In a recent study of 35 ninth-grade students, the mean number of hours per week that they played video games was 16.6. The standard deviation of the population was 2.8.
a. Find the best point of estimate of the population mean
b. Find the 95% confidence level of the mean of the time playing video games
c. Find the 99% confidence interval of the mean time playing video games
d. Which is larger? Explain why.
Answers
Answer:
a) 16.6
b) The 95% confidence level of the mean of the time playing video games is between 15.7 and 17.5 hours.
c) The 99% confidence level of the mean of the time playing video games is between 15.4 and 17.8 hours.
d) The margin of error increases as the confidence level increases, due to the value of z, which means that the 99% confidence interval is larger.
Step-by-step explanation:
a. Find the best point of estimate of the population mean
The best estimate for the population mean is the sample mean, which is 16.6
b. Find the 95% confidence level of the mean of the time playing video games
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.95}{2} = 0.025\)
Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.
Now, find the margin of error M as such
\(M = z\frac{\sigma}{\sqrt{n}}\)
In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.
\(M = 1.96\frac{2.8}{\sqrt{35}} = 0.9\)
The lower end of the interval is the sample mean subtracted by M. So it is 16.6 - 0.9 = 15.7 hours
The upper end of the interval is the sample mean added to M. So it is 16.6 - 0.9 = 17.5 hours
The 95% confidence level of the mean of the time playing video games is between 15.7 and 17.5 hours.
c. Find the 99% confidence interval of the mean time playing video games
Following the same logic as above, we have that \(Z = 2.575\). So
\(M = 2.575\frac{2.8}{\sqrt{35}} = 0.9\)
The lower end of the interval is the sample mean subtracted by M. So it is 16.6 - 1.2 = 15.4 hours.
The upper end of the interval is the sample mean added to M. So it is 16.6 + 1.2 = 17.8 hours.
The 99% confidence level of the mean of the time playing video games is between 15.4 and 17.8 hours.
d. Which is larger? Explain why.
The margin of error increases as the confidence level increases, due to the value of z, which means that the 99% confidence interval is larger.
The mean is 16.6, 95% confidence interval is between 15.68 to 17.52, the 99% confidence interval is between 15.39 to 17.81, and the 99% confidence interval is larger.
It is given that the in recent study of 35 ninth-grade students the mean number of hours per week is 16.6 with standard deviation of the population was 2.8.
It is required to find the best point of estimate of the population mean, 95% confidence interval, and 99% confidence interval.
What is a confidence interval for population standard deviation?It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.
We have confidence level = 95% = 0.95
We know:
\(\alpha = \frac{1-0.95}{2}\) = 0.025
\(\rm Z_1 _-_\alpha = Z_{0.975} = 1.96\) (from the Z table)
The sample size n = 35
We know the Margin of error formula:
\(\rm M =Z\frac{\sigma}{\sqrt[]{n} }\) ( \(\rm \sigma\\\) = 2.8 )
\(\rm M =1.96\frac{2.8}{\sqrt[]{35} }\)
M = 0.92
The 95% interval will be:
= X - M ⇒ 16.6 - 0.92 ⇒15.68
= X+ M ⇒ 16.6+0.92 ⇒ 17.52
For 99% confidence level:
\(\alpha = \frac{1-0.90}{2} = 0.005\)
\(\rm Z_1 _-_\alpha = Z_{0.005} = 2.575\) (from Z table)
\(\rm M =2.575\frac{2.8}{\sqrt[]{35} }\)
M = 1.21
The 99% interval will be:
=16.6 - 1.21 ⇒ 15.39
= 16.6+ 1.21 = 17.81
As the value of M increases the confidence value increases due to the value of Z that means 99% confidence interval is larger.
Thus, the mean is 16.6, 95% confidence interval is between 15.68 to 17.52, the 99% confidence interval is between 15.39 to 17.81, and the 99% confidence interval is larger.
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Related Questions
Can someone please explain this to me and help me
Answers
Answer:
ok
Step-by-step explanation:
Factor the expression. x^2-12x-45
Answers
Answer:
(x + 3)(x - 15)
Step-by-step explanation:
To factor the expression x^2 - 12x - 45, we need to find two numbers that multiply to -45 and add to -12. Let's use the method of decomposition to find these two numbers:
x^2 - 12x - 45
We need to find two numbers that multiply to -45 and add to -12. Let's try -15 and 3:
x^2 - 12x - 45 = x^2 - 15x + 3x - 45
Now we can group the first two terms and the last two terms:
x^2 - 15x + 3x - 45 = x(x - 15) + 3(x - 15)
We can see that both terms have a common factor of (x - 15), so we can factor this out:
x(x - 15) + 3(x - 15) = (x + 3)(x - 15)
Therefore, the expression x^2 - 12x - 45 can be factored as (x + 3)(x - 15).
