Scaling up, David has 220 coins in his collection with 5% of 11 of the coins kept in his box.
What is a scale up?A scale up represents an increase or growth.
Scale factors are ratios comparing two quantities or values.
Proportionately, if 5% represent 11 coins, 100% will be 220 coins.
The number of coins David keeps in his box = 11
The percentage of the coins kept in the box = 5%
Thus, proportionately, 11 = 5%; therefore, 100% = 220 (11 ÷ 5%).
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Find the volume of a right circular cone that has a height of 20 ft and a base with a radius of 18 ft. Round your answer to the nearest tenth of a cubic foot
Answer:
The answer should be 20,365.714 but I am not sure
Step-by-step explanation:
If the width and length of a rectangle is 3 by 8 what is the width and length actually if the width is 10. 5
The new length of the rectangle is approximately 2.29 units. We use the formula for the area of a rectangle to solve for the new length, given the new width.
If the width and length of a rectangle are 3 and 8, respectively, and the width is increased to 10.5, we can calculate the new length of the rectangle using the formula for the area of a rectangle, which is length multiplied by width.
The original area of the rectangle is 3 x 8 = 24 square units. If we increase the width to 10.5, the new area of the rectangle becomes: 10.5 x length = 24 Solving for the length, we get: length = 24/10.5 = 2.29 (rounded to two decimal places)
It's important to note that changing one dimension of a rectangle can affect the other dimension, especially if we want to maintain the same area.
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suppose you have 4 pairs of socks and 4 pairs of shoes. if you can wear any combination of socks and shoes, including mismatched pairs, how many different possible footwear choices can you make
There are a total of 32 different possible footwear choices that we can make.
Given, The number of pairs of socks = 4
The number of pairs of shoes = 4
We are to find out the number of possible footwear choices we can make if we can wear any combination of socks and shoes, including mismatched pairs.
So, We can wear any pair of socks with any pair of shoes including a mismatch.
Thus, for each pair of socks, there are 4 possible pairs of shoes.
And for each pair of shoes, there are 4 possible pairs of socks.
Therefore, we can form,
Total number of possible footwear choices = 4 pairs of socks * 4 pairs of shoes * 2 (considering the case of mismatched pairs) = 32 pairs.
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Consider the system of equations
below. What is the solution of the
system?
y=4x-8
4x + 2y = 20
Answer:
x = 3, y = 4
Step-by-step explanation:
Substitute 4x - 8 in for y and then solve for x:
4x + 2(4x - 8) = 20
Then, 4x + 8x - 16 = 20 --> 12x = 36 --> x = 3.
Once you have x, you can solve for y.
y = 4x - 8 = 4(3) - 8 = 12 - 8 = 4
So, x = 3, y = 4
as a television executive, you have been given 24 shows to choose from to run during your prime time slots each week. if you have to choose 16 shows to run on your network, how many ways can you choose which shows to pick up?
As per the combination concept, there are 735,471 ways to choose 16 shows from a set of 24.
To find the number of ways to choose 16 shows from a set of 24, we can use the formula for combinations, which is:
ⁿCₓ = n! / x!(n-x)!
Where n is the total number of objects in the set (in this case, 24), and x is the number of objects we want to choose (in this case, 16). The exclamation mark (!) denotes the factorial function, which means multiplying the number by all positive integers less than itself.
Plugging in the numbers, we get:
²⁴C₁₆ = 24! / 16!(24-16)! = 735471
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A particle of mass 1. 2 kg is moving with speed of 8 ms inn a straight line on a horizontal table. A resistance force is app. Lied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, ao that F=0,3v^2
The speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2[/tex], or 19.2 N.
A particle of mass 1.2 kg is moving with a speed of 8 m/s in a straight line on a horizontal table. A resistance force is applied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, such that [tex]F=0.3v^2[/tex]
The force of resistance is an opposing force that acts to reduce the speed of the particle. As the particle moves faster, the resistance force increases. The force is proportional to the square of the speed, meaning that if the speed doubles, the force is multiplied by four. The force is also in the same direction as the motion, meaning that it will reduce the speed of the particle.
