Answer:
177,147
Step-by-step explanation:
9x9x9x9x9= 59,049
3x59,049= 177,147
given the following details: function: x3 - x2 4 initial approximation: 1 tolerance: .001 how many iterations before we find the approximate root below the error threshold?
The process takes approximately 14 iterations to reach the desired accuracy.
The Bisection Method will take approximately 14 iterations to find the approximate root of the equation within an error tolerance of 0.001. The mathematics calculations involve finding the midpoint of a given interval [a, b] and then determining whether the midpoint is a root of the equation. If it is not a root, then the interval is divided into two halves, and the process is repeated on the subinterval where the sign of the function changes. This process is repeated until the midpoint is within the desired error tolerance.
To calculate the number of iterations required, we begin by noting that the initial interval used is [1, 0]. The midpoint of this interval is 0.5. This value is then plugged into the function to determine if it is a root. Since it is not, the interval is then divided into two halves and the process is repeated. This process is repeated until the midpoint is within the desired error tolerance of 0.001. In this case, it takes approximately 14 iterations to reach the desired accuracy.
The complete question is:
Given the function f(x) = x^3 - x^2 - 4 and an initial approximation of x = 1, how many iterations of the Bisection Method are required to find the approximate root of the equation within an error tolerance of 0.001?
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Evaluate lim f(x) and lim f(x) for the following function. Use [infinity] or - [infinity] where appropriate. Then give the horizontal asymptote(s) off (if any). f(x) = 3x^2+2/x^3√4x^6+1
The limits of the function as x approaches infinity and negative infinity are 0 and negative infinity, respectively, and the horizontal asymptote is y = 0.
A function is a mathematical rule that assigns a unique output for each input.
For the function
=> f(x) = 3x²+2/x³√4x⁶+1,
we will evaluate the limits as x approaches infinity and negative infinity. We will also determine the horizontal asymptote of the function.
When x approaches infinity, the denominator
=> x³√4x⁶+1
becomes very large, so the value of the function becomes very small. Thus, the limit of the function as x approaches infinity is 0.
To determine the horizontal asymptote, we need to look at the degree of the numerator and denominator.
The numerator has a degree of 2 and the denominator has a degree of 3. Since the denominator has a higher degree, the horizontal asymptote is y = 0.
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how do you know the sum of (-2 3/4) and 5/9 is rational?
Answer:
Step-by-step explanation:
Because the numbers -2 3/4 and 5/9 are rational, and the sum of 2 rational numbers are always rational.
find the area of the region that is bounded above by the curve f(x)=(x 10)2 and the line g(x)=−x−4 and bounded below by the x-axis.
By definite integrals, we find that the area of the region bounded by the functions f(x) and g(x) described in the statement is equal to 4.5 units.
In this problem we must determine the area between two functions, a quadratic equation f(x) and a linear equation g(x).
First, we need to determine the limits of the interval of x-values with the help of a graphing tool, represented by the points of intersection of the two functions.
The points of intersection of the two functions are (x₁, y₁) = (- 5, 4) and (x₂, y₂) = (- 2, 1), respectively. Then, the area is defined by the following definite integral:
[tex]I=\int_{-5}^{-2}[g(x)-f(x)]dx\\\\I=\int_{-5}^{-2}(-x-1)-(x+3)^2]dx\\\\I=4.5 unit^2[/tex]
The area of the region represented by the definite integral introduced above is equal to 4.5 units.
The complete question is -
Find the area of the region that is bounded above by the curve f(x) = (x + 3)² and the line g(x) = - x - 1 and bound above the x-axis.
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Suppose in 2009 you bought a new snowmobile for $500. As time passes, the value of your snowmobile loses
value. Your snowmobile depreciates by an average of 15% each year.
a. Write an exponential equation to model the value of your snowmobile. Remember to define your variables.
Edina
By applying exponential decay concept, it can be concluded that the exponential equation to model the value of the snowmobile is A = 500 · 0.85ⁿ where n is the times (in years).