Refer to the attachment ^-^
Hope Helpful ~
Irinkers or both? Acme electronics manufactures MP3 players at three locations. The plant 50% of the MP3 players and 1% are defective. The plant at Memphis manu that plant are defective. The plant at Fort Meyers manufactures 20% and 3% If an MP3 player is selected at random, what is the probability that it is defe Refer to Problem 6.101. An MP3 player is found to be defective. What is th manufactured in Fort Meyers?
Answers
The probability that an MP3 player manufactured in Fort Meyers is defective is 0.37%.
To calculate the probability that an MP3 player is defective, we need to consider the manufacturing plants and their respective defect rates.
Given:
Plant at Memphis manufactures 50% of the MP3 players, and 1% of those manufactured at that plant are defective.
Plant at Fort Meyers manufactures 20% of the MP3 players, and 3% of those manufactured at that plant are defective.
No information is provided about the defect rate of the third plant.
To find the overall probability of an MP3 player being defective, we need to consider the probability of selecting a defective player from each plant and then weigh it by the probability of selecting a player from each plant.
Let's calculate the overall probability:
Probability of selecting a defective player from Memphis plant = 50% * 1% = 0.50% or 0.005 (since 50% is equivalent to 0.50 in decimal form)
Probability of selecting a defective player from Fort Meyers plant = 20% * 3% = 0.60% or 0.006 (since 20% is equivalent to 0.20 in decimal form)
To calculate the overall probability, we need to weigh these probabilities by the probability of selecting an MP3 player from each plant:
Probability of selecting from Memphis plant = 50% = 0.50 (decimal form)
Probability of selecting from Fort Meyers plant = 20% = 0.20 (decimal form)
Overall probability of selecting a defective MP3 player is given by:
Overall probability = (Probability from Memphis plant * Probability of selecting a defective player from Memphis) + (Probability from Fort Meyers plant * Probability of selecting a defective player from Fort Meyers)
Overall probability = (0.50 * 0.005) + (0.20 * 0.006) = 0.0025 + 0.0012 = 0.0037 or 0.37%
Therefore, the probability that an MP3 player, manufactured in Fort Meyers, is defective is 0.37%.
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square root of 10 times square root of 8
Answers
may you please help me with this
Answers
Answer:
C). 8/9n - 1 1/3
Step-by-step explanation:
Answer:
\(\frac{8}{9} n - 1\frac{1}{3}\)
Step-by-step explanation:
Using the distributive property \(\frac{4}{9}\) times 2 equals \(\frac{8}{9}\) and \(\frac{4}{9}\) times 3 equals \(\frac{4}{3}\) which simplifies to \(1\frac{1}{3}\)
What is the smallest positive integer $n$ such that $\sqrt[4]{56 \cdot n}$ is an integer?
Answers
The smallest positive integer n such that t \($\sqrt[4]{56 \cdot n}$\) is an integer is 686.
We have to find the smallest positive integer n such that \($\sqrt[4]{56 \cdot n}$\) is an integer
To find the smallest positive integer n such that \($\sqrt[4]{56 \cdot n}$\) is an integer, we need to determine the factors of 56 and find the smallest value of n that, when multiplied by 56, results in a perfect fourth power.
The prime factorization of 56 is:
56 = 2³ × 7
The prime factors of 56 need to be raised to multiples of 4.
Therefore, we need to determine the smallest value of n that includes additional factors of 2 and 7.
To make the expression a perfect fourth power, we need to raise 2 and 7 to the power of 4, which is 2⁴ × 7⁴
The smallest value of n that satisfies this condition is:
n = 2 × 7³ = 2× 343 = 686
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Avery's recipe ask for 100ml of milk. She only has a 10ml measuring cup. How many times will she need to fill her measuring cup to get the right amount of milk for her recipe
Answers
Ten times to get the required amount of 100ml of milk for her recipe.
Avery needs to measure 100ml of milk for her recipe but she only has a 10ml measuring cup.
Therefore, she needs to determine how many times she will need to fill her 10ml measuring cup to get the required amount of milk.
To calculate this, we can divide the required amount of milk by the capacity of the measuring cup. In this case, we divide 100ml by 10ml to get:
100ml ÷ 10ml = 10
This means that A very will need to fill her 10ml measuring cup 10 times to get the required amount of milk for her recipe.
