The 99.7% confidence interval for the mean of the population is (112.82, 125.18).
What is standard deviation?The degree of variance or dispersion in a collection of data is measured by standard deviation. It is a statistic that gauges how much values deviate from the dataset's mean (average).
To calculate the 99.7% confidence interval for the mean of the population, we need to use the formula:
Confidence Interval = X ± Z(α/2) * (σ/√n)
where:
X is the sample mean
Z(α/2) is the critical value of the standard normal distribution at α/2 level of significance (α is the level of significance)
σ is the population standard deviation (unknown)
n is the sample size
In this case, X = 119, σ = 16, n = 64, and α = 0.003 (because 99.7% corresponds to the area under the curve outside the range of ±3 standard deviations from the mean, and the standard normal distribution is symmetric around the mean, so we need to split the area of 0.003 equally between the two tails).
Using a standard normal distribution table or calculator, we find that Z(α/2) = Z(0.0015) = 3.090.
Plugging in the values, we get:
Confidence Interval = 119 ± 3.090 * (16/√64)
Confidence Interval = 119 ± 6.18
Therefore, the 99.7% confidence interval for the mean of the population is (112.82, 125.18).
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Add. State the sum in simplest form.
(2x+3)/(x+4)+(x-1)/(x^2+2x-8)
Group of answer choices
(3x+2)/(x^2+3x-4)
(3x+2)/(x^2+2x-8)
(2x^2+x-7)/(x^2+2x-8)
(2x^2-7)/(x^2+2x-8)
The simplified sum is (2x²+x-7)/[(x+4)(x-2)] of the expression (2x+3)/(x+4)+(x-1)/(x²+2x-8)
In the expression there are two fractions
To add the two fractions, we need to have a common denominator.
The denominator of the first fraction is x+4, while the denominator of the second fraction is x²+2x-8=(x+4)(x-2).
Therefore, we can write:
(2x+3)/(x+4) + (x-1)/(x²+2x-8) = (2x+3)/(x+4) + (x-1)/[(x+4)(x-2)]
Now, we can sum the fractions by finding a common denominator and adding the numerators:
(2x+3)/(x+4) + (x-1)/[(x+4)(x-2)] = [(2x+3)(x-2) + (x-1)(x+4)]/[(x+4)(x-2)]
= (2x²+x-7)/[(x+4)(x-2)]
Therefore, the simplified sum is (2x²+x-7)/[(x+4)(x-2)], which is option (C).
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Find the measure of 4
its 90 degree because
∠2 and ∠4 are vertical angles. Their measures are equal, so m∠4 = 90 .
∠3 and ∠4 form a straight angle, so∠4=120°.
angle four measures 45°
Answer:
147°
Step-by-step explanation:
∠4 and 33° are unilateral angles (the sum of them is equal to 180°)
[tex]∠4 = 180° - 33° = 147°[/tex]
Find the radius when arc length is 18pi/7 and 0=6pi/7
Answer:
r = 3
Step-by-step explanation:
the arc length is calculated as
arc = circumference of circle × fraction of circle , then
[tex]\frac{18\pi }{7}[/tex] = 2πr × [tex]\frac{0}{2\pi }[/tex] ( cancel 2π on numerator/ denominator )
[tex]\frac{18\pi }{7}[/tex] = r × [tex]\frac{6\pi }{7}[/tex] ( multiply both sides by 7 to clear the fractions )
18π = r × 6π ( divide both sides by 6π )
3 = r
5) Given that the graph below represents the graph of f(x), sketch the graph of -f(x+1). Plot and label at least
three points on the transformed graph.
Answer:
Step-by-step explanation:
The graph of f(x + 1) will be the same shape as f(x) except every point will be shifted 1 unit to the left. So, for example, the point (2, 2) will move to (1, 2) and (4, -2) will move to (3, -2). The whole graph moves 1 unit to the left.
-f(x + 1) will be f(x + 1) flipped over the x axis.
