A diving instructor ordered snorkels. The table shows the cost based on the number of snorkels ordered.

If the diving instructor spent $1,024, how many snorkels did he order? Use numbers and words to explain your answer.


Number of snorkels: 1,2,3,4
Cost ($), c: 32,64,96,128

Therefore, the percent concentration of the first solution is 25%.

Let's call the percent concentration of the first solution x.

When we mix the two solutions, we end up with a total of 3 + 2 = 5 gallons of the new solution.

We can start by writing an equation based on the amount of pure alcohol in each solution:

[tex]3x + 2(0.65) = 5(0.41)[/tex]

The left side of the equation represents the total amount of pure alcohol in the mixture. The first term, 3x, represents the amount of pure alcohol in the 3 gallons of the first solution. The second term, 2(0.65), represents the amount of pure alcohol in the 2 gallons of the second solution.

The right side of the equation represents the total amount of pure alcohol in the final 5-gallon mixture, which is the product of the 41% concentration and the 5 gallons of the mixture.

Simplifying the equation, we get:

[tex]3x + 1.3 = 2.05[/tex]

Subtracting 1.3 from both sides, we get:

[tex]3x = 0.75[/tex]

Dividing both sides by 3, we get:

[tex]x = 0.25[/tex]

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the area of the trapezoid is 10√3 km² (approximately 17.3 km²).To find the area of a trapezoid, we use the formula A = (1/2) * (b₁ + b₂) * h

what is trapezoid ?

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The height (or altitude) of a trapezoid is the perpendicular distance between the two bases. The formula for the area of a trapezoid

In the given question,

To find the area of a trapezoid, we use the formula:

A = (1/2) * (b₁ + b₂) * h

where A is the area, b₁ and b₂ are the lengths of the parallel sides of the trapezoid, and h is the height (or perpendicular distance between the parallel sides).

In this case, we are not given the height, but we can still find the area if we make some assumptions. Let's assume that the trapezoid is isosceles, which means that the two non-parallel sides are equal in length. Then we can draw an altitude from one of the vertices to the opposite base, which will bisect the base and create two right triangles.

Using the Pythagorean theorem, we can find the length of the altitude:

a² + (b₁ - b₂)² = (2a)²

Simplifying and solving for a, we get:

a² + (b₁- b₂)² = 4a²

3a² = (b₁ - b₂)²

a = (1/√3) * |b₁ - b₂|

Since we know that the sum of the non-parallel sides is 10 km, we can write:

b₁ + b₂ = 10

Let's assume that b1 is the longer base, so we can write:

b₁ = 8 km

b₂ = 10 - b₁ = 2 km

Substituting these values into the formula for the altitude, we get:

a = (1/√3) * |8 - 2| = (1/√3) * 6 = 2√3 km

Now we can use the formula for the area of a trapezoid to find the area:

A = (1/2) * (b1 + b2) * h

A = (1/2) * (8 + 2) * 2√3

A = 10√3 km²

Therefore, the area of the trapezoid is 10√3 km² (approximately 17.3 km²).

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Answer:

100

Step-by-step explanation:

12x + 2y ← substitute x = 7 and y = 8 into the expression

= 12(7) + 2(8)

= 84 + 16

= 100

Answer:

=10 m

Step-by-step explanation:

PYTHAGOREAN THEOREM

8^2+6^2=64+36=100

=√100m

=10 m

This means that he can take up to 5.5 minutes to decorate each cookie and still have enough time to prepare the gift bags within the 90-minute time limit.

In mathematics, an inequality is a statement that compares two values or expressions, indicating whether they are equal, not equal, greater than, less than, greater than or equal to, or less than or equal to each other. Inequalities are represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

Here,

To determine how many minutes Winston can take to decorate each cookie, we need to use an inequality that takes into account the total time available and the time it takes to decorate each cookie and prepare each gift bag.

Let x be the number of minutes it takes Winston to decorate each cookie.

The total time Winston has available is 90 minutes, and he needs to decorate 12 cookies and prepare 12 gift bags. The time it takes him to prepare each gift bag is 2 minutes. Therefore, the total time it takes him can be expressed as:

Total time = Time to decorate 12 cookies + Time to prepare 12 gift bags

Total time = 12x + 12(2)

Total time = 12x + 24

To determine the maximum time Winston can take to decorate each cookie, we need to find the largest value of x that satisfies the total time constraint. Since he has exactly 90 minutes, we can use the inequality:

12x + 24 ≤ 90

Subtracting 24 from both sides, we get:

12x ≤ 66

Dividing both sides by 12, we get:

x ≤ 5.5

Therefore, the inequality that can be used to determine how many minutes Winston can take to decorate each cookie is:

x ≤ 5.5

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To determine who cut the larger piece of pie, we need to compare the size of the two pieces.

