If the area of the circular base of a cone is 9π cm². lateral area of the cone is 36π cm² and the the total surface area painted black is approximately 43.2π square feet.
How to find the lateral area and total surface area?1. Let's call the radius of the circular base "r". The area of the circular base is 9π, so:
r² = 9
r = 3
Since the slant height is four times the radius, the slant height is 4 * 3 = 12.
The lateral area of a cone can be calculated using the formula:
A = π * r * l
Where:
r = radius
l = slant height
Plugging in the values, we get:
A = π * 3 * 12
A = 36π
2. Let's call the radius of each cone "r" and the circumference of the base of each cone is 8π, so:
2 * π * r = 8π
r = 4
The lateral surface area of a cone can be calculated using the formula:
A = π * r * l
Where:
r = radius
l =slant height
Plugging in the values, we get:
A = π * 4 * 12
A = 48π
Since 70% of the lateral surface area is painted red, 30% is painted black. So, the total surface area painted black for each cone is:
0.3 * 48π
= 14.4π
And the total surface area painted black for all three cones is:
3 * 14.4π
= 43.2π
Therefore the approximate lateral area of the cone is 36π cm² and the total surface area painted black is approximately 43.2π square feet.
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what is the soulution 8x + 4x = 0
Answer:
0
Step-by-step explanation:
8x + 4x = 0
12x = 0
x = 0/12
x = 0
Step-by-step explanation:
combine like terms[tex]8x + 4x = 0[/tex]
[tex]12x = 0[/tex]
divide both sides by the same factor[tex] \frac{12x}{12} = \frac{0}{12} [/tex]
cancel terms that are in both the numerator and denominator[tex] \frac{12x}{12} = \frac{0}{12} [/tex]
[tex]x = \frac{0}{12} [/tex]
which is basically 0
new car is purchased for 21100 dollars. The value of the car depreciates at 10.5% per year. What will the value of the car be, to the nearest cent, after 6 years:
The value of the car can be, to the nearest cent, after 6 years is, 108454 cents
What is the percentage?The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.
Formula for percentage;
Percentage = (present quantity/whole quantity)×100
Given that,
New car is purchased for 21100 dollars
The value of the car depreciates at 10.5% per year
The value of the car after 6 years = ?
After 1 year,
Value = 21100 - 10.5% of 21100
= 21100 - (10.5x21100)/100
= 21100 - 0.105x21100
= 21100(1 - 0.105)
After 2 year,
Value = 21100(1 - 0.105) - 10.5% of 21100(1 - 0.105)
= 21100(1 - 0.105) - 0.105x21100(1 - 0.105)
= 21100(1 - 0.105)(1 - 0.105)
= 21100(1 - 0.105)²
Similarly, After n years,
Value = 21100(1 - 0.105)ⁿ
So, After 6 years,
Value = 21100(1 - 0.105)⁶
= 21100x0.895⁶
= 21100x0.514
= $10845.4
It is known that,
1 dollar = 100 cents,
So, value in cents after 6 years,
⇒ 10845.4x100
⇒ 108454
Hence, the value after 6 year is 108454 cents
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what was the ending balance? a sample bank statement. responses $597.35 $597.35 $715.26 $715.26 $751.58 $751.58 $880.88 $880.88
The final balance of the bank statement was $880.88. This amount reflects deposits, withdrawals, fees, and interest accrued during the statement period.
The final balance of a bank statement is the amount of money that is in the account after all deposits, withdrawals, fees, and interest have been accounted for during the statement period. To calculate the ending balance, start with the beginning balance and then add any deposits that were made during the statement period. Then, subtract any withdrawals, fees, and interest that were charged during the statement period. The final balance will be the amount that remains after all transactions have been accounted for. In this example, the ending balance was $880.88.
The complete question:
what was the ending balance? a sample bank statement.
A) $597.35
B) $715.26
C) $751.58
D)$880.88.
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Short answer need please.
The surface area of the right prism is equal 142 square inches.
How to calculate the surface area of a right prism
Surface area is the sum of the areas of all faces in a solid, herein we find the case of a right prism with six rectangular faces. The area formula for a rectangle is shown below:
A = w · l
Where:
A - Area, in square inches. w - Width, in inches.l - Length, in inches.Now we calculate the surface area of the rectangular prism:
A = 2 · (7 in) · (3 in) + 2 · (5 in) · (7 in) + 2 · (3 in) · (5 in)
A = 42 in² + 70 in² + 30 in²
A = 142 in²
The right prism has a surface area of 142 square inches.
