The first expression can be simplified to 3bm-bn and the second expression can be simplified to m²-1.
The distributive property is a fundamental property of algebra that allows you to simplify expressions by distributing or multiplying a value to each term within parentheses. The property is commonly stated as:
a(b + c) = ab + ac
1. b ( 3m - n )
distribute the terms:
3bm - bn
The FOIL method is a useful technique when multiplying binomials and simplifying expressions. The property is commonly stated as:
(a + b)(c + d) = (ac) + (ad) + (bc) + (bd)
2. (m - 1)(m + 1)
FOIL the expression:
m²-1m+1m-1
combine the like terms:
m²-1
Learn about the distributive property:
The correct question is:-
Simplify the following expressions:
1) b(3m-n)
2) (m-1)(m+1)
Assume double[][] x = new double[4][5], what are x.length and x[2].length? a. 4 and 4
b. 4 and 5 c. 5 and 4 d. 5 and 5
The x.length is the number of rows, which is 4. x[2].length is the number of columns in the 3rd row, which is 5. The expression "new double[4][5]" creates a 2D array of doubles with 4 rows and 5 columns. The correct answer is (b) 4 and 5.
The expression double[][] x = new double[4][5] creates a 2D array x with 4 rows and 5 columns. Therefore, x.length gives the number of rows, which is 4. And x[2].length gives the number of columns in the 3rd row (since array indices start at 0), which is 5. Therefore, the correct option is (b) 4 and 5.
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true or false: double integral can be used to compute the area of a region d in a plane simply by integrating the function f(x,y)
True. The double integral can be used to compute the area of a region d in a plane by integrating the function f(x,y). In fact, the double integral of f(x,y) over a region D in the xy-plane gives the volume of the solid between the surface z=f(x,y) and the xy-plane over the region D.
However, if we take the function f(x,y) to be the constant function 1, then the double integral of f(x,y) over the region D is simply the area of the region D. Therefore, we can compute the area of a region D in a plane by integrating the constant function 1 over the region D using the double integral. Integrating over two variables requires calculating two separate integrals, so the answer is more than 100 words.
True. A double integral can be used to compute the area of a region D in a plane by integrating the function f(x, y). To find the area, you would integrate the function f(x, y) = 1 over the region D, as the double integral represents the sum of the function values over the entire area. The double integral can be thought of as a generalization of single-variable integration, allowing us to find the area in two dimensions.
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(PLEASE ANSWER ASAP I NEED HELP IM FR SO BAD AT FRACTIONS BUT PLEASE EXPLAIN ASWELL
Answer:
1 1/4
Step-by-step explanation:
okay so to make 1 blanket she needs 4 1/2 yards of wool
the goal here is to add the fractions then subtract from the 4 1/2 to see how much more she needs.
STEP 1:
turn the fractions into mixed numbers\(\frac{3}{2}\ \frac{9}{4}\)
STEP 2:
next you have to find the least common multiple.(in this case 4) now we convert them(3x2 and 2x2)6/4 and since the second one is already 4 it stays as 9/4.
STEP 3: add 6/4 and 9/4= 15/4 then turn it into an improper fraction, 4 goes into 15 3 times with 1 left over so 3 1/4
STEP 4: subtract 4 1/2 and 3 1/4
once again convert to mixed numbers, subtract the numerators then change it back to an Improper fraction.
A football team consists of 20 each freshmen and sophomores, 15 juniors, and 10 seniors. Four players are selected at random to serve as captains. Find the probability that
On solving the provided question, we can say that Probability ( At least one of the students is a senior) = 0.4632 approx
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
P(All four players are senior) = 0.00033 approx
P(There is one each: freshman, sophomore, junior and senior) = 0.0944 approx.
P(There are 2 sophomores and 2 freshman) = 0.0568 approx
P( At least one of the students is a senior) = 0.4632 approx
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Complete the solution of the equation. Find th
value of y when x equals -4.
- 8x + y = 37
Enter the correct answer.