So for example (3, -2) ----> (3, 2) and (1, 2) -----> (1, -2)
I need help with this question
In the given diagram, the area of the sector is 61.25 square units
The arc length is 17.5 units
Calculating the area of sector and arc lengthFrom the question, we are to calculate the area and arc length for the given sector.
If we need to determine the area of a sector when the angle is given in radians, we will use the formula
Area of sector = (1/2) × r²θ
Where θ is the angle subtended at the center (in radians)
and r is the radius of the circle
From the given information,
r = 7
θ = 2.5
Thus,
Area of the sector = (1/2) × 7² × 2.5
Area of the sector = 61.25 square units
To determine the arc length, we will use the fromula
L = rθ
where L is the arc length
r is the radius of the circle
and θ is the angle measured in radians
Thus,
The arc length = 7 × 2.5
The arc length = 17.5 units
Hence, the arc length is 17.5 units
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A store rents movies. If the rental fee is $4 each, the store knows they can rent 110 movies per week. For each additional $1 increase in the rental fee, the store loses 11 rentals per week. What
rental fee should the store charge for a movie to maximize their revenue?
The store's revenue will be maximized if they charge $___for each movie rental.
Store revenue will be maximised, if they charge 7 dollars for each movie rental.
What is revenue?The entire amount of money received by an organisation's operations over a predetermined period of time is the basic definition of revenue.
A company's revenue is its total revenue before any expenses are subtracted. According to the definition, revenue is the total sum of money obtained through conducting commercial activities like sales.
Let store charge x $ for each movie.
No.of rented movies per weak = 108-9x(x-z)
Total revenue = x*[108-9(x-2)]
= x*[108-9x+18]
= x*[126-9x]
= 126x-9x^2
Total revenue will be maximised when dT/dx = 0
dT/dx = 126-9*2x
= 126-18x = 0
18x = 126
x = 7$
Store revenue will be maximised, if they charge 7 dollars for each movie rental.
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20. Find a solution to the following system of equations.
-3x + 3y = -9
-3x+y=7
O
O
O
(5,2)
(-5, -8)
(-2,2)
To find a solution to the system of equations, we can use the elimination method, which involves adding or subtracting the equations to eliminate one of the variables. Here are the steps:
[tex]\begin{align}
-3x + 3y &= -9 \
-3x + y &= 7 \
\end{align}[/tex]
We can eliminate $x$ by subtracting the second equation from the first equation:
[tex]\begin{align}
-3x + 3y &= -9 \
(-3x + y &= 7) \
\end{align}[/tex]
This gives us:
[tex]\begin{align}
4y &= -16 \
y &= -4 \
\end{align}[/tex]
Now, we can use the second equation to solve for $x$:
[tex]\begin{align}
-3x + y &= 7 \
-3x + (-4) &= 7 \
-3x &= 11 \
x &= -\frac{11}{3} \
\end{align}[/tex]
So the solution to the system of equations is $\boxed{(-\frac{11}{3}, -4)}$.
[tex]\huge{\colorbox{black}{\textcolor{lime}{\textsf{\textbf{I\:hope\:this\:helps\:!}}}}}[/tex]
[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{blue}{\small\texttt{If you have any further questions,}}[/tex] [tex]\textcolor{blue}{\small{\texttt{feel free to ask!}}}[/tex]
♥️ [tex]{\underline{\underline{\texttt{\large{\color{hotpink}{Sumit\:\:Roy\:\:(:\:\:}}}}}}\\[/tex]
Julian missed 4% of the free throws he attempts in a season how many total free throws did he attempt if he missed 65
The total number of free throws are 1625.
Given that, Julian missed 4% of the free throws he attempts in a season.
Here, the number of throw Julian missed is 65.
Let the total number of throws be x.
Now, 4% of x=65
4/100 ×x=65
0.04x=65
x=65/0.04
x=1625
Therefore, the total number of free throws are 1625.
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What is % 5/16 of $8400?