Exponential decay occurs when the amount of something decreases at a rate proportional to the amount left.
A = P (1 - r)ⁿ where:
A = final amount
P = initial amount
r = decay factor
n = time
We have the following information:
P = $500
r = 15%
The exponential equation to model the value of the snowmobile can be written as follows:
A = P (1 - r)ⁿ
A = 500 (1 - 15%)ⁿ
A = 500 · 0.85ⁿ
Thus, the exponential equation to model the value of the snowmobile is A = 500 · 0.85ⁿ where n is the times (in years).
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A touri begin walking along a 31-mile road to a mountian' ummit. He travel at a rate of 4 mph. After a while, he get tired and call a taxi. The taxi, traveling at a contant ped of 50 mph reach hi detination 2 hour after he tarted walking, what ditance doe he have to pay the taxi driver
The total distance the tourist has to pay the taxi driver is the sum of the distance the tourist walked and the distance the taxi drove, or 8 miles + 100 miles = 108 miles.
The distance the tourist has to pay the taxi driver can be calculated using the formula for distance = rate x time.
First, let's find out how far the tourist walked. We know that he walked at a rate of 4 mph for 2 hours, so the distance he walked is 4 mph x 2 hours = 8 miles.
Next, let's find out how far the taxi drove. The taxi reached the destination 2 hours after the tourist started walking, so the time it took for the taxi to reach the destination is 2 hours. The taxi was traveling at a constant speed of 50 mph, so the distance it drove is 50 mph x 2 hours = 100 miles.
Finally, the total distance the tourist has to pay the taxi driver is the sum of the distance the tourist walked and the distance the taxi drove, or 8 miles + 100 miles = 108 miles.
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Complete question:
A tour begins walking along a 31-mile road to a mountain summit. He travels at a rate of 4 mph. After a while, he gets tired and calls a taxi. The taxi, traveling at a constant ped of 50 mph reached his destination 2 hours after he started walking, what distance doe he have to pay the taxi driver
a bathroom tile pattern has blue, red and white tiles in the ratio 3 : 4 : 8 there are 300 tiles . how many tiles are there of each colour
There are 60 blue tiles, 80 red tiles, and 160 white tiles in the bathroom pattern
How to determine the tiles in each colourLet's call the number of individual tiles "x".
Using the given ratio, we have
Then there are 3x blue tiles, 4x red tiles and 8x white tiles.
The total number of tiles is:
3x + 4x + 8x = 300
Evaluate the like terms
15x = 300
Dividing both sides by 15
x = 300 / 15 = 20
So, we have
Blue = 3 * 20 = 60
Red - 4 * 20 = 80
White = 8 * 20 = 160
So there are 60 blue tiles, 80 red tiles, and 160 white tiles.
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find the intervals on which the given function is increasing and the intervals on which it is decreasing. (enter your answers using interval notation.)h(x) = (x 4)2 3x − 7
The intervals can be written as (-∞, 4) and (4, ∞) for increasing, and [4, 4] for decreasing.
The function h(x) = (x - 4)² - 3x + 7 is a parabolic function that opens upwards.
The function has a critical point at x = 4, where it changes direction from decreasing to increasing.
To determine the intervals on which the function is increasing or decreasing, we need to look at the sign of the first derivative of the function, which will tell us if the function is increasing or decreasing at any given x value.
In this case, the derivative of
=> h(x) = 2(x - 4) - 3.
Setting this equal to zero and solving for x, we find that x = 4 is the only critical point.
The second derivative of h(x) is 2, which is positive.
This tells us that the first derivative is increasing, which means the original function is increasing.
Therefore, the intervals on which the function is increasing are all x values greater than 4 or all x values less than 4. The intervals on which the function is decreasing are all x values between 4 and 4.
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How to Use the Exponential Equation Calculator?
The exponential function calculator available online at BYJU speeds up the calculation and displays the value of the variable quickly.
What is an Exponential Equation Calculator?The e key must be pressed first on the majority of graphing calculators, followed by the exponent key and the exponent input keys, in order to raise e to a power.