Answer:
64
Step-by-step explanation:
The quotient of a number and 8 is 47
Answer:
The way I am reading this is 16=(x/3)-8. In that case, x=72. I hope that's the right way of interpreting this :)
Step-by-step explanation:
i need help solving this question, please show work tysm!
The solution to m + (-38) = 15 is 53.
Answer:
it is true because when you do 53-38 it will be the same as 53+-38 both will have the sum of 15
Step-by-step explanation:
emilythompson35464
hope this helps srry if it doesn't tho
Answer:
YES!!!!! m=53
Step-by-step explanation:
m + (-38) = 15
m - 38 = 15
m = 53
A tunnel is constructed with a semielliptical arch. The width of the tunnel is 70 feet, and the maximum height at the center of the tunnel is 20 feet. What is the height of the tunnel 10 feet from the edge? round your answer to the hundredths place.
Considering the equation of an ellipse, it is found that the height of the tunnel 10 feet from the edge is of 14 feet.
The following is the equation for a horizontal ellipse of center with coordinates (h,k):
(x - h)²/a² + (y - k)²/b² = 1.
In relation to this issue, we have that:
The origin is where the center is.
Since the major axis is 70, 2a = 70 and a = 35.
The maximum height is 20, therefore b is equal to 20.
As a result, the ellipse's equation is as follows:
x²/35² + y²/20² = 1.
It is determined that x = 25 when the tunnel is 10 feet from the edge since 35 – 10 = 25; therefore, the height y is calculated as follows:
25²/35² + y²/20² = 1
0.51 + y²/20² = 1
y²/20² = 0.49
y² = 20² x 0.49
y =√(20² x 0.49)
y = 14 feet.
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declare two double variables, one named length with a value of 3.5 and the other named width with a value of 1.55.
named width in java with a value of 1.55.
double length = 3.5; double width = 1.55;
Double is a data type in Java that supports storing decimal numbers. It is used to represent values that include a fractional component and is a 64-bit floating-point data type. When exact decimal numbers are required, as in financial or scientific computations, the double data type is frequently utilized. A double's range is roughly ±\(5.0 \times 10^{-324}\) to ±\(1.7 \times 10^{308\) having a 15–17 decimal digit degree of accuracy.
For example:
double myDouble = 3.14; Alternatively, you may define a double variable without first giving it a value and then give it one later on in your code.
3.5 double length, 1.55 double width;
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Probability of being a boy in this class is 1/3 and there are 12 girls. Find the total
number of students.
Answer:
18
Step-by-step explanation:
The fraction 1/3 is equal to 6/18. There are 12 girls, and 6+12=18, so there is a total of 18 students.
Answer:
18
Step-by-step explanation:
By knowing that 1/3 is the probability of being in the class, you can find that 12 girls and 6 boys would sound perfect to the question. Mathematically you would solve it by 12/0.33333 and it equals 18 of total number of students. If you need more help text me on insta it's jason_lee093
Please help please...
Answer:
(2x + 5)
Step-by-step explanation:
2(x + 1) + 6x = 4(2x + 5) + 2
2x + 2 + 6x = 8x + 20 + 2
8x + 2 = 8x + 22
Because both sides are 8x it will have no solution
Second one is "all of these are correct"
With respect to the average cost curves, the marginal cost curve: Intersects average total cost, average fixed cost, and average variable cost at their minimum point b. Intersects both average total cost and average variable cost at their minimum points Intersects average total cost where it is increasing and average variable cost where it is decreasing d. Intersects only average total cost at its minimum point
With respect to the average cost curves, the marginal cost curve: intersects both average total cost and average variable cost at their minimum points that is option B.
The fixed cost per unit of production is the average fixed cost (AFC). AFC will reduce consistently as output grows since total fixed costs stay constant. The variable cost per unit of production is known as the average variable cost (AVC). AVC generally declines until it reaches a minimum and then increases due to the growing and then lowering marginal returns to the variable input. The average total cost curve's (ATC) behaviour is determined by the behaviour of the AFC and AVC.