Another way to think about it is to consider that 100ml is ten times the capacity of the 10ml measuring cup. Therefore, Avery will need to fill the measuring cup ten times to get the required amount of milk.
In summary, Avery will need to fill her 10ml measuring cup ten times to get the required amount of 100ml of milk for her recipe. t
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Rewrite as an exponential equation: log6 = -2
Answers
Answer:
Step-by-step explanation:
log6 = -2
When there is no base, the base is 10
10⁻² = 6
If m∠A = m∠B and m∠A + m∠C = ∠D, then m∠B + m∠C = ∠D.
Which property is shown?
reflexive property
substitution property
symmetric property
transitive property
Answers
Answer:
substitution property
Step-by-step explanation:
When you replace m∠A in the second equation with its equal, as defined by the first equation, you are making use of the substitution property.
That property says you can replace anything by its equal.
Answer:
subsitution
Step-by-step explanation:
i jus took the quiz
Please help 50 points!
1. A cylindrical jar has a radius of 6 inches and a height of 10inches. The jar is filled with marbles that have a volume of 20 in3. Use 3.14 for pi. Show work. Complete sentences.
What is the volume of the jar?
Answers
The volume of the jar is 1130.4 in³. The number of marbles that is filled the jar is 56.
What is the cylindrical shape?
The three-dimensional shape of a cylinder is made up of two parallel circular bases connected by a curved surface. The right cylinder is created when the centers of the circular bases cross each other. The axis, which represents the height of the cylinder, is the line segment that connects the two centers.
Given that the radius of cylindrical jar is 6 inches and the height is 10 inches.
The volume of a cylindrical shape is \(\pi r^2h\).
Where r is the radius of the cylinder and h is the height of the cylinder.
Given that, the radius of the cylindrical jar is 6 inches and height is 10 inches.
The volume of a cylindrical shape is 3.14 × 6² × 10 = 1130.4 in³.
The number of marbles by which the jar can be filled is 1130.4/20 = 56.52 = 56 (approx.)
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One year had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of . Also, had the lowest ERA of any female pitcher at the school with an ERA of . For the males, the mean ERA was and the standard deviation was . For the females, the mean ERA was and the standard deviation was . Find their respective z-scores. Which player had the better year relative to their peers, or ? (Note: In general, the lower the ERA, the better the pitcher.)
Answers
Answer:
Thomas had the better year relative to their peers.
Step-by-step explanation:
The complete question is: One year Thomas had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 3.31. Also, Karla had the lowest ERA of any female pitcher at the school with an ERA of 3.02. For the males, the mean ERA was 4.837 and the standard deviation was 0.541. For the females, the mean ERA was 4.533 and the standard deviation was 0.539. Find their respective z-scores. Which player had the better year relative to their peers, or ? (Note: In general, the lower the ERA, the better the pitcher.)
We are given that for the males, the mean ERA was 4.837 and the standard deviation was 0.541. For the females, the mean ERA was 4.533 and the standard deviation was 0.539.
As, we know that the z-score is calculated by the following formula;
Z = \(\frac{X-\mu}{\sigma}\) ~ N(0,1)
where, \(\mu\) = population mean
\(\sigma\) = standard deviation
Now, firstly we will calculate the z score for Thomas;
z-score = \(\frac{X-\mu}{\sigma}\)
= \(\frac{3.31-4.837}{0.541}\) = -2.823
{Here, the mean ERA for the males was 4.837 and the standard deviation was 0.541}
Similarly, we will calculate the z score for Karla;
z-score = \(\frac{X-\mu}{\sigma}\)
= \(\frac{3.02-4.533}{0.539}\) = -2.807
{Here, the mean ERA for the females was 4.533 and the standard deviation was 0.539}
Now, it is stated in the question that the lower the ERA, the better the pitcher.
So, we can clearly see that Thomas had a lower ERA of z-score as -2.823 < -2.807. This means that Thomas had the better year relative to their peers.
Find the missing side of the triangle. Round to the nearest tenth where necessary (one decimal place). WRITE ONLY THE NUMERICAL VALUE (10 yd = 10).
Answers
Answer:
35.6
Step-by-step explanation:
By the Pythagorean Theorem:
\( {x}^{2} + {91.3}^{2} = {98}^{2} \)
\(x = \sqrt{ {98}^{2} - {91.3}^{2} } = 35.6\)
Need help is this right or what is the right answer
Answers
Answer:
A
Step-by-step explanation:
the answer is A and not C. equation in form of y=mx+b
so start off by (0,2) and you can see the graph go by 1 x and 1 y.