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elzny I NEED HELP PLS
Answer:
105
vsvsbbshshsbxhxhxhggxxggxgx
if you laid a billion dollars worth of 10-dollar 10 -dollar bills side by side, how many dollar bills would you use? how many miles long would the trail be? (the width of a 10-dollar 10 -dollar bill is 2.61 inches.) is 2.61 inches.) (give your answers to the nearest whole number.)
The correct answer is it will stretch far 59.3 lakh miles .
Given that,
If a billion 10-dollar bills were placed side by side, the total value would be $1.
To find :What amount of dollars would you use? How far would the trail stretch?
A dollar bill is 2.61 inches wide.
The dimensions of a billion dollar bill are 2.61 x 1,000,000,000 inches.
Divide this by 12 to convert to feet: 2.61 x 1,000,000,000 / 12.
Divide that by 5280 to convert it to miles: 2.61 x 1,000,000,000 x 12 /5280.
(Instead of 2.61 inches, use 6.14 inches if you meant to say it from end to end, the long way.)
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Using a list of the radical expressions for numbers between 1 and 100 that will reduce, create a list of the reduced radical values. The values should be either a whole number or a radical expression.
The radical expression whose value is a whole number will be √2, √3, √4, √5, √6, √7, √8, √9, √10, ∛2, ∛3, ∛4, the fourth root of 2 and 3, the fifth root of 2, and the sixth root of 2.
What is the simplest radical form?If the power of the variable "a" is b/c. Then the simplest radical form of the expression will be given as,
[tex]\rm \left ( a \right )^{\rm \frac{b}{c}} = \rm \sqrt[\rm c]{\rm a^b}[/tex]
Using a list of the radical expressions for numbers between 1 and 100 will reduce, create a list of the reduced radical values.
The number whose square lies between 1 to 100 is given as,
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
The number whose cube lies between 1 to 100 is given as,
2³ = 8
3³ = 27
4³ = 64
And some other values are given as,
2⁴ = 16, 2⁵ = 32, 2⁶ = 64, and 3⁴ = 81
The radical expression whose value is a whole number will be √2, √3, √4, √5, √6, √7, √8, √9, √10, ∛2, ∛3, ∛4, the fourth root of 2 and 3, the fifth root of 2, and the sixth root of 2.
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Neil rents a canopy for $21.75 per
hour with a $25 delivery and
set-up fee. The rental costs a
total of $155.50. For how many
hours does Neil rent the canopy?
Create and solve the equation.
Answer:
21.75x + 25 = 155.50
-25 = -25
21.75x = 130.50
divide your slope from your variable
x = 6
At the nut farm, the cost price of a bag of almonds is R290. It is sold with a profit of 45%. What is the selling price?
The selling price of the bags of almonds that yields a profit of 45% is $420.5
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
The formula for profit is given by:
Profit = [(selling price - cost price) / cost price] * 100%
At the nut farm, the cost price of a bag of almonds is R290. It is sold with a profit of 45%. Hence, substituting:
45% = [(selling price - 290)/290] * 100%
0.45 = (selling price - 290)/290
selling price - 290 = 130.5
selling price = 420.5
The selling price is $420.5
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Chelsea left the WHite House and traveled toward the capital at an average speed of 34km/h. Jasmine left at the same time and traveled in the opposite direction with an average speed of 65km/h. Find Jasmine's and Chelsea's time, rate, and distance.
The distance traveled by Jasmine and Chelsea is given by the equations of speed and J = 20.4 km and C = 39 km , where T is the time taken and T = 0.6 hours
What is Speed?Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude
Speed = Distance / Time
Given data ,
Let the speed of Jasmine be represented as S₁ = 34 km/h
Let the speed of Chelsea be represented as S₂ = 65 km/h
Now , the distance traveled by Jasmine = J
And , the distance traveled by Chelsea = C
The measure of J = measure of C
So , the distances are the same
Let the time taken by both Jasmine and Chelsea be T
Now , Speed = Distance / Time
Substituting the values in the equation , we get
Distance D = 34T
And , distance D = 65T
Now , the total distance D = 59.4 km
So , 34T + 65T = 59.4
On simplifying the equation , we get
99T = 59.4
T = 0.6 hours
Hence ,
The distance traveled by Jasmine and Chelsea are 20.4 km and 39 km respectively
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HELP PLEASEEEEEEEEEEE i will give brainliest<33
Answer:
The unit rate of pages per hour is 39 pages and the unit rate of hour per pages is 1/39 hours
Step-by-step explanation:
We can solve this problem using proportion.