The equation for the force of resistance is [tex]F=0.3v^2[/tex], where v is the speed of the particle. Therefore, if the speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2,[/tex] or 19.2 N. This means that the force of resistance acting on the particle is 19.2 N.
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What are the integer solutions to the inequality below?
−
1
≤
x
≤
3
Answer:
i don't know i haven't done integers in a long time
Step-by-step explanation:
you're playing a game in which the probability of winning each round is .20. if you play five times, what is the probability of winning exactly 2 of the 5 times?
the probability of winning exactly 2 of the 5 times is 0.2048, or approximately 20.48%
define probabilityProbability refers to the measure of the likelihood or chance of a particular event occurring. It is represented by a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty.
The formula for the binomial distribution can be used to resolve this issue:
P(X=k) = (n choose k) × pᵇ×(1-p)ⁿ⁻ˣ
where:
The number of trials, n, is five in this instance.
bis the number of successes we want (in this case, b = 2)
p is the probability of success on each trial (in this case, p = 0.20)
So, plugging in the values:
P(X=2) = (5 choose 2) ×0.20² × (1-0.20)⁵⁻²
= 10 × 0.04×0.512
= 0.2048
Therefore, the probability of winning exactly 2 of the 5 times is 0.2048, or approximately 20.48%.
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Find the missing of dimension of the cone. Round you answer to the nearest tenth. Volume=13. 4m³
Radius=3. 2m
Height=h
The missing dimension of the cone is its height, which is approximately 2.5 m when rounded to the nearest tenth.
We can use the formula for the volume of a cone, which is:
Volume = (1/3)πr²h
where r is the radius of the base and h is the height of the cone.
We are given the volume of the cone as 13.4 m³ and the radius as 3.2 m. Substituting these values into the formula, we get:
13.4 = (1/3)π(3.2)²h
Multiplying both sides by 3 and dividing by π(3.2)², we get:
h = 3 × 13.4 / π(3.2)²
h ≈ 2.5 m
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Can someone please help me these questions are due tn
Answer:
$10.98
Step-by-step explanation:
$10.98
0.06 x 183 = $10.98
WILL GIVE BRIANLIAT TO BEST ABWWER
The graph of an exponential of the form y = ab contains the points (2, 60) and (4, 960). What are the values of a and b
Answer:
(15/4)4^x
Step-by-step explanation:
Substituting the x and y values of the first point, we get:
y = ab
60 = ab^(2)
Substituting the x and y values of the second point, we get:
y = ab
960 = ab^(4)
Now we can solve for a and b by eliminating one of the variables. One way to do this is to divide the second equation by the first equation:
960/60 = (ab^(4))/(ab^(2))
16 = b^(2)
Taking the square root of both sides, we get:
b = ±4
Since an exponential function can only have positive values for b, we choose b = 4. Now we can solve for a by substituting b = 4 into one of the original equations:
60 = a(4^(2))
60 = 16a
a = 60/16
a = 15/4
Therefore, the values of a and b are a = 15/4 and b = 4, and the exponential function is y = (15/4)4^x.
the sum of the numbers (20cba)16 and (a02)16 is ( (click to select) )16 and their product is ( (click to select) )16.
To solve this problem, we need to convert the hexadecimal numbers (20cba)16 and (a02)16 to decimal form, add them together, and then convert the result back to hexadecimal form.
(20cba)16 = 2x16^4 + 12x16^3 + 11x16^2 + 10x16^1 = 131402
(a02)16 = 10x16^2 + 0x16^1 + 2x16^0 = 256
Adding the two decimal numbers together gives us:
131402 + 256 = 131658
To convert this decimal number back to hexadecimal form, we can use the repeated division method.