Answer:
Step-by-step explanation:
8400/5.16=1627.9069
3x+6 divided by -8x+7
Answer:
-3/8 -69/(64x -56)
Step-by-step explanation:
You want the result of dividing (3x+6) by (-8x+7).
Polynomial long divisionThe steps in polynomial long division are substantially identical to the steps in numerical long division. The quotient term at any step is the ratio of the leading terms of the dividend and divisor. The new dividend is found by subtracting the product of the quotient and divisor from the dividend.
First quotient termThe first quotient term is (3x)/(-8x) = -3/8.
RemainderThe remainder is the difference of the dividend and the product of the quotient and divisor:
remainder = (3x +6) -(-3/8)(-8x +7) = 3x +6 -3x +21/8 = 8 5/8 = 69/8
The degree of this remainder is less than the degree of the divisor, so the division is finished.
ResultWe often like to have the polynomials have positive leading coefficients, so we will express the result that way:
[tex]\dfrac{3x+6}{-8x+7}=\boxed{-\dfrac{3}{8}+\dfrac{\left(\dfrac{69}{8}\right)}{-8x+7}}\\\\\\=-\dfrac{3}{8}-\dfrac{\left(\dfrac{69}{8}\right)}{8x-7}=\boxed{-\dfrac{3}{8}-\dfrac{69}{64x-56}}[/tex]
What is tan(45 degrees)
Answer: 1
Step-by-step explanation:
Tan(45°)= 1
Answer:
1
Step-by-step explanation:
tangent of a 45 degree angle is 1
to find tangent, it is the length of the side opposite to an angle divided by the adjacent side
so the tangent of the top angle (which measures 45 degrees) is 1/1 since the adjacent and opposite sides both measure 1, therefore the tangent is 1 bc 1/1=1.
this proves that the tangent of a 45 degree angle is 1
In need of assistance! If possible, I'd appreciate it!
The parallelogram's diagonal represents the vector sum a + b, which has origin (0, 0) and destination (5, 1). We can therefore write: a + b = (5, 1)
What is vector?A vector is a symbol used to represent in mathematics a quantity that has both a magnitude (length) and a direction.
We begin by creating vectors for a and b using the provided coordinates in order to represent a + b using the parallelogram approach.
We choose (0, 0) and (3, -1) as the starting and ending points for vector a, respectively, using the Vector tool. We choose (0, 0) as the vector b's starting point and (2, 2) as its ending point.
By drawing a line segment from the terminal points of vectors a and b, we can finally finish the parallelogram. After that, a line segment is drawn from the starting point of vector b to the point where the two line segments converge. The vectors a and b define the sides of a parallelogram formed by this.
The diagonal of the parallelogram, which begins at the origin of vector a and ends at the opposite corner of the parallelogram, is the final representation of the vector sum a + b.
To symbolise a + b using the parallelogram approach, follow these simple steps:
Choose (0, 0) and (3, -1) as the starting and ending points for the vector a, respectively, using the Vector tool.
Select the starting point for vector b at (0, 0) and the ending point at (2, 2) using the Vector tool once more.
Draw a line segment from the terminal point of vector a to the terminal point of vector b.
From the starting point of vector b to the intersection of the two line segments, draw a line segment.
Draw the parallelogram's diagonal, which begins at the origin of the vector a and finishes at the opposite corner.
Indicate a + b as the vector sum.
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7. What is the classification of the triangle by its angles and
by its sides?
A. acute, equilateral
B. right, equilateral
C. obtuse, isosceles
D. obtuse, equilateral
A
I NEED HELP ASAP PLSSS
WILL GIVE BRAINLIEST
Miguel wants to put 3 roses in each of 18 vases. The roses are sold in bounches of a dozen. How many bounches Must he buy?
Using the mathematical operations of multiplication and division, Miguel must buy 5 bunches to put 3 roses in each of the 18 vases if the roses are sold in bunches of a dozen.
How the number is determined:The number of bunches of roses that Miguel needs to buy can be determined using mathematical operations.