Since Miguel's piece is not described in terms of angle, we cannot compare the size of his piece to Mariah's piece directly in terms of their angles. Instead, we can use the fact that the area of a circular sector (a "pie slice") is proportional to the angle that the sector subtends at the center of the circle, and to the square of the radius of the circle:

Area of sector = (θ/360) x πr^2

where θ is the angle of the sector in degrees, and r is the radius of the circle.

Let's assume that the two pieces of pie have the same radius r.

If we assume that the original pie was a complete circle, then it had an angle of 360 degrees, and we can calculate the area of the whole pie as follows:

Area of whole pie = (360/360) x πr^2 = πr^2

Since Miguel's piece is not described in terms of angle, let's assume that it has a central angle of 300 degrees (i.e., he cut a sector with an angle of 300 degrees). The area of Miguel's piece is then:

Area of Miguel's piece = (300/360) x πr^2 = 5/6 x πr^2

Now consider Mariah's piece. We are told that she cut a sector with an angle of 60 degrees. The area of her piece is:

Area of Mariah's piece = (60/360) x πr^2 = 1/6 x πr^2

Since 5/6 is greater than 1/6, Miguel's piece is larger than Mariah's piece.

Therefore, we can conclude that Miguel cut the larger piece of pie.

Answer:

6 years = $22,536.50

12 years = $25,394.69

18 years = $28,615.38

Step-by-step explanation:

The find the value of the investment after the given number of years, first create an equation for A in terms of t using the compound interest formula.

[tex]\boxed{\sf A=P\left(1+\frac{r}{n}\right)^{nt}}[/tex]

where:

Given values:

Substitute the given values into the formula to create an equation for the value of the investment, A, in terms of time in years, t:

[tex]\implies \sf A=20000\left(1+\dfrac{0.02}{2}\right)^{2t}[/tex]

[tex]\implies \sf A=20000\left(1+0.01\right)^{2t}[/tex]

[tex]\implies \sf A=20000\left(1.01\right)^{2t}[/tex]

[tex]\hrulefill[/tex]

To find the value of the investment after 6 years, substitute t = 6 into the equation:

[tex]\implies \sf A=20000\left(1.01\right)^{2\cdot 6}[/tex]

[tex]\implies \sf A=20000\left(1.01\right)^{12}[/tex]

[tex]\implies \sf A=20000(1.12682503...)[/tex]

[tex]\implies \sf A=22536.5006026...[/tex]

Therefore, the value of the investment after 6 years is $22,536.50 rounded to the nearest cent.

[tex]\hrulefill[/tex]

To find the value of the investment after 12 years, substitute t = 12 into the equation:

[tex]\implies \sf A=20000\left(1.01\right)^{2 \cdot 12}[/tex]

[tex]\implies \sf A=20000\left(1.01\right)^{24}[/tex]

[tex]\implies \sf A=20000\left(1.2697346...\right)[/tex]

[tex]\implies \sf A=25394.69297...[/tex]

Therefore, the value of the investment after 12 years is $25,394.69 rounded to the nearest cent.

[tex]\hrulefill[/tex]

To find the value of the investment after 18 years, substitute t = 18 into the equation:

[tex]\implies \sf A=20000\left(1.01\right)^{2\cdot 18}[/tex]

[tex]\implies \sf A=20000\left(1.01\right)^{36}[/tex]

[tex]\implies \sf A=20000\left(1.43076878...\right)[/tex]

[tex]\implies \sf A=28615.37567...[/tex]

Therefore, the value of the investment after 18 years is $28,615.38 rounded to the nearest cent.

According to the given information, the function has no cusp.

What is a function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

The given piecewise function is:

c(x) = 39, when x ≤ 6

c(x) = 39 + 5(x - 6), when x > 6

A cusp is a point on the graph where the function changes direction very abruptly, like a sharp turn. This happens when the derivative of the function is not defined at that point.

The derivative of the function is:

c'(x) = 0, when x ≤ 6

c'(x) = 5, when x > 6

Since the derivative is defined and continuous at x = 6, there is no cusp at that point. Therefore, the function has no cusp.

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yes is answer   for all option   .we can check it by rules of rounding off numbers .

what is rounding ?

Rounding is the process of approximating a number to a nearby value that is easier to work with or more appropriate for a given context. When rounding, we take a number with many decimal places or significant figures and adjust it to a simpler or more convenient value with fewer decimal places or significant figures.

In the given question,

Yes, each number is rounded correctly to the nearest hundred thousand based on the rules of rounding.

To round to the nearest hundred thousand, we look at the digit in the hundred thousand place and the digit to its right (i.e., in the ten thousand place).

If the digit in the ten thousand place is 5 or greater, we round up the digit in the hundred thousand place by adding 1.

If the digit in the ten thousand place is less than 5, we leave the digit in the hundred thousand place as it is.