Using the free online tool known as the exponential function calculator, you can see the exponent's fluctuating value. The calculation is accelerated by the use of BYJU's online exponential function calculator, which also shows the variable's value in a little amount of time.
Directly below the display area, there is a row of sophisticated operators and features. The Down arrow to the right can be used to access more complex operators and functions. pi (π), superscript for exponents (^), cosine (cos), tangent (tan), logarithm (ln, log), and square root (√) are some of the buttons you'll encounter.
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Use the triangles shown.
B
A
E
20
D
C
(8x-6)°
F
12
Describe the restrictions on x.
H
konta
50°
G
I am sorry but I cannot answer your question with the contained elements.
Tyrion says that a system of linear equations must have exactly one solution If the lines have the same y-intercept.
For example, the equations y = 2x + 6 and y = -7x + 6 Intersect at their y -Intercept, (0, 6).
Select the system of linear equations that disproves Tyrion's claim.
A
B
y = -3+1
2y = 4x + 2
y = 22 +3
+y = 3
S y = 3x + 4
y=x+4
y = x - 1
2 = 2x - 2
C
{
In analytical geometry, a y-intercept, also known as a vertical intercept, is the point where the graph of a function or relation intersects the y-axis of the coordinate system using the widely accepted convention that the horizontal axis represents a variable x and the vertical axis represents a variable y. Therefore, x = 0 is satisfied at these sites.
What is an analytic geometry?Geometrical problems are represented and solved using algebraic symbolism and techniques in analytical geometry, also known as coordinate geometry. Analytic geometry is significant because it creates a relationship between algebraic equations and geometric curves.Analytic geometry, commonly referred to as coordinate geometry or Cartesian geometry in mathematics, is the study of geometry with a coordinate system. Synthetic geometry is the opposite of this. Engineering and physics, as well as aviation, rocketry, space research, and spaceflight, all require analytical geometry. Geometry involving numbers is known as analytical or coordinate geometry. Vertices and special points have coordinates in analytical geometry, such as (x, y) in the 2D plane, (x, y, z) in 3D space, etc.y = -3+1
2y = 4x + 2
y = 22 +3
+y = 3
S y = 3x + 4
y=x+4
y = x - 1
2 = 2x - 2
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 A small square field has an area of 4900 square feet. What is the measure of each side of the field?
Answer:
700
Step-by-step explanation:
A=hxw
A square has all equal sides
700×700=4900
A cell phone carrier charges a fixed monthly fee plus a constant rate for each minute used. Part 1. In January, the total cost for 150 minutes was $ 69 while in February, the total cost for 275 minutes was $ 76. 5. The constant charge for each minute used is:
A. 0. 08
B. 0. 07
C. 0. 06
Part 2. The fixed montly fee charged by the carrier is; fee = $__________________
Cellphone carriers charge a monthly fee and a per-minute rate. Every minute costs $0.06, so Option C is correct. Part 2, the carrier charges $60 monthly.
The constant Charge for Each Minute UsedTo obtain the constant rate of 0.06, we can use the two equations from January and February to solve for x, the constant rate:
Let x be the constant rate and y be the fixed monthly fee.
For January: y + 150x = $69For February: y + 275x = $76We can use these two equations to find the constant rate. Solving for x in the first equation, we get:
y + 150x = $69150x = $69 - yx = ($69 - y) / 150Next, we substitute this expression for x into the second equation:
y + 275x = $76y + 275(($69 - y) / 150) = $76y + ($69 - y) * (275 / 150) = $76y + $69 * (275 / 150) - y * (275 / 150) = $76y + $69 * (275 / 150) = $76 + y * (275 / 150)$69 * (275 / 150) = ($76 - y) / yFinally, we solve for x:
x = ($69 * (275 / 150) - $76) / (275 / 150)x = ($69 * (275 / 150) - $76) / (275 / 150)x = ($69 * 1.83 - $76) / 1.83x = ($127.57 - $76) / 1.83x = $51.57 / 1.83x = 0.06So, the constant rate is 0.06 dollars per minute.