131658 / 16 = 8228 remainder 10 (A)
8228 / 16 = 514 remainders 4 (4)
514 / 16 = 32 remainder 2 (2)
32 / 16 = 2 remainder 0
2 / 16 = 0 remainder 2
Therefore, (20cba)16 + (a02)16 = (131658)10 = (2002A)16.
To find their product, we can multiply the two decimal numbers together and then convert the result to hexadecimal form.
131402 x 256 = 33559552
Converting this decimal number to hexadecimal form gives us:
33559552 / 16 = 2097472 remainder 0
2097472 / 16 = 131092 remainder 0
131092 / 16 = 8193 remainder 4 (4)
8193 / 16 = 512 remainders 1 (1)
512 / 16 = 32 remainder 0
32 / 16 = 2 remainder 0
2 / 16 = 0 remainder 2
Therefore, the product of (20cba)16 and (a02)16 is (33559552)10 = (2011004)16.
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Kathy had 20 dollars to spend on 3 gifts. She spent 10 7/10
dollars on gift A and 6 2/5 dollars on gift B. How much money did she have left for gift C?
If Kathy had $20 to spend on 3 gifts and she spent $10⁷/₁₀ on Gift A and $6²/₅ on Gift B, the (balance) amount left for Gift C is $3.89.
How is the balance determined?The balance can be determined using subtraction operation.
Subtraction operation is one of the four basic mathematical operations, including addition, multiplication, and division.
Subtraction operation involves the minuend ($20), the subtrahends ($10.07 and $6.04), giving a difference or balance of $3.89.
The total spending budget that Kathy has = $20
The number of gifts to buy = 3
The amount spent on Gift A = $10.07 ($10⁷/₁₀)
The amount spent on Gift B = $6.04 ($6²/₅)
The amount left for Gift C = $3.89 ($20 - $10.07 - $6.04).
Thus, after spending on Gifts A and B, the amount left for Gift C is determined using subtraction operation as $3.89.
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How would you solve for m<ACD
The measure of angle ACD is approximately 109.5 degrees.
What are parallel lines ?
Parallel lines can be defined in which the lines which are equidistant to each other and they never intersect.
To solve for m<ACD, we can use the fact that the sum of the angles in a triangle is 180 degrees.
We can start by finding the measure of angle ACD, which is opposite to the known side length of 10 units. Using the Law of Cosines, we have:
cos(ACD) = (AD * AD + CD * CD - 100) / (2 * AD * CD)
We know that AD = 8 units and CD = 6 units, so plugging in these values, we get:
cos(ACD) = (64 + 36 - 100) / (2 * 8 * 6) = -1/3
Since -1/3 is negative, we know that angle ACD is obtuse, meaning it measures between 90 and 180 degrees. Therefore, we can take the inverse cosine of -1/3 to find its measure:
cos(ACD) = (-1/3) ≈ 109.5 degrees
Therefore, the measure of angle ACD is approximately 109.5 degrees.
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alexis puts dimes and quarters aside for the parking meter. she has a total of 20 coins and they are worth $3.80. how many quarters does alexis have?
Alexis has 12 quarters and 8 dimes.
Let's use d to represent the number of dimes and q to represent the number of quarters. We know that Alexis has a total of 20 coins, so d + q = 20.
We also know that the value of these coins is $3.80. Since dimes are worth $0.10 and quarters are worth $0.25, we can write an equation for the total value in cents:
10d + 25q = 380
To make things easier, let's divide both sides of the equation by 5:
2d + 5q = 76
Now we can use the first equation to solve for d in terms of q:
d + q = 20
d = 20 - q
Substituting this into the second equation gives:
2(20 - q) + 5q = 76
Expanding the parentheses and simplifying, we get:
40 - 2q + 5q = 76
3q = 36
q = 12
Therefore, Alexis has 12 quarters. We can check this by plugging q back into the first equation to find that she has 8 dimes as well:
d + q = 20
d + 12 = 20
d = 8
The total value of 12 quarters and 8 dimes is:
12 quarters x $0.25 per quarter + 8 dimes x $0.10 per dime = $3.00 + $0.80 = $3.80
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Help meee plssssss!!!!!!11
Write an explicit formula that can be used to find the number of bacteria cells after each generation. Then use the formula to find how many cells there are after 10 generations.