The mathematical operations include multiplication and division.
The total number of roses in each vase = 3
The total number of vases = 18
The total number of roses required = 54 (3 x 18)
1 dozen = 1 bunch
12 roses = 1 dozen
Dozens or bunches to buy = 4.5 (54 ÷ 12)
= 5 bunches or dozens
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Days supply Needed: 30
Dosage instructions: 2 tablets, 2x per day Tablets Per bottle: 13
Enter total quantity needed: how many full bottles and how many additional tablets? How do I find the additional pills?
Answer:
Step-by-step explanation:
If the dosage is 2 tablets, 2 times per day, then the total number of tablets needed for 30 days would be:
2 tablets/dose x 2 doses/day x 30 days = 120 tablets
Since each bottle contains only 13 tablets, you would need to purchase multiple bottles to obtain the required number of tablets. To calculate how many full bottles and additional tablets you need, you can divide the total number of tablets needed by the number of tablets per bottle:
120 tablets ÷ 13 tablets/bottle = 9.23 bottles
Since you can't buy a fraction of a bottle, you would need to round up to the nearest whole number of bottles, which is 10. So you would need to purchase 10 full bottles.
To determine the additional tablets needed, you can multiply the number of bottles by the number of tablets per bottle and then subtract the total number of tablets needed:
10 bottles x 13 tablets/bottle = 130 tablets
130 tablets - 120 tablets = 10 additional tablets needed
Therefore, you would need to purchase 10 full bottles and an additional 10 tablets. The additional tablets can be obtained by purchasing an extra bottle and taking 2 tablets from it.
decrease 448 by 25%.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 448}}{\left( \cfrac{25}{100} \right)448}\implies 112\hspace{5em}\stackrel{ 448~~ - ~~112 }{\text{\LARGE 336}}[/tex]
Please help ASAP with this math problem
Answer:
D
Step-by-step explanation:
[tex]\sqrt{20x^{5} y^{2} }[/tex]
Can be written
[tex]\sqrt{(2)(2)(5)xxxxxyy}[/tex] Pull out the pairs
2[tex]x^{2}[/tex]y[tex]\sqrt{5x}[/tex]
Helping in the name of Jesus.
3/4- blank= 2/3 what fraction minus 3/4 is equal to 2/3?
The fraction that we need to subtract from 3/4 to get 2/3 is 1/12.
Let's use x to represent the fraction that we need to subtract from 3/4 to get 2/3.
We can set up an equation:
3/4 - x = 2/3
3/4 - x = 2/3
x = 2/3 - 3/4
To subtract these fractions, we need to find a common denominator. The least common multiple of 3 and 4 is 12, so we can rewrite the fractions with a denominator of 12:
x = (2/3) * (4/4) - (3/4) * (3/3)
x = 8/12 - 9/12
Now we can combine the fractions:
x = -1/12
Therefore, the fraction that we need to subtract from 3/4 to get 2/3 is 1/12.
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Emma, Sarah and Mark earn £60 selling donuts at a farmers' market. Emma worked for 3 hours, Sarah for 5 hours and Mark for 2 hours. They share the money in proportion to the number of hours worked.
How much money does Sarah earn?
Step-by-step explanation:
draw a table including all numbers
ANSWER 30 GOT MIXED UP WITH NUMBERS SORRY
Answer:
Sarah earns 30 pounds, Emma earns 18 pounds, and Mark earns 12.
Step-by-step explanation:
Lets say that Emma earns 3x pounds, Sarah earns 5x pounds, and Mark earns 2x pounds.
All of their wages add up to 60 pounds.
3x+5x+2x=60pounds
10x=60
x=60/10
x=6 pounds
Multiply this with the amount of hours Sarah worked: 6×5, and you get that Sarah earned 30 pounds.
What is the difference between Theoretical Probability and Experimental Probability?