The Monthly Charge by The CarrierTo find the fixed monthly fee, we can use the constant rate of 0.06 and one of the equations from January or February.
For January: y + 150x = $69
Substituting the constant rate x = 0.06, we have:
y + 150x = $69y + 150(0.06) = $69y + 9 = $69y = $69 - 9y = $60So, the fixed monthly fee is $60.
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Could anyone explain?
Both Isaac and Micah are using a compass and straightedge for their constructions.
The similarities between their construction steps include:They both start by drawing a line segment.They both use a compass to mark points on the line segment.They both use a straightedge to connect the marked points.The differences between their construction steps are:
Isaac is constructing congruent segments, which means he is dividing the original line segment into equal parts, while Micah is constructing a segment bisector, which means he is dividing the line segment into two equal parts and finding the midpoint.
Isaac only needs to mark one point on the line segment with his compass to get two congruent segments, while Micah needs to mark two points and then find the midpoint between them.
The final results of their constructions are different: Isaac will have two congruent line segments, while Micah will have one line segment bisector that splits the original line segment in half.
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The position of a bug moving along the x axis is given by x(t)=at+b, where a and b are both nonzero. Find the acceleration of the bug at any given time t.
The acceleration of the bug at any given time t is a.
The theory used in this question is the equation of motion.
This equation states that the position of an object is equal to the product of the acceleration and the time plus a constant.
Given:
The equation x(t)=at + b,
where a and b are both nonzero, describes the position of an insect travelling along the x axis.
The equation x(t)=at + b can be rewritten as x(t)=a(t) + b.
This equation states that the position of the bug is equal to the product of the acceleration (a) and the time (t) plus a constant (b).
Therefore, the acceleration of the bug at any given time t is a.
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One day, a person went to a horse racing area. Instead of counting the number of humans and horses, he counted 74 heads and 196 legs. How many humans and horses were there? A. 37 humans and 98 horses B. 24 horses and 50 humans C. 31 horses and 74 humans D. 24 humans and 50 horses
Answer:
d
Step-by-step explanation:
D. 24 humans and 50 horses.
We can use a system of equations to solve for the number of horses (x) and number of humans (y):
x + y = 74 (the total number of heads)
y = 196 - 4x (the total number of legs, with each horse having 4 legs)
Substituting the second equation into the first:
x + (196 - 4x) = 74
5x = 122
x = 24.5 (number of horses rounded down to the nearest whole number)
y = 74 - x = 50 (number of humans)
Answer:
Answer should be
Step-by-step explanation:
The volume of a sphere is 36m in. Find the radius
Answer: The volume of a sphere can be calculated using the formula:
V = (4/3)πr^3
Where V is the volume and r is the radius of the sphere.
Given that the volume is 36 cubic inches, we can substitute into the formula:
36 = (4/3)πr^3
Dividing both sides by (4/3)π:
36 / (4/3)π = r^3
Taking the cube root of both sides:
r = ∛(36 / (4/3)π)
The radius of the sphere is approximately 2.74 inches.
Step-by-step explanation:
Can you please help me
Dalia has two children, phoenix, age 6, and darius, age 9. Phoenix and darius attended daycare after school. Dalia paid $12,000 in child care expenses in 2022. Her agi is $80,000. What is the amount of her child and dependent care credit?.
Dahila's Child and Dependent Care Credit in 2022 would be $6,000.
The Kid and Ward Care Credit is a tax cut that can assist with balancing the expenses of really focusing on qualified youngsters and wards. How much the not entirely set in stone by the person's changed gross pay (AGI) and the sum they spend on care? In the event that the AGI is underneath $125,000, the individual can get a credit equivalent to half of their childcare costs.
In 2022, Dahila brought about $12,000 in kid care expenses and has an AGI underneath $125,000, so her Kid and Ward Care Acknowledge would be determined as follows:
$12,000 x 50% = $6,000
Therefore, Dahila's Child and Dependent Care Credit in 2022 would be $6,000.