C=n+2
Answer:
A
Step-by-step explanation:
its starting point is 2 up to +2 and it goes up at out by 1 so n also ik this was already answered but i want the brainly points
What fraction is less than 5/8
Answers
Answer:
1/2 is 1 example
Step-by-step explanation:
what
A fraction that is less than 5/8 is 4/8
How to determine the fraction?The fraction is given as:
Fraction = 5/8
A fraction less than 5/8 will have the same denominator but a smaller numerator compared to 5/8
Take for instance, the numerator can be
1 to 4
So, we have;
Smaller fraction = 4/8
Hence, a fraction that is less than 5/8 is 4/8
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What is -20/2(7 2/3)
Answers
The simplified form of -20/2(7 2/3) is -230/3.
To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.
First, let's convert the mixed number 7 2/3 to an improper fraction.
7 2/3 = (7 * 3 + 2) / 3 = 23/3
Now, let's substitute the value back into the expression:
-20/2 * (23/3)
Next, we simplify the multiplication:
-10 * (23/3)
To multiply a fraction by a whole number, we multiply the numerator by the whole number:
-10 * 23 / 3
Now, we perform the multiplication:
-230 / 3
Therefore, the simplified form of -20/2(7 2/3) is -230/3.
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Amir is in charge of getting oranges for today's soccer game. He buys 2 bags with
6 oranges in each bag. He also buys 4 loose oranges.
Choose all the expressions that can be used to find the number of oranges Amir gets
in all.
Answers
The expression that shows the total oranges amir got in total is x-12 = 4. And amir got 16 oranges in all
What is linear expressions?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1. For example, x² is a variable raised to the second power, but x is a variable raised to the first power.
example of linear expression is 2x+2y = 5. This is a linear expression with two variables x and y.
Let's represent the total no of oranges by x.
Therefore ,
2 bags of oranges with 6 in each bag will amount to 2×6 = 12 oranges.
an addition of 4 loose oranges . Therefore the total number of oranges = 12+4 = x
x = 12+4 or x-12 = 4
= 16
therefore amir got 16 oranges in all
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A bag contains 150 marbles. Some are blue, and the rest are white. There are 21 blue marbles for every 4 white marbles.
Answers
Answer:
84
Step-by-step explanation:
none
The number of blue marbles are 126 and the number of red marbles are 24.
Given that, a bag contains 150 marbles.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
There are 21 blue marbles for every 4 white marbles.
Here, the ratio of blue marbles to red marbles is 21:4
The number of blue marbles = 21x and the number of red marbles =4x
So, 21x+4x=150
⇒ 25x=150
⇒ x=150/25
⇒ x=6
Then blue marbles=21x=126 and red marbles = 4x =24
Therefore, the number of blue marbles are 126 and the number of red marbles are 24.
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"Your question is incomplete, probably the complete question/missing part is:"
A bag contains 150 marbles. Some are blue, and the rest are white. There are 21 blue marbles for every 4 white marbles. How many blue marbles are in the bag?
I NEED HELP PLS HURRY
1. Write each expression with a single exponent:
a. (10^7)²
b. (10^9)³
c. (10^6)³
d. (10^2)³
e. (10³)²
f. (10^5)^7
Answers
b. 10^27
c. 10^18
d. 10^6
e. 10^6
f. 10^35
multiply the exponents.
Answer:
We use the rule,
\((a^b)^c = a^{bc}\)
a. (10^7)²
\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)
10^14
b. (10^9)³
\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)
10^27
c. (10^6)³
\(10^{(6)(3)}= 10^{18}\)
10^18
d. (10^2)³
\(10^{(2)(3)} = 10^{6}\)
10^6
e. (10³)²
\(10^{(3)(2)}=10^{6}\)
10^6
f. (10^5)^7
\(10^{(5)(7)} = 10^{35}\)
10^35
Step-by-step explanation:
Polygon C has an area of 7 square units. Jennie drew a scaled version of Polygon C and labeled it Polygon D. Polygon D has an area of 28 square units.
What scale factor did Jennie use to go from Polygon C to Polygon D?
Answers
The scale factor used by Jennie to go from Polygon C to Polygon D can be found to be 4 .
How to find the scale factor ?To determine the scale factor used by Jennie to transform Polygon C to Polygon D, compare their respective areas. The scale factor is the ratio of the areas of the two polygons .
Area of Polygon C is 7 square units while that of Polygon D is 28 square units.