From the question; Leo reads 13 pages in 1/3 hours.
The first part of the question is to find the unit rate for pages per hour.
To find this;
Let x = the number of pages read in 1 hour
13 pages = 1/3 hours
x = 1 hour
Cross-multiply
1/3 × x = 13 × 1
= 13
Multiply both-side of the equation by 3
× 3 = 13× 3
x = 39 pages
Therefore, the number of pages read in 1 hour is 39 which implies the unit rate for pages per hour is 39
For the second part of the question, we are to find the unit rate for hours per page, that is; how many hours can he use to read a page.
Let x = the number of hour use to read a page
13 pages = 1/3 hour
1 pages = x
Cross-multiply
13x = 1/3
To get the value of x, we will divide both-side of the equation by 1/13
13x × = ×
x = hour
Therefore, the number of hour taken to read 1 page is , which implies the unit rate of hours per page is
What is 10x9+2
Anyways can someone help me with my other question on english.
Answer: 92
Step-by-step explanation: multiply first. 9x10=90. now add the two to the answer we just got. 90+2? 92.
Question located in picture below:
Answer:
5a^2 + 1
Step-by-step explanation:
7a^2 - 4 - 2a^2 + 5
5a^2 + 1
Answer:
5a^2+1
Step-by-step explanation:
Combining like terms in polynomials can go based on the degree it has.
Since 7a^2 and -2a^2 have the same degree as one another, we can just add them, which gives us 5a^2
Now since -4 and 5 dont have any degree, they are liked terms.
Add: -4+5=1
Now when simplified, we get:
5a^2+1
.......................
Answer:
hi
Step-by-step explanation:
Distributive property 42÷3
Answer: 14
Step-by-step explanation: 42 divided by 3 is 14.
As a fraction: 42/3
Answer:
42÷3= 14?
Step-by-step explanation:
a large lot of manufactured items contains 10% with exactly one defect, 7% with more than one defect, and the remainder with no defects. ten items are randomly selected from this lot for sale. if y1 denotes the number of items with one defect and y2, the number with more than one defect, the repair costs are y1 3y2. find the mean, in dollars, and variance of the repair costs.
The mean of the repair cost is 2.1 dollars and the variance of the repair cost is 0.
Let's call the number of items with no defects x. Then, we have:
x + y1 + y2 = 10
And we know that:
[tex]y1 = 10 * 0.10 = 1[/tex]
y2 =[tex]10 * 0.07 = 0.7[/tex]
x = 10 - y1 - y2 = 10 - 1 - 0.7 = 8.3
So, the expected number of items with one defect is E(y1) = 1 and the expected number of items with more than one defect is E(y2) = 0.7.
The expected repair cost is [tex]E(cost) = E(y1) * 3 * E(y2) = 1 * 3 * 0.7 = 2.1.[/tex]
The variance of the number of items with one defect is Var(y1) = E(y1^2) - [tex](E(y1))^2 = 1^2 - 1^2 = 0[/tex] and the variance of the number of items with more than one defect is [tex]Var(y2) = E(y2^2) - (E(y2))^2 = 0.7^2 - 0.7^2 = 0.[/tex]
Using the formula for the variance of a sum of independent variables, we can calculate the variance of the repair cost as:
[tex]Var(cost) = Var(y1 * 3 * y2) = 3^2 * Var(y1) * Var(y2) = 9 * 0 * 0 = 0[/tex]
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a number n is rounded to 2 decimal place
the result is 3.87
using inequalities write down the error interval for n
Answer:
3.90
hope its help
Step-by-step explanation:
y=3.87
n=d/3.90
Excute. by down interval 34.0
the college board reports that in the recent year, the mean mathematics sat score was 514 and standard deviation of 118. a sample of 50 scores is chosen. a) the probability that the sample mean score is less than 500 is [ select ] b) [ select ] c) the 80th percentile of the sample scores is [ select ]
The College Board reported that in a recent year, the mean mathematics SAT score was 514 and the standard deviation was 118. A sample of 65 scores was chosen.
a) The probability that the sample mean score is less than 500 can be found by using the mean and standard deviation of the SAT scores population. The formula to calculate this probability can be found in 3.
c) The 80th percentile of the sample scores is also not mentioned in the search results. To find the 80th percentile, a probability distribution of the sample mean scores must be created and then solved for the desired percentile.
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How do you solve
-6y+2=4x
y-2=x
In elimination for linear equations
The solution to the given system of linear equations is (x, y) = (-1, 1).