Answer:
N = N0 x 2^n
Step-by-step explanation:
The formula for calculating the number of bacteria cells after n generations is N = N0 x 2^n, where N is the total number of cells after n generations, N0 is the initial number of cells, and 2^n represents the number of times the population doubles after n generations. Assuming an initial population of 100 cells, there will be approximately 102,400 cells after 10 generations.
Answer:
The explicit formula for the number of bacteria cells after each generation can be written as:
N = N0 * r^n
Where:
N is the number of bacteria cells after n generations
N0 is the initial number of bacteria cells (at n=0)
r is the growth rate (how many new cells are produced per existing cell)
Assuming that each bacteria cell doubles in number with each generation (i.e. r=2), the formula can be simplified to:
N = N0 * 2^n
To find the number of cells after 10 generations, we can substitute n=10 into the formula:
N = N0 * 2^10
Since we don't have a specific value for N0, we can't find the exact number of cells after 10 generations. However, we can make some assumptions. For example, if we assume that there are initially 100 bacteria cells (N0=100), we can calculate:
N = 100 * 2^10 = 102,400
So, if each bacteria cell doubles in number with each generation and there were initially 100 cells, there will be 102,400 cells after 10 generations.
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The student enrollement of a high school was 1350 in 2012 and increases 9% each year. What is the estimated enrollment in 2022
The estimated enrollment of a high school in 2022 is approximately 2775 students.
To calculate the estimated enrollment in 2022, we need to use the formula for compound interest:
A =[tex]P(1 + r)^t[/tex]
where:
A = final amount (enrollment in 2022)
P = initial amount (enrollment in 2012)
r = annual interest rate (increase rate)
t = number of years (10)
We know that P = 1350 and r = 0.09 (9%). We can plug these values into the formula:
A = [tex]1350(1 + 0.09)^{10[/tex]
A = [tex]1350(1.09)^{10[/tex]
A = 2774.92
Therefore, the estimated enrollment in 2022 is approximately 2775 students.
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Find a power series representation for the function. (Center your power series representation at x = 0.) f(x) = 1/5 + x f(x) = sigma^infinity_n = 0 ((1/5 + x)^n) Determine the interval of convergence.
a) The power series representation of f(x) = 1/5 + x f(x) centered at x = 0 is f(x) = sigma^infinity_n = 0 ((x/5)^n)
b) The interval of convergence is (-5, 5)
To find the power series representation of f(x), we can use the formula for the geometric series
1 / (1 - r) = sigma^infinity_n = 0 (r^n)
where r is a constant.
In this case, we have
f(x) = 1/5 + x f(x)
We can solve for f(x) to get
f(x) = 1/5 / (1 - x)
Using the formula for the geometric series with r = x/5, we have
f(x) = sigma^infinity_n = 0 ((x/5)^n)
Multiplying both sides by 5, we get
5f(x) = sigma^infinity_n = 0 (x^n
So the power series representation of f(x) centered at x = 0 is
f(x) = sigma^infinity_n = 0 ((x/5)^n)
To determine the interval of convergence, we can use the ratio test
| (x/5)^(n+1) | / | (x/5)^n | = |x/5|
The series converges if the limit of |x/5| as n approaches infinity is less than 1. This is true when |x| < 5, so the interval of convergence is (-5, 5).
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Write a proportion to determine the missing measure.
A lighthouse casts a 72-yard shadow at the same time as a 32-foot tall billboard casts a 19-foot shadow.
What is the height of the lighthouse?