Answer:
Theoretical probability is a mathematical concept that represents the likelihood of an event occurring based on mathematical reasoning or calculation. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes in a given situation. For example, the theoretical probability of flipping a coin and getting heads is 1/2, because there is one favorable outcome (heads) out of two possible outcomes (heads or tails).
Experimental probability, on the other hand, is based on actual observations or experiments. It is calculated by conducting an experiment and counting the number of times an event occurs, then dividing that by the total number of trials. For example, if you flip a coin 100 times and get heads 55 times, the experimental probability of getting heads is 55/100 or 0.55.
The main difference between theoretical and experimental probability is that theoretical probability is based on mathematical calculations and reasoning, while experimental probability is based on actual observations and experiments. Theoretical probability is used to predict the likelihood of an event occurring, while experimental probability is used to estimate the likelihood of an event occurring based on observed data.
Find the standard form of the equation of the hyperbola with the given characteristics.
Vertices:
(3, −4), (3, −8);
passes through the point
(7, −12)
The standard equation of the parabola is ( y + 6 )²/4 + ( x - 3 )²/b² = 1
Given data ,
Let the vertices of the parabola be V₁ ( 3 , -4 ) and V₂ ( 3 , -8 )
So , the center of the parabola is C [ ( 3 + 3 )/2 , ( -4 - 8 ) / 2 ]
C = C ( 3 , -6 )
Now , the distance between the center and one of the vertices (which is the distance from the center to either vertex).
Using the distance formula:
d = √((x2 - x1)² + (y2 - y1)²)
d = √((3 - 3)² + (-4 - (-6))²)
d = 2 units
The given point is (7, -12). If this point is closer to the x-axis (horizontally) than the center of the hyperbola, then the hyperbola is horizontally oriented.
The distance between the point P ( 7 , -12 ) and center is d₂ = √52 units
Now , the equation of the parabola is
((y - k)^2 / a^2) - ((x - h)^2 / b^2) = 1
where (h, k) is the center of the hyperbola, and a and b are the distances from the center to the vertices and the foci, respectively.
Plugging in the values we found:
Center: (h, k) = (3, -6)
a = 2
Hence , the equation is ( y + 6 )²/4 + ( x - 3 )²/b² = 1
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Express each set using the roster method.
A. The set of natural odd numbers greater than 2, but less than 11.
B. {x|x€N and 4
Answer:
A. { 3, 4, 5, 6, 7, 8, 9, 10}
B. {4}
Step-by-step explanation:
A. { 3, 4, 5, 6, 7, 8, 9, 10}
⇒ We didn't include 2 in this because 2 = 2, not greater than 2.
⇒ We also didn't include 11 for the same reason. 11 = 11, not less than 11.
B. First of all, this tells us that x is a natural number, i.e. x ≥ 1
The second thing it tells us is that x = 4. So the answer is {4}
(I may have misunderstood B. If I'm not correct, I'm really sorry. )
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How many times greater is 9.52 x 10-5 than 1.7 x 10-6? Express your answer
using either standard notation or scientific notation.
The number of times 9.52 x 10-5 is greater than 1.7 x 10-6 is 56
How many times greater is 9.52 x 10-5 than 1.7 x 10-6?From the question, we have the following parameters that can be used in our computation:
9.52 x 10-5 than 1.7 x 10-6
The number of times is the quotient of both numbers
So, we have
Times = (9.52 x 10^-5)/(1.7 x 10^-6)
Evaluate
Times = 56
Hence, it is 56 times greater
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the figure shown is composed of two cubes.
Which equation shows the surface area
of the figure?
S.A. = 6(5-5) + 6(3-3) 2(3-3)
What is the surface area of
the figure shown?
S.A.
cm²
8
3 cm
5 cm
Answer:
186
Step-by-step explanation:
what is the radius of this shape?
The radius of the circle in this problem is given as follows:
6.25 inches.
What is the radius of a circle?The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle.
In this problem, we have four segments, each with length of 6.25 inches, all four representing the radius of the circle, as all these four segments begin on the center of the circle and end at the circumference of the circle.