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find measure angle 1
Answer:
37° and 63°
Step-by-step explanation:
the measure of a secant- secant angle and a tangent- tangent angle is half the measure of the intercepted arcs.
5
∠ 1 = [tex]\frac{1}{2}[/tex] (108 - 34)° = [tex]\frac{1}{2}[/tex] × 74° = 37°
6
the sum of the arcs in a circle is 360° , then
minor arc = 360° - 243° = 117°
∠ 1 = [tex]\frac{1}{2}[/tex] (243 - 117)° = [tex]\frac{1}{2}[/tex] × 126° = 63°
Calculate length of CD
Give answer to 3sf
Answer:
12.7
Using the Pythagorean theorem, you can easily calculate the length of BC.
So:
BC = sqrt(12^2 - 6^2) = sqrt(144 - 36) = sqrt(108) = 10.39230485
Now consider triangle BCD. You know all three angles and one side. Using the law of sines you know that ratio of the sine of each angle over the opposite side is constant. So:
BC/sin(55) = CD/sin(90)
BC/sin(55) = CD/sin(90)
sin(90)BC/sin(55) = CD
1*BC/sin(55) = CD
BC/sin(55) = CD
10.39230485/0.819152044 = CD
12.68666167 = CD
12.7 = CD
Step-by-step explanation:
A store in Greenpoint purchased a silver coat rack at the cost of $48 and marked it up at 25%. Later on,Prithia brought the silver coat rack. If the sales tax in Greenpoint is 15%, how much did she pay in all?
Answer:
$69.
Step-by-step explanation:
he store marked up the silver coat rack for $48 * 25/100 = $12.
So the silver coat rack was sold for $48 + $12 = $60.
The sales tax is $60 * 15/100 = $9.
Thus, Prithia paid a total of $60 + $9 = $69.
For a recent eion, there were 14 more Democrat than Republican in the tate enate. Thi reulted in a ratio of 6 Democrat to 5 Republican. How many enator were Democrat and how many were Republican?
There were 70 Republicans and 84 Democrats in the state senate.
Let x be the number of Republicans in the state senate.
Then the number of Democrats is x + 14.
We know the ratio of Democrats to Republicans is 6 to 5.
According to the given conditions, we can write the equation as follows -
x / (x + 14) = 5 / 6
Cross multiplying, we get,
6x = 5x + 70
Subtracting 5x from both sides of the equation, we get,
x = 70
Therefore, we get that there were 70 Republicans and 84 Democrats in the state senate.
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-5(-2)x−4y=−10 using the system of substitution please! I dont understand how to do that.
The equation cannot be solve using substitution
How to solve the system using substitutionFrom the question, we have the following parameters that can be used in our computation:
-5(-2)x−4y=−10
The above equation is a lone equation
For an equation to be solved using substitution, there must be at least two equations
Hence, the equation has no solution
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Graph y< 1/2
on a number line.
The number line of y < 1/2 is repesented below
How to determine the number lineFrom the question, we have the following parameters that can be used in our computation:
y < 1/2
A number line represents all real numbers on a line and is usually represented as a horizontal line with numbers increasing from left to right.
The symbol "<" in the equation y < 1/2 means "less than."
So, all values of y that are less than 1/2 would be graphed to the left of 1/2 on the number line.
The number line would look like this:
-1.0 -0.5 0.0 0.5 1.0
____________|______________|____________|____________
y < 1/2 1/2
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What is a Normal Probability Plot?
Answer: The normal probability plot is a graphical technique for assessing whether or not a data set is approximately normally distributed. The data are plotted against a theoretical normal distribution in such a way that the points should form an approximate straight line.
Step-by-step explanation:
The sorted data are shown with an approximation to the means or medians of the associated order statistics to create the normal probability plot.
What is a Normal Probability Plot?The normal probability plot is a graphical method for determining whether or not a data set is roughly normally distributed . The points in the data are displayed against a hypothetical normal distribution such that they should roughly form a straight line.