The scale factor :
= Area of Polygon D / Area of Polygon C
= 28 square units / 7 square units
= 7
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how am i supposed to prove that theyre collinear
Answers
Answer:
They are collinear if they are on the same line
A certain sum of money is divided among A, B, C in the ratio 2: 3 : 4. If A's share is RS. 20000, find the share of B and C.
Answers
Therefore, B's share is Rs. 30,000 and C's share is Rs. 40,000.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.
Here,
Let the total sum of money be x.
Then, according to the given ratio, A's share is 2/9 of the total sum, so we have:
2/9 * x = 20000
Multiplying both sides by 9/2, we get:
x = 90000
Now, we can find the shares of B and C as follows:
B's share = 3/9 * 90000 = 30000
C's share = 4/9 * 90000 = 40000
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A $5000 investment pays 3% interest compounded monthly. To the nearest cent, what will be the value of the investment after 10 years?
Answers
Answer:
We can use the formula for compound interest to solve this problem. The formula is:
A = P * (1 + r/n)^(n*t)
where:
A = the amount of money after t years
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = $5000, r = 0.03, n = 12 (since the interest is compounded monthly), and t = 10. Plugging these values into the formula, we get:
A = 5000 * (1 + 0.03/12)^(12*10)
A = 5000 * (1.0025)^120
A ≈ $6,621.36
So the investment will be worth approximately $6,621.36 after 10 years.
Estimate the sum of the weights of Frailyn 10.2 pounds +611/12 pounds. Which statements are true about the estimate CHECK ALL THAT APPLY
Answers
6 11/12 should be rounded to 7
The estimated sun is 17 lbs
To find the estimated sun add 10+7
X -6= 11 - 11(x + 7)
HELPPP PLSSS
Answers
Answer:
x = -5
Step-by-step explanation:
X -6= 11 - 11(x + 7)
Distribute
x-6 = 11 -11x -77
Combine like terms
x-6 = -11x -66
Add 11x to each side
x-6+11x = -11x-66+11x
12x-6 = -66
Add 6 to each side
12x -6+6 = -66+6
12x = -60
Divide by 12
12x/12 = -60/12
x = -5
I need the answer plzz I need help
Answers
God bless everyone vankka is correct!
Answer:
1) False
2) False
3) True
4) True
Step-by-step explanation: Looked at graph.
Hope this helps!
Look for factors that will help you determine what type of economy exists in Country A.
Based on the clues in this passage, what type of economy does Country A have?
developed
developing
transitioning
command
Answers
developing:
a low GDP
an economy based on agriculture
Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.
PLEASE HELP ME!! My grades are bad and I need the answer before Friday. Somebody PLEASE help!!! I rlly need to get this done!!
Answers
Step-by-step explanation:
Just telling you, if your grades are bad,
you should listen to the teacher more in class time,
take notes, and more.
Btw, the equation is...
I hope this will help you.
I cannot give answers for everything.
I hope this helps!
5. A map is drawn to a scale of 1: 20 000. (a) The perimeter of a lake is 2.5 km. Find, in cm, the perimeter of the lake on the map. (b) The area of the lake on the map is 12.5 cm². Find, in km², the actual area of the lake.
Answers
Step-by-step explanation:
2.5 km = 250000 cm
250000 cm /20000 = 12.5 cm on the map
12.5 cm ^2 x 20 0000 x 20 000 = 5 000 000 000 cm^2 = 500 000 m^2
Could I get help? Please answer if you only are 100 percent sure it will be correct.
Answers
Answer:
(aa)•(aaa)
Step-by-step explanation:
(aa)•(aaa) is the answer
let the value of the variable xval be 6 and the value of the variable yval be 5. which of the following code segments can be used to draw the figure?
Answers
Code segment to draw a figure with xval = 6 and yval = 5.
Code segment: ctx.fillRect(0, 0, xval, yval);
The code segment to draw a figure with xval = 6 and yval = 5 can be written using the fillRect() method in the Canvas API. This method requires four arguments: the x and y coordinates of the top-left corner of the figure, and the width and height of the figure. In this case, we want the top-left corner of the figure to be at (0, 0), and the width and height to be 6 and 5, respectively. Therefore, we can write the code segment as ctx.fillRect(0, 0, xval, yval);, where xval is 6 and yval is 5. This code segment will draw a figure with a width of 6 and a height of 5. To draw other figures, all you need to do is change the values of xval and yval to the desired width and height respectively.
The complete question: Let the value of the variable xVal be 6 and the value of the variable yVal be 5. Which of the following code segments can be used to draw the figure?
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