The marginal cost is the cost added to the overall cost of producing one extra unit of output. MC initially falls until it hits a minimum and then increases. When both AVC and ATC are at their minimal points, MC equals both. Also, when AVC and ATC are dropping, MC is lower; when they are growing, it is higher.Initially, the marginal cost of manufacturing is lower than the average cost of preceding units. When MC falls below AVC, the average falls. The average cost will reduce as long as the marginal cost is smaller than the average cost.When MC surpasses ATC, the marginal cost of manufacturing one more extra unit exceeds the average cost.Learn more about Marginal cost curve:
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Complete question:
With respect to the average cost curves, the marginal cost curve:
A) Intersects average total cost, average fixed cost, and average variable cost at their minimum point
B) Intersects both average total cost and average variable cost at their minimum points
C) Intersects average total cost where it is increasing and average variable cost where it is decreasing
D) Intersects only average total cost at its minimum point
Discount vacation is giving a 20% discount on all vacations booked in January. A vacation to Cancun costs $2400 What will the sale price be?
12,000
3,000
1,920
480
Answer:
480
Step-by-step explanation:
Take 20% of 2400
Answer:
1920
Step-by-step explanation:
20% of 2400 = 480
2400-480= 1920
In the fraction 1/2, the number 1 is:?
Answer:
the numerator
Step-by-step explanation:
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.When Sally is depressed, she listens to music. I saw her today listening to music, so she must have been depressed.Question content area bottomPart 1Choose the correct answer below.A.The statement makes sense. Sally listens to music when she is depressed. If she is listening to music, then Sally must be depressed. B.The statement makes sense. Sally listens to music when she is depressed. The statement clearly communicates that this is the only time Sally listens to music.C.The statement does not make sense. Sally listens to music when she is depressed. If she is listening to music, then Sally must not be depressed. D.The statement does not make sense. Sally listens to music when she is depressed, but the statement does not clearly state that this is the only time Sally listens to music.
Based on the given statement, the correct answer would be:
option A. The statement makes sense. Sally listens to music when she is depressed. If she is listening to music, then Sally must be depressed.
The given statement is discussing a potential relationship between Sally's emotional state of being depressed and her behavior of listening to music. The question asks whether the statement makes sense, is clearly true, or does not make sense, and provides four options to choose from.
Option A states that the statement makes sense and suggests that if Sally is listening to music, then she must be depressed. This option is reasonable because the statement establishes a connection between Sally's depression and her behavior of listening to music. It implies that listening to music is a coping mechanism or an activity she engages in when she experiences depressive feelings.
Therefore, if someone observes Sally listening to music, it can be inferred that she might be in a depressed state at that moment.
On the other hand, options B and C can be eliminated because they make extreme and unsupported claims. Option B suggests that Sally only listens to music when she is depressed, which is not explicitly stated in the given statement. Option C states that if Sally is listening to music, then she must not be depressed, which contradicts the initial connection established between depression and listening to music in the statement.
Option D highlights the incomplete nature of the statement but does not render it entirely senseless. It acknowledges that the statement mentions Sally's behavior of listening to music when she is depressed but does not provide information about other potential reasons she might listen to music.
In summary, option A is the most appropriate choice as it aligns with the established correlation between Sally's depression and her listening to music, while considering the possibility of other reasons for her music listening behavior.
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dana said that 0.6 divided by 30 = 0.02. is she correct? explain.
Answer:
It can be said that Dana is correct when she says that 0.6 divided by 30 gives 0.02 as a reminder.
Step-by-step explanation:
It is given that we need to rectify whether 0.6 divided by 30 = 0.02 or not.
Firstly, let us understand how does simplification work;
In mathematics, the operation and interpretation of a function to make it simple or easier to grasp is known as simplifying, and the process is known as simplification.