The sorted data are shown with an approximation to the means or medians of the associated order statistics to create the normal probability plot. It is applied to ascertain if a tiny amount of data is representative of a normal distribution.
A graphical method for locating significant deviations from normalcy is the normal probability plot. Outliers, skewness, kurtosis, the requirement for transformations, and mixes are some examples of this. The raw data, residuals from model fits, and estimated parameter values are used to create normal probability charts.
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ngsss benchmark mini assessment
The population of Florida is about 1.8 × 10^ 7
people. The land area of Florida is about
5.4 × 10^4 square miles. About what is the
population density of Florida?
A. 0.33 people/mi^ 2
B. 3.3 people/mi ^2
C. 3.3 × 102 people/mi^2
D. 3.3 × 103 people/mi^2
Correct option is D, the population density of Florida is 3.3 × 103 people/mi^2.
The population density, or the number of people divided by the area's size, is determined by the number of people who reside there. Many different creatures' distribution, growth, and migration can all be described using population density.
The average number of people in a population per unit of area or volume is known as population density. For instance, the density of a population of 100 insects living in a 100 square metre area is equal to one bug per square metre.
Three alternative methods are frequently used to determine population density. There are three types of density: agricultural, physiological, and mathematical.
Given,
population of Florida is about 1.8 × 10^ 7 people
land area of Florida is about 5.4 × 10^4 square miles
population density = the number of individuals / size of the area
population density = 1.8 × 10^ 7 / 5.4 × 10^4
= 3.3 × 103 people/mi^2.
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Which of these angles must be a right angle?
Answer:
ang. PQR
Step-by-step explanation:
The diameter which subtends an angle to the circumference of the circle is equal to 90 degrees. Hence, either ang. PQR and ang. PSR are both right angles.
Elena and jada each make money by helping out their neighbors. Elena babysits. her earnings are given by the equation y= 8.40x, where x represents how many hours she works and y represents how much money she earns.
Elena receives a higher value per hour, she earns $16.8 more than Jada.
What is unit rate?A unit rate means a rate for one of something.
Given that, Elena's earning can be given by, y = 8.40x where x represents how many hours she works and y represents how much money she earns. And Jada earns $7 per hour
We need to calculate the total income for 12 hours:
Therefore,
For Elena =
y = 8.40 x 12
y = $100.8
For Jada =
y = 7 x 12
y = $84
Thus, $100.8 - $84 = $16.8
Hence, Elena receives a higher value per hour, she earns $16.8 more than Jada.
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how many numbers are there in all from 4000 to 4999 (both 4000 and 4999 included) having at least one of their digits repeated?
2084 is the total number of integers between 4000 and 4999 with at least one repeated digit.
An integer is a whole number, which can be positive, negative, or zero. A repeated digit refers to a digit that appears more than once in the number.
First, let's count the number of integers between 4000 and 4999 that have no repeated digits. We have 4 choices for the thousands place, as it must be 4. For each of the remaining three places, we have 9 choices for digits (0 to 9, except for 4 in the thousands place). So, the total number of integers between 4000 and 4999 with no repeated digits is 4 * 9 * 9 * 9 = 2916.
Next, we need to count the number of integers with one repeated digit. For this, we need to consider two cases:
When the repeated digit is in the thousands place. In this case, there are only 9 choices for the other three digits, as they cannot be 4. The total number of integers in this case is 9 * 9 * 9 = 729.
When the repeated digit is not in the thousands place. In this case, there are 9 choices for the repeated digit and 8 choices for the other two digits. So, the total number of integers in this case is 9 * 9 * 8 = 648.
Adding the total number of integers in both cases, we get 729 + 648 = 1377 integers between 4000 and 4999 with at least one repeated digit.
Finally, subtracting the number of integers with no repeated digits from the total number of integers between 4000 and 4999, we get 5000 - 2916 = 2084. This is the total number of integers between 4000 and 4999 with at least one repeated digit.
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