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
The system of equations is given in the question, as follows:
-6y + 2 = 4x
y - 2 = x
Here's how to solve this system of equations using the elimination method:
Multiply the first equation by 2:
-12y + 4 = 8x
Add the two equations:
-12y + 4 + y - 2 = 8x + x
-11y + 2 = 9x
Solve for x:
x = (2 - 11y)/9
Substitute the value of x back into one of the original equations to find y:
-6y + 2 = 4x
-6y + 2 = 4((2 - 11y)/9)
-6y + 2 = (8 - 44y)/9
-54y + 18 = 8 - 44y
26y = 26
y = 1
Use the value of y to find x:
x = (2 - 11y)/9
x = (2 - 11 * 1)/9
x = (2 - 11)/9
x = -9/9
x = -1
Thus, the solution is (x, y) = (-1, 1).
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John is measuring a piece of glass to fit in a triangular frame. He can only remerber to sides of the frame, which are 6 centimeters and 11 centimeters. Between what wwo numbers must the tried side of the frame fall?
The length of the third side should be between 5 and 17.
What are triangles?A triangle is a three-sided polygon because it has three edges and three vertices. The most important attribute of a triangle is the sum of its internal angles to 180 degrees.
Given John is measuring a piece of glass to fit in a triangular frame,
the two sides of the frame are 6 cm and 11 cm,
let the third side be x,
Any two sides of a triangle can be added together to have a length larger than the third side. Similar to this, any two triangle sides have length differences between them that are smaller than the length of the third side.
i.e. 11 - 6 < x < 11 + 6
5 < x < 17
Hence the third side should vary from 5 cm to 17 cm.
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a scientist looks at small pond organisms using a microscope. in his view, one of the organisms is 2.2 cm long when magnified to 100 times its actual size. What is its actual length, in mm?
The actual length of Organism is 0.22 mm.
What is Scale Factor?A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure.
Given:
The size of Organisms is 2.2 cm when magnified to 100 times its actual size.
So, the actual size in cm
= 2.2/ 100
= 0.022 cm
Now, we know 1 cm = 10 mm
= 0.022 x 10
= 0.22 mm
Hence, the actual size is 0.22 mm.
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Miguel went for a drive in his new car. He drove at a speed of 53 miles per hour for 84.8 miles
Time taken by Miguel car to drive is, 1.6 hour.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
Miguel went for a drive in his new car. He drove at a speed of 53 miles per hour for 84.8 miles.
We know that;
⇒ Speed = Distance / Time
⇒ Time = Distance / Speed
Here, Speed = 53 miles per hour
Distance = 84.8 miles
Hence, We get;
⇒ Time = 84.8 / 53
⇒ Time = 1.6 hour
Thus, Time taken by Miguel car to drive is, 1.6 hour.
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what are the gametes that can be produced by the following individuals? a. bgbg(1 point) b. bbgg x bbgg (1 point)
The gametes that can be produced by individual bgbg are B, and G, and the gametes that the offspring can produce are BB, BG, BG, BG, BG, BG, BG, and GG.
a. bgbg
The individual bgbg can produce gametes that are either B or G, as they carry one allele of each. Therefore, the gametes that can be produced by this individual are:
B, G
b. bbgg x bbgg
The individuals bbgg x bbgg are heterozygous for two different traits (B and G). In this cross, each parent can contribute either a B or a G allele to the offspring.
There are four possible combinations of gametes for each parent, for a total of 16 possible offspring combinations:
BB x BB = B offspring: BB, BG, BG, BB
BB x BG = B offspring: BB, BG, BG, BG
BB x GG = B offspring: BG, BG, BG, BG
BG x BG = B offspring: BG, BG, BG, BG
BG x GG = G offspring: BG, BG, BG, GG
GG x GG = G offspring: GG, GG, GG, GG
So, the gametes that can be produced by the offspring are:
BB, BG, BG, BG, BG, BG, BG, and GG
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consider the grid of points shown here. suppose that, starting at the point labeled a, you can go one step up or one step to the right at each move. this procedure is continued until the point labeled b is reached. how many different paths from a to b are possible?
The following is an excerpt from A First Training in Probability by Sheldon Ross. (74) = 35 is the right response.
Total moves required are 7, as follows:
Three steps up as well as four steps right.
Remember that perhaps the number of paths equals the number of arranged 7-tuples with 3 U's and 4 R's. As instance, the word URRURRU indicates to travel up, right, up, right, right, up.
There are 7 ways to arrange these letters, 7 ways to arrange the corresponding Us, and 7 ways to arrange the comparable Rs, for a total of 7!3!4! (74).