Now, let us understand what exactly is arithmetic;
According to the assertions, it deals with a number of operations in mathematics. Addition, subtraction, multiplication, and division are the four main arithmetic operators.
Now, let us equate the given condition that is;
=> 0.6 can also be expressed as 6/10
Now, let us divide the above numbers with each other as given in the question;
=> (6/10) ÷ 30
=> 6/300
On dividing both the numbers with each other we get;
=> 0.02 which can be expressed as 2/100
Therefore, it can be said that Dana is correct when she says that 0.6 divided by 30 gives 0.02 as a reminder.
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Answer:
Step-by-step explanation:
Complete the table to show the interest earned for different savings principals, interest rates, and time periods
The interest earned increases with higher principal amounts, higher interest rates, and longer time periods.
Principal (P) | Interest Rate (r) | Time Period (t) | Interest Earned (I)
$1,000 | 2% | 1 year | $20
$5,000 | 4% | 2 years | $400
$10,000 | 3.5% | 3 years | $1,050
$2,500 | 1.5% | 6 months | $18.75
$7,000 | 2.25% | 1.5 years | $236.25
To calculate the interest earned (I), we can use the simple interest formula: I = P * r * t.
For the first row, with a principal of $1,000, an interest rate of 2%, and a time period of 1 year, the interest earned is calculated as follows: I = $1,000 * 0.02 * 1 = $20.
For the second row, with a principal of $5,000, an interest rate of 4%, and a time period of 2 years, the interest earned is calculated as follows: I = $5,000 * 0.04 * 2 = $400.
For the third row, with a principal of $10,000, an interest rate of 3.5%, and a time period of 3 years, the interest earned is calculated as follows: I = $10,000 * 0.035 * 3 = $1,050.
For the fourth row, with a principal of $2,500, an interest rate of 1.5%, and a time period of 6 months (0.5 years), the interest earned is calculated as follows: I = $2,500 * 0.015 * 0.5 = $18.75.
For the fifth row, with a principal of $7,000, an interest rate of 2.25%, and a time period of 1.5 years, the interest earned is calculated as follows: I = $7,000 * 0.0225 * 1.5 = $236.25.
These calculations show the interest earned for different savings principals, interest rates, and time periods.
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solve for each variable found each answer to the nearest tenth
The value of variable x is 5 unit.
What is Pythagoras theorem?The square of the hypotenuse side in a right-angled triangle equals the sum of the squares of the other two sides. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
Given:
Perpendicular= 3
Base= 4
Hypotenuse = x
Using Pythagoras theorem
H² = P² + B²
x² = 4² + 3²
x² = 16 + 9
x² = 25
x= 5
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3+k<10; 6,7,8
lesson 5 extra practice
inequalities
Answer:
Your answer is 7
Step-by-step explanation:
Here you go mate
Step 1
3+k<10 Equation/Question
Step 2
3+k<10 simplify by subtracting
Answer
k<7
Answer:
\(\displaystyle 7 > k\)
Step-by-step explanation:
3 + k < 10
- 3 - 3
________
\(\displaystyle k < 7\)
I am joyous to assist you at any time.
Find the angle of x (view picture)
Answer:
i dont understand this qustion\
Step-by-step explanation:
Answer:
60
The 2 angles in the triangle add up to 120, there are 180 degrees so the last one is 60. 60 is equal to x because of co-interior angles
6) Find the quotient
This year 20% of city employees ride the bus to work. Last year only 18% of city employees rode the bus to work. a. Find the absolute change in city employees who ride the bus to work. b. Use the absolute change in a meaningful sentence. c. Find the relative change in city employees who ride the bus to work. Round to whole number percent. d. Use the relative change in a meaningful sentence.
a. The absolute change in city employees who ride the bus to work is 2%.
b. The relative change in city employees who ride the bus to work is approximately 11%.
c. The relative change in city employees who ride the bus to work is approximately 11%.
d. The relative change of around 11% indicates an increase in the proportion of city employees riding the bus to work compared to last year.