A 121.3 yd
B 64.8 yd
C 42.8 yd
D 118.4 ft
Answer:
Step-by-step explanation:
First, we need to make sure that we are comparing the units in the same system, either yards or feet. Let's convert 32 feet to yards:
32 feet * 1 yard/3 feet = 10.67 yards
Now we have:
Lighthouse height / Lighthouse shadow = Billboard height / Billboard shadow
Let x be the height of the lighthouse in yards.
x / 72 yards = 10.67 yards / 19 feet
We can simplify the equation by converting everything to yards:
x / 72 = 10.67 / 3.28
x / 72 = 3.25
To solve for x, we can cross-multiply:
x = 72 * 3.25
x = 234
Therefore, the height of the lighthouse is 234 yards.
Answer: A) 121.3 yd.
What are the values of x and y? *
Pls help!
Answer:
x = 8
y = 12
Step-by-step explanation:
m∠A = sin⁻¹(9/15) = 36.87⁰
cos36.87 = y/15
y = 15(cos36.87) = 12
sin36.87 = 12/(12+x)
12 + x = 12/(sin36.87)
x = 12/(sin36.87) - 12 = 8
For the given figure, can you conclude mlln? Explain.
A plane ticket to Barcelona cost £175 the price decreases by 6% work out the new price of the plane ticket
Answer:
£164.50
Step-by-step explanation:
If the discount is 6%, then the discounted price is 94% of the original price.
95% of £175 = 0.94 × £175 = £164.50
What is the volume of the cone expressed in terms of pi?
A rectangular photograph is 8 inches by 10 inches. It will be put into a rectangular frame that is 2 inches wide on all sides. What is the area of the photograph when it is put into the
frame?
Answer:
the area of the photograph when it is put into the frame is 80 square inches, and the area of the frame is 88 square inches.
Step-by-step explanation:
Answer: 36 inches(2)
Step-by-step explanation:
4in 5in 6in 6in 8in 7in triangular prism surface area
the surface area of the given triangular prism with sides of 4in, 5in, 6in, 6in, 8in, and 7in is 146 square inches.
To calculate the surface area of a triangular prism, you need to find the area of each of the faces and add them up.
First, let's find the area of the two triangular faces. To do this, we need to find the base and height of each triangle. Since the prism is isosceles, the base of each triangle is 6 inches (the length of one of the sides of the equilateral triangle). The height of each triangle can be found using the Pythagorean theorem. We have two sides of the triangle: 4 inches and 5 inches. Using the Pythagorean theorem, we can find the height:
[tex]h^2 = 5^2 - 4^2\\h^2 = 25 - 16\\h^2 = 9\\h = 3[/tex]
So the height of each triangular face is 3 inches. Now we can find the area of each triangular face:
Area of one triangular face = (1/2) x base x height
= (1/2) x 6 x 3
= 9 square inches
Since there are two triangular faces, the total area of the triangular faces is:
Total area of triangular faces = 2 x 9 = 18 square inches
Next, let's find the area of the three rectangular faces. We have two rectangles with sides of 6 inches by 8 inches, and one rectangle with sides of 4 inches by 8 inches. The area of each rectangular face is:
Area of rectangular face = length x width
So the area of the rectangular faces are:
Area of rectangular face 1 = 6 x 8 = 48 square inches
Area of rectangular face 2 = 6 x 8 = 48 square inches
Area of rectangular face 3 = 4 x 8 = 32 square inches
Therefore, the total surface area of the triangular prism is:
Total surface area = 18 + 48 + 48 + 32 = 146 square inches
So the surface area of the given triangular prism with sides of 4in, 5in, 6in, 6in, 8in, and 7in is 146 square inches.
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A circle with radius of 2 cm sits inside a circle with of 4 cm
Answer:
Diameter is equal to twice the radius. Given, radius is 4 cm. Diameter = 2(4) = 8 cm. Hence, diameter of the circle with radius as 4 cm is 8 cm.