For each NxN grid, we may write the following as a generalization of our formula: It should be noted that there's a simpler method of writing this: D = N! / (K! * (N-K))! additionally known as the binomial coefficient.
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select the two values of x that are roots of this equation x^2-5x+5=0
The solution of the quadratic equation is [tex]x = \dfrac{5\pm\sqrt5}{2}[/tex].
A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given that the quadratic equation is x²-5x+5=0. The equation can be solved as below:-
x²-5x+5=0
a = 1 , b = -5 , c = 5
[tex]x = \dfrac{-b \pm\sqrt{(b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{5\pm\sqrt{25 - 4\times1\times5}}{2}[/tex]
[tex]x = \dfrac{5\pm\sqrt5}{2}[/tex]
The value of x for the quadratic equation will be [tex]x = \dfrac{5\pm\sqrt5}{2}[/tex].
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assuming that this population successfully colonizes the island and persists until the present, add a histogram of the 21st century island population to your figure (make sure that they can be easily compared to each other). describe the population in terms of light, medium, and dark individuals. write a brief statement justifying your graph and answer.
a) A histogram representing coat color for the initial colony your graph is given below.
b) Due to the fact that beach mice, which often have light coast colors, outnumber Oldfield colonizers by a factor of several, making dark coat colors less prevalent as time passes.
a) It's critical to understand the geographic distribution of Oldfield mice prior to the histogram presentation. Santa Rosa Island is classified into two primary geographic locations: inland and coastal, although having various different geographical settings.
Oldfield mice come in a variety of colors; fawn-colored (medium or dark) individuals are typically found in inland regions, whilst lighter or white individuals are found in coastal regions. As a result, Santa Rosa Island should have more colored mice and the beach should have more light-hued mice.
b) Oldfield colonists have predominantly dark coat colors, according to the image. The second histogram shows the coast color of the population following 6000 years of Oldfield and beach mouse hybridization. This is due to the fact that beach mice, which often have light coast colors, outnumber Oldfield colonizers by a factor of several, making dark coat colors less prevalent as time passes.
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The complete question is:
Imagine you have a time machine and are able to go back in same so 6,000 years ago. You are standing on newly formed Santa Rosa Island, a barrier island off the coast of Florida that consists entirely of beach habitate. You see that a large and genetically diverse mainland population of oldfield mice have just colonized the island Using all of the information in this case study, answer the following questions and justify your answers with reasoning Questions ists on the island. Write a brief statement justifying.
1. Draw a histogram representing coat color for the initial colony your graph. Describe the population in terms of the proportion of light, medium, and dark individuals.
2. Assuming that this population successfully colonizes the island and persists until the present, add a histogram of the 21" century island population to your figure (make sure that they can be easily compared to each other) Describe the population in terms of light, medium, and dark individuals. Write a brief statement justifying your graph and answer
Find the reciprocals of the numbers below.
The reciprocal of 19 is [?]
The reciprocal of 1/6 is[?]
Answer: 1/19, 6/1 (6)
Step-by-step explanation: To find the reciprocal of a fraction, switch the numerator and the denominator (the top and bottom of the fraction, respectively). So, simply speaking, the reciprocal of a/b is b/a. To find the reciprocal of a number, divide 1 by the number. So for example, the reciprocal of 5 would be 1/5
what is the slope and y intercept of the graph of y=3x-5
i need help whatsb the answer
Answer:Simplify the expression.
Exact Form:
35
8
Decimal Form:
4.375
Mixed Number Form:
4 3/8
Step-by-step explanation:
if the average service rate is 6 customers per hour, and assuming the negative exponential distribution is used to describe the randomness of the service time distribution, what is the probability that the service time will be less than or equal to 6 minutes? a. 0.451 b. 0.549 c. 0.017 d. 0.632
If the average service rate is 6 customers per hour, and assuming the negative exponential distribution is used to describe the randomness of the service time distribution. The probability that the service time will be less than or equal to 6 minutes is 0.549 [B]
The average service rate of 6 customers per hour corresponds to a mean service time of 1/6 = 0.1 hour = 6 minutes. To find the probability that the service time will be less than or equal to 6 minutes, we need to find the cumulative distribution function (CDF) of the exponential distribution evaluated at 6 minutes. The CDF of the exponential distribution is given by:
F(x) = 1 - exp(-λx)
where,
λ = 1/mean = 1/0.1 = 10. Plugging in x = 6, we get:
F(6) = 1 - exp(-10 * 6) = 1 - exp(-60) ≈ 0.549
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