a. The absolute change in city employees who ride the bus to work can be calculated as the difference between this year's percentage (20%) and last year's percentage (18%):
Absolute change = 20% - 18% = 2%
b. The absolute change of 2% indicates that the number of city employees riding the bus to work has increased by 2 percentage points compared to last year.
c. The relative change in city employees who ride the bus to work can be calculated as the absolute change divided by the previous year's percentage, multiplied by 100:
Relative change = (Absolute change / Previous year's percentage) * 100
Relative change = (2% / 18%) * 100 ≈ 11%
d. The relative change of approximately 11% implies that the proportion of city employees riding the bus to work has increased by around 11% compared to last year.
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Use series to approximate the definite integral I to within the indicated accuracy. I=∫014xcos(x3)dx
the series approximation of the definite integral is: I ≈ 2 - 1/2 + 1/8! - 1/20!
To approximate the definite integral I = ∫[0,1] 4x*cos(x²3) dx using series, we can expand the cosine function as a power series. The power series representation of cosine is:
cos(x) = 1 - (x²2)/2! + (x²4)/4! - (x²6)/6! + ...
Now, let's substitute x²3 for x in the power series expansion of cosine:
cos(x²3) = 1 - ((x²3)²2)/2! + ((x²3)²4)/4! - ((x²3)²6)/6! + ...
Simplifying the terms:
cos(x²3) = 1 - (x²6)/2! + (x²12)/4! - (x²18)/6! + ...
Now, let's substitute this series expansion into the integral:
I = ∫[0,1] 4x * (1 - (x²6)/2! + (x²12)/4! - (x²18)/6! + ...) dx
We can now integrate each term of the series individually:
∫[0,1] 4x dx - ∫[0,1] (4x²7)/2! dx + ∫[0,1] (4x²13)/4! dx - ∫[0,1] (4x²19)/6! dx + ...
Integrating each term:
[2x²2] [0,1] - [(x²8)/2!] [0,1] + [(x²14)/4!] [0,1] - [(x²20)/6!] [0,1] + ...
Simplifying:
2(1²2 - 0²2) - (1²8)/2! + (1²14)/4! - (1²20)/6! + ...
The terms with x²2, x²8, x²14, and x²20 evaluate to 1, 1/2, 1/8!, and 1/20!, respectively. We can neglect the terms beyond x^20 as the accuracy requirement is not specified.
Therefore, the series approximation of the definite integral is:
I ≈ 2 - 1/2 + 1/8! - 1/20!
This approximation provides an estimate of the definite integral I to the indicated accuracy based on the terms included in the series.
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A box contains 8 red marbles and 3 green ones. Six draws are made at random without replacement. True or false: the chance that the 3 green marbles are drawn equals 6! 313! () ()
False. The chance of drawing all three green marbles in six draws without replacement is 4/33, not 6!/(313!).
The statement provided is false. Let's calculate the actual probability of drawing all three green marbles in six draws without replacement.
In the given box, there are a total of 11 marbles: 8 red and 3 green. The number of ways to choose 6 marbles out of 11 without replacement is denoted as "11 choose 6" and can be calculated using the binomial coefficient formula:
11C6 = 11! / (6! * (11 - 6)!) = 462.
Now, we need to determine the number of ways to draw all three green marbles in these six draws. There are 3 green marbles in the box, and we need to choose all 3 of them. The remaining 3 draws out of the 6 should be red marbles. This can be calculated as follows:
3C3 * 8C3 = 1 * (8! / (3! * (8 - 3)!)) = 56.
Finally, we divide the number of favorable outcomes (56) by the total number of possible outcomes (462) to obtain the probability:
P(drawing all three green marbles) = 56 / 462 = 8 / 66 = 4 / 33.
Therefore, the correct probability is 4/33, not 6!/(313!) as stated in the question.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided The top five test scores in Mr. Rhodes's class were 98, 92, 96, 97, and 97. What is the mean absolute deviation?