Step-by-step explanation:
please
give brianliest
Answer: Area = 0
Step-by-step explanation:
((2*2)*3.14)-(4*3.14) = 0
F(x)=1/x squared -3x +1 then iind the inverse
The inverse function for the given function F(x)=1/x² -3x +1 is given by
f⁻¹(x) =(3 ± √(9 + 4/(x - 1))) /2.
Function f(x) is equals to,
F(x)=1/x² -3x +1
Inverse of a function, we need to swap the positions of the x and y variables and then solve for y.
Let's start with the original function
f(x) = 1/x^2 - 3x + 1
Now we will swap x and y,
⇒ x = 1/y^2 - 3y + 1
Next, Solve for y in terms of x
⇒ x = 1/y^2 - 3y + 1
⇒ x - 1 = 1/y^2 - 3y
⇒ 1/(x - 1) = y^2 - 3y
⇒ 1/(x - 1) = y(y - 3)
⇒ y(y - 3) = 1/(x - 1)
⇒ y^2 - 3y - 1/(x - 1) = 0
Using the quadratic formula, solve for y to get inverse function we have,
y = (3 ± √(9 + 4/(x - 1))) / 2
Therefore, the inverse function of f(x) is equal to f⁻¹(x) =(3 ± √(9 + 4/(x - 1))) /2.
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The above question is incomplete, the complete question is:
F(x)=1/x squared -3x +1 then Find the inverse
in general, which point size would you use if you wanted each character to be approximately one inch in size? a.) 1 pt b.) 72 pts c.) 24 pts d.) 36 pts
If you want each character to be approximately one inch in size, you would use a point size of 72 pts.
Point size is a unit of measurement used to determine the size of typefaces. It represents the height of the characters in a font. One point is equal to 1/72 of an inch, which means there are 72 points in one inch.
Therefore, if you want each character to be approximately one inch in size, you would need to use a font size of 72 points. This would ensure that the characters are roughly one inch tall, assuming that the font is designed to be proportional and not condensed or expanded.
Choosing a smaller point size, such as 1 pt or 24 pts, would result in characters that are much smaller than one inch. Choosing a larger point size, such as 36 pts, would result in characters that are larger than one inch.
Therefore the correct answer is option b.) 72 pts.
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Help Please
m-6=50
i need to find the value of m
please urgent
Answer:
m = 50 + 6
m= 56
lol easy ques
This one is easy. All you have to do is add 6 to both sides to get the value of m
m-6=50
m=50+6
m=56
help please image attached
The first inequality -4 ≤ x ≤ 3 represents the values of x that fall between the two vertical lines, while the second inequality 1 ≤ y ≤ 6 represents the values of y that fall between the two horizontal lines.
Describe Inequality?An inequality is a mathematical statement that compares two quantities or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).
Inequalities can involve variables or constants, and can be expressed in one variable or multiple variables. The solution to an inequality is the set of values that satisfy the inequality.
For example, the inequality 2x + 3 > 7 is true for values of x that are greater than 2, since if we substitute x = 2, we get 2(2) + 3 = 7, which is not greater than 7. On the other hand, if we substitute x = 3, we get 2(3) + 3 = 9, which is greater than 7, so the inequality is true for x > 2.
Inequalities have many applications in mathematics and other fields, such as economics, physics, and engineering. They are used to represent constraints in optimization problems, to model relationships between variables, and to describe ranges of possible values for a quantity or variable.
To determine the double inequalities that define the shaded region, we need to find the equations of the two boundary lines that form the sides of the shaded region.
The two vertical lines are x=-4 and x=3. The two horizontal lines are y=1 and y=6.
The shaded region is enclosed by these four lines, so the double inequalities that define it are:
-4 ≤ x ≤ 3 and 1 ≤ y ≤ 6
The first inequality -4 ≤ x ≤ 3 represents the values of x that fall between the two vertical lines, while the second inequality 1 ≤ y ≤ 6 represents the values of y that fall between the two horizontal lines. Together, they define the rectangular shaded region with vertices (-4,1), (-4,6), (3,6), and (3,1).
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