Using these rules, we can see that:

350000 rounded to the nearest hundred thousand is 400000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.

555555 rounded to the nearest hundred thousand is 560000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.

137998 rounded to the nearest hundred thousand is 200000 because the digit in the ten thousand place is 7, so we round up the digit in the hundred thousand place.

792314 rounded to the nearest hundred thousand is 800000 because the digit in the ten thousand place is 3, so we leave the digit in the hundred thousand place as it is.

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Answer:

a. The circumference of the base is 2πr, where r is the radius of the cylinder. Therefore, the circumference of the base is:

2π(10) = 20π

So the circumference of the base is 20π.

b. The area of the base is πr^2, where r is the radius of the cylinder. Therefore, the area of the base is:

π(10)^2 = 100π

So the area of the base is 100π.

c. The lateral area of the cylinder is given by the formula 2πrh, where r is the radius of the cylinder and h is the height (or length) of the cylinder. Therefore, the lateral area of the cylinder is:

2π(10)(2) = 40π

So the lateral area of the cylinder is 40π.

d. The total surface area of the cylinder is the sum of the lateral area and the areas of the two bases. The area of each base is πr^2, which we already calculated to be 100π. Therefore, the total surface area of the cylinder is:

2(100π) + 40π = 240π

So the total surface area of the cylinder is 240π.

e. The volume of the cylinder is given by the formula πr^2h, where r is the radius of the cylinder and h is the height (or length) of the cylinder. Therefore, the volume of the cylinder is:

π(10)^2(2) = 200π

So the volume of the cylinder is 200π.

The range of the relation whose graph is shown include the following: C. -1 ≤ y ≤ 1.

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-4, 4} or -4 ≤ x ≤ 4.

Range = {-1, 1} or -1 ≤ y ≤ 1.

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Question A) A 99% confidence interval estimate of his population mean finishing time of 100 meters race is (12.8081,15.5919)

Question B) Option II) narrower is the correct Option.

What is  linear equation?

An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.

                         The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.

Let X be the time required to finish 100 meters race competition with Tom ( in seconds.)

A) A 99% confidence interval estimate of his population mean finishing time of 100 meters race is (12.8081,15.5919)

x = 14.2

s^2= 0.9867

s= 0.9933

α/2, n-1 = 3.7074

Margin of error= 1.3919

lower bound= 12.8081

upper bound= 15.5919

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Based on the data in the sample, we can estimate that 900 people in attendance would prefer mustard on a hot dog.

According to the data provided, out of the 150 people surveyed, 27 people prefer mustard on a hot dog.

To estimate how many people in attendance would prefer mustard on a hot dog, we can use a proportion:

27/150 = x/5000

Where x is the number of people in attendance who would prefer mustard on a hot dog.

To solve for x, we can cross-multiply:

27 x 5000 = 150 x

Simplifying the equation, we get:

x = (27 x 5000)/150

x = 900

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Answer:

42.15 as a decimal is 0.4215 and you can multiply 0.4215 by a number to get 42.15 percent of that number.

Step-by-step explanation:

So the answer is 0.4215

Hope this helps! =D

Answer:0.4215

Step-by-step explanation:

42.15%÷100=0.4215

Answer:

0

Step-by-step explanation:

0

By assuming that the farmer has goat and cows in the ratio 3:4, the  number of cows in the farm will be 32 cows.

To find out how many cows are in the farm, we need to know the total number of animals in the farm. Assuming the ratio of goats to cows is 3:4, we can write this as: [tex]3x : 4x[/tex]

Where 3x represents the number of goats, and 4x represents the number of cows. If we know that there are 24 goats, we can set up an equation to solve for x:

3x = 24

Dividing both sides by 3, we get:

x = 8

Now that we know the value of x, we can find the number of cows:

= 4x

= 4(8)

= 32

Therefore, there are 32 cows in the farm.

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[tex]7.24 * 10^4 - 7.21 * 10^3[/tex] in scientific notation is [tex]6.519 * 10^4[/tex].

What is scientific notation?

Scientific notation is a way of expressing a number as a number between 1 and to multiplied by a power of 10.

To subtract these two numbers, we need to make sure they have the same exponent. We can do this by rewriting [tex]7.21 * 10^3[/tex] as [tex]0.721 * 10^4[/tex] (since [tex]7.21 * 10^3 = 0.721 * 10^4[/tex]).

Now we can perform the subtraction:

[tex]7.24 * 10^4 - 0.721 * 10^4 = 6.519 * 10^4[/tex]

Therefore, [tex]7.24 * 10^4 - 7.21 * 10^3[/tex] in scientific notation is [tex]6.519 * 10^4[/tex].