Step-by-step explanation:
mad = 98 + 92 + 96 + 97 + 97 / 5
= 480/5
= 96
mad = (98 -96) + (92 - 96) + (96 -96) + (97- 96) + (97 -96) / 5
= 2 + (-4) + 0 + 1 + 1 / 5
=0/5
mad = 0
brainliest is appreciated
Answer:
1.6
Step-by-step explanation:
To find the mean absolute deviation of the data, start by finding the mean of the data set. Find the sum of the data values, and divide the sum by the number of data values. Find the absolute value of the difference between each data value and the mean: |data value – mean|.
98+92+96+97+97=480
480/5 values=96 is the mean or average of the set of numbers
so we just find the absolute value of the data value minus the mean.
For the first one it would be |98-96|=2
then continue on and get a set of values
{2,4,0,1,1}
now find the average of that to get the mean absolute deviation
2+4+0+1+1=8
8/5 values
1.6
Hope that helps :)
Find an equation for the line below. Thanks !
Answer:
\(\huge\boxed{y=\frac{1}{4}x + \frac{13}{4}}\)
Step-by-step explanation:
In order to find the equation to this line, we need to note that we see two points on this graph. Using these two points, we can use them to find the slope of the graph and use one to find the y-intercept.
We know that the slope of a line is defined by \(\frac{\Delta y}{\Delta x}\) (change in y / change in x). Therefore, we can use our two points that we know - (-5, 2) and (3, 4) to find the slope.
The change in y is \(4 - 2 = 2\), and the change in x is \(3 - (-5) = 3+5= 8\). Therefore, our slope is \(\frac{2}{8} = \frac{1}{4}\).
Now that we know our slope, our equation in slope-intercept form looks something like this.
\(y = \frac{1}{4}x + b\)
However, we still have b to solve for. We can solve for this by substituting a point we already know into the equation. Let's substitute (3, 4) inside.
\(4 = \frac{1}{4} \cdot 3+b\) \(4 = \frac{3}{4} + b\) \(b = \frac{16}{4}- \frac{3}{4}\) \(b = \frac{13}{4}\)So now we know that the y-intercept is \(\frac{13}{4}\). Plugging that into our equation finishes it off, leaving our final equation to be \(y = \frac{1}{4}x + \frac{13}{4}\).
Hope this helped!
Answer:
y= 1/4 + 13/4
Step-by-step explanation:
mark brainless please..
;-;
(did this question before)
lol
If t represents the amount of time Neda has spent typing the second letter, which equation states the rule used to determine the number of words, W, Neda has typed today?
Answer:
W = t + 200
Step-by-step explanation:
Number of words typed in the first letter = 200
The relationship between the total words typed, W and the number of seconds, t spent on the second letter :
W = number of words typed in first letter + t
W = 200 + t
Choosing any pair of values from the table :
W = 245 ; t = 45
W = 200 + 45
W = 245
Therefore, the number of words, W typed today can be represented as
W = 200 + t
Rhombus EFGH is rotated 90 degrees counterclockwise about vertex G. How many pairs of parallel sides does the rotated figure have?
Please explain your answer.... Thank you!
A) 0
B) 1
C)2
D) 4
Answer:
try your self more and more times you can easily solve
the gram-schmidt process produces from a linearly independent set {x1, x2, . . . , xp} an orthogonal set {v1, v2, . . . , vp} with the property that span{v1, . . . , vk}
The statement is true.
An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process.
Given that,
From a linearly independent collection of {x₁, x₂,..., xp}, the gram-Schmidt process creates an orthogonal set of {v₁, v₂,..., vp} with the feature that for each k, the vectors v₁...vk span the same subspace as that spanned by x₁...xk.
Whether the claim is true or false must be determined.
The statement is true.
An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process. An orthogonal set is further linearly independent. The orthogonal set produced by the Gram-Schmidt process and the original set will cover the same subspace if their dimensions are the same.
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