200n[/tex]
We want to know the value of n at which V is 5,135
[tex]5,135=42,935-4,200n[/tex]
Solving for n
[tex]n=\frac{42,935-5,135}{4,200}[/tex]
n=9 years
The truck will depreciate to a value of $5,135 in approximately 9 years, given a yearly depreciation rate of $4,200.
Explanation:This problem involves finding the duration it will take for the truck to depreciate from $42,935 to $5,135, given it depreciates at a rate of $4,200 per year. The difference in value is $42,935 - $5,135 which equals $37,800. This depreciation amount has to be distributed over the years so we divide it by the yearly depreciation rate. This is represented by the equation 37,800 = 4,200x, with x being the number of years. Thus, solving for x gives x = 37,800 / 4,200 which is approximately 9 years. Therefore, it will take about 9 years for the truck to depreciate to a value of $5,135.
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Which of the following point-slope form equations could be produced with the points (2, -6) and (4, -3)?
y - 6 = 3/2(x + 2)
y - 6 = 3/2(x - 2)
y + 6 = 3/2(x - 2)
y + 6 = -3/2(x + 2)
Answer:
y+6=[tex]\frac{\textbf{3}}{\textbf{2}}[/tex](x-2)Step-by-step explanation:
A line passes through the points [tex](2,-6)[/tex] and [tex](4,-3)[/tex].
To find the point-slope form of the line, we need a point on the line and the slope of the line.
As we have two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex], the slope can be calculated as [tex]\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
Slope of the line = [tex]\dfrac{-3-(-6)}{4-2}=\dfrac{3}{2}[/tex]
Given a line with slope [tex]m[/tex] and a point [tex](x_{1},y_{1})[/tex], slope-point form is [tex]y-y_{1}=m(x-x_{1})[/tex]
Line is given by [tex]y+6=\frac{3}{2}(x-2)[/tex]
∴ The line is given by [tex]y+6=\frac{3}{2}(x-2)[/tex]
Final answer:
The correct point-slope form equation with the points (2, -6) and (4, -3) is y + 6 = 3/2(x - 2), after finding the slope of 3/2 and applying it to the point-slope formula using either of the points.
Explanation:
Firstly, let's find the slope of the line passing through the points (2, -6) and (4, -3). The slope formula is
(y₂ - y₁) / (x₂ - x₁), so plug in the values to get (-3 - (-6)) / (4 - 2) = 3 / 2.
Now we know the slope is 3/2, we can write a point-slope form equation, which is y - y₁ = m(x - x₁). We can use either of the given points; let's use (2, -6). Substituting these values into the point-slope formula gives us: y - (-6) = 3/2(x - 2).
Thus, the correct point-slope form equation produced with the points (2, -6) and (4, -3) is: y + 6 = 3/2(x - 2).
Solve for k 1/4 k=3(-1/4K+3)
Answer:
k=9
Step-by-step explanation:
1/4k=3(-1/4k+3)
1/4k=-3/4k+9
1/4k-(-3/4k)=9
1/4k+3/4k=9
k=9
What is the slope of a line perpendicular to the line -3x + 6y = -15?
Answer:
slope of a line perpendicular to the line -3x + 6y = -15 is -2
Step-by-step explanation:
-3x + 6y = 15
solve for y,
y = 1/2 x + 15/6
slope of a line perpendicular is the "negative reciprocal" of the slope of the original line, thus
y = -2 x + b
Determine algebraically whether the function is even, odd, or neither even nor odd. f(x) = x + 4/x
Answer:
The given function is an odd function.
Step-by-step explanation:
We define a function f(x) as even function when f(-x) = f(x) and odd function when f(-x) = - f(x) and otherwise it is neither even nor odd function.
Now, we are given a function of x as [tex]f(x) = x + \frac{4}{x}[/tex] and we have to deternime whether the function f(x) is even, odd, or neither even nor odd.
Now, [tex]f(-x) = - x + \frac{4}{- x} = - x - \frac{4}{x} = - [x + \frac{4}{x}] = - f(x)[/tex]
Therefore, the given function is an odd function. (Answer)
What is Y/2 +3.2=5.06
Answer:
y=3.72
Step-by-step explanation:
y/2+3.2=5.06
y/2=5.06-3.2
y/2=1.86
y=1.86*2
y=3.72
Answer:
y= 3.72
Step-by-step explanation:
reverse the operations
5.06-3.2= 1.86
1.86*2= 3.72
y=3.72
Why there is 1/3 cup of fruit in half a smoothie
Answer: because the other half is used on the base solution
Step-by-step explanation:
What is another way to write 75 ?
5×5×5×5×5×5×5
7+7+7+7+7
7×7×7×7×7
5+5+5+5+5+5+5
Answer:
All Of these Answer are INCORRECT!
Step-by-step explanation:
You Can tell by the first three fives in the first answer..
5*5=25*5=125=NOT GONNA WORK!
7+7+7+7+7=35= NOT GONNA WORK!
7x7 wont make it= NOT GONNA WORK!
There Never Gonna Work!
The factors of a number is are those which produce the same number when two numbers are multiplied together. It can be written as 3 × 5² or also as 15 × 5 and also as 1 × 75. The given options are not correct.
What are factors of 75?The factors of 75 are defined as the numbers which are multiplied in pairs resulting in the original number 75. In other words, the factors of 75 are also the numbers which divide the number 75 exactly without leaving the remainder.
Here 75 is a composite number and it has many factors other than the number itself. The factors of 75 are 1, 3, 5, 15, 25 and 75. In order to obtain a pair factor, multiply the two numbers in a pair to get the original number.
The pair factors of 75 are:
3 × 25 = 75
5 × 15 = 75
25 × 3 = 75
15 × 5 = 75
So the given options are not correct.
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