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I need help please with this activity is
F(x)=(x+2)^2-1
Answer: (4,35); (3,24); (2,15); (1,8)
Step-by-step explanation:
Please help with calculus. Thank you.
Answer:
[tex]\left(4, \sqrt{13}\right)\;\textsf{and}\;\left(4, -\sqrt{13}\right)[/tex]
Step-by-step explanation:
Let the point on the curve be (x, y).
Use the distance formula to create an equation for the distance between (8, 0) and (x, y):
[tex]\implies d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\implies d=\sqrt{(x-8)^2+(y-0)^2}[/tex]
[tex]\implies d=\sqrt{(x-8)^2+y^2}[/tex]
Since x² - y² = 3, then y² = x² - 3.
Substitute this into the equation so that we have an equation for d in terms of x:
[tex]\implies d=\sqrt{(x-8)^2+x^2-3}[/tex]
Simplify:
[tex]\implies d=\sqrt{x^2-16x+64+x^2-3}[/tex]
[tex]\implies d=\sqrt{2x^2-16x+61}[/tex]
[tex]\implies d^2=2x^2-16x+61[/tex]
Minimize d by taking the derivative of d with respect to x::
[tex]\implies \dfrac{\text{d}}{\text{d}x}d^2=\dfrac{\text{d}}{\text{d}x}2x^2-\dfrac{\text{d}}{\text{d}x}16x+\dfrac{\text{d}}{\text{d}x}61[/tex]
[tex]\implies 2d\dfrac{\text{d}d}{\text{d}x}=4x-16[/tex]
[tex]\implies \dfrac{\text{d}d}{\text{d}x}=\dfrac{4x-16}{2d}[/tex]
[tex]\implies \dfrac{\text{d}d}{\text{d}x}=\dfrac{2x-8}{d}[/tex]
Set it to zero and solve for x:
[tex]\implies \dfrac{2x-8}{d}=0[/tex]
[tex]\implies 2x-8=0[/tex]
[tex]\implies 2x=8[/tex]
[tex]\implies x=4[/tex]
Therefore, the value of x that minimizes d is x = 4.
To find the y-coordinate(s), substitute x = 4 into the equation of the curve:
[tex]\begin{aligned}x=4 \implies (4)^2-y^2&=3\\16-y^2&=3\\y^2&=13\\y&=\pm \sqrt{13}\end{aligned}[/tex]
Therefore, the points on the curve x² - y² = 3 that are closest to the point (8, 0) are (4, √13) and (4, -√13).
Solve the system: x+y=12 x-2y=0
Answer:
x=8, y=4
Step-by-step explanation:
I solved it using the substitution method, but any works really.
x+y=12
x-2y=0
x=12-y
Plug in given value of x:
12-y-2y=0
12-3y=0
-3y=-12
y=4
Plug in given value of y into first equation:
x+y=12
x+4=12
x=12-4
x=8
We can also do this using the Gauss method:
x+y=12 (Multiply this equation by -1)
x-2y=0
-x-y=-12 (Add both equations together)
x-2y=0
x-x-2y-y=-12+0 (Cancel out x and -x)
-3y=-12
y=4
Plug in given value of y:
x+y=12
x+4=12
x=8
Hope this helps!
You are 9 miles away from home. You start biking home at a speed of
2 miles per hour.
Answer: unit conversions?
Step-by-step explanation:
determine the absolute value of -13 and explain how you could use a number line to determine the absolute valure of -13
The absolute value of -13 is equal to 13.
What is an absolute value?The absolute value (also known as the modulus) of a number is the non-negative value of that number without regard to its sign.
For example, the absolute value of 5 is 5, and the absolute value of -5 is also 5.
The absolute value of a number is denoted by vertical bars on either side of the number. For instance, the absolute value of x is written as |x|.
Define number?A number is a mathematical object that is used to represent a quantity or value. Numbers can be classified into different types, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.
Therefore 13 is the absolute value.
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