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(a) (i) The probability that 10 or more are extroverts is 0.965. (ii) the probability that 5 or more are extroverts 0.999. (iii) the probability that all are extroverts is 0.035. (b) (i) 0.03125 (ii) 0.5 (iii) 0.031.

The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has a constant probability of success. The distribution is named after the 17th-century mathematician James Bernoulli, who introduced it in his Ars Conjectandi.

The binomial distribution is commonly used in statistical inference, hypothesis testing, and decision making in various fields such as economics, finance, psychology, and biology. It is used to model the probability of events such as the number of heads in a series of coin tosses, the number of defective items in a batch of products, or the number of individuals in a population who have a certain characteristic.

(a) Let X be the number of extroverts in a group of 15 marketing personnel. X follows a binomial distribution with parameters n = 15 and p = 0.8.

(i) The probability that 10 or more are extroverts is:

P(X ≥ 10) = 1 - P(X < 10) = 1 - P(X ≤ 9)

Using a binomial distribution table or a calculator with a binomial probability function, we can find:

P(X < 10) = 0.0352

Therefore,

P(X ≥ 10) = 1 - P(X < 10) = 1 - 0.0352 = 0.9648

So the probability that 10 or more marketing personnel are extroverts is approximately 0.965.

(ii) The probability that 5 or more are extroverts is:

P(X ≥ 5) = 1 - P(X < 5) = 1 - P(X ≤ 4)

Using a binomial distribution table or a calculator with a binomial probability function, we can find:

P(X < 5) = 0.0008

Therefore,

P(X ≥ 5) = 1 - P(X < 5) = 1 - 0.0008 = 0.9992

So the probability that 5 or more marketing personnel are extroverts is approximately 0.999.

(iii) The probability that all 15 marketing personnel are extroverts is:

P(X = 15) = (15 choose 15) * 0.8^15 * 0.2^0 = 0.0352

So the probability that all 15 marketing personnel are extroverts is approximately 0.035.

(b) Let Y be the number of introverts in a group of 5 computer programmers. Y follows a binomial distribution with parameters n = 5 and p = 0.5.

(i) The probability that none are introverts is:

P(Y = 0) = 0.5⁵ = 0.03125

So the probability that none of the 5 computer programmers are introverts is approximately 0.031.

(ii) The probability that 3 or more are introverts is:

P(Y ≥ 3) = P(Y = 3) + P(Y = 4) + P(Y = 5)

Using a binomial distribution table or a calculator with a binomial probability function, we can find:

P(Y = 3) = 0.3125

P(Y = 4) = 0.15625

P(Y = 5) = 0.03125

Therefore,

P(Y ≥ 3) = 0.3125 + 0.15625 + 0.03125 = 0.5

So the probability that 3 or more of the 5 computer programmers are introverts is 0.5.

(iii) The probability that all 5 computer programmers are introverts is:

P(Y = 5) = 0.5⁵ = 0.03125

So the probability that all 5 computer programmers are introverts is approximately 0.031.

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Answer:

Step-by-step explanation:

To determine the most you should pay for the annuity, you can use the present value formula for an annuity.

PV = C * [(1 - (1 + r)^(-n)) / r]

where PV is the present value, C is the annual cash flow, r is the interest rate, and n is the number of periods.

In this case, C is $1,000, r is 6%, and n is 5 years. Plugging these values into the formula, we get:

PV = $1,000 * [(1 - (1 + 0.06)^(-5)) / 0.06]

PV = $4,212.10

Therefore, the most you should pay for the annuity is $4,212.10. If you pay more than this amount, you would be better off investing your money elsewhere at a 6% interest rate.

Answer:

14.4

Step-by-step explanation:

percentage for corn =30

total no. of acres of the land=48

=30 × 48

100

=14.4

Answer:

9/16 of a square inch

Step-by-step explanation:

[tex] \frac{3}{4} \times \frac{3}{4} = \frac{9}{16} [/tex]

Answer:

9 /16 inches^2

Step-by-step explanation:

To find the area of the tile, multiply the length by the width

A = 3/4 * 3/4

A = 9 /16 inches^2

By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.

What is the parallel lines?

Parallel lines are two lines in a plane that never intersect.

1. Orientation of Lines:

Parallel lines are lines that never intersect and remain equidistant from each other at all points.

When constructing parallel lines, the lines are drawn in the same direction and maintain the same distance between them throughout their entire length. They do not meet or cross each other.

On the other hand, perpendicular lines are lines that intersect at a right angle (90 degrees). When constructing perpendicular lines, the lines are drawn so that they intersect at a right angle, forming four right angles at the point of intersection.

2. Tools/Methods Used:

Constructing parallel lines and constructing perpendicular lines may require different tools or methods.

To construct parallel lines, one common method is to use a straightedge and a compass. A straightedge is used to draw a straight line, and a compass is used to measure and transfer distances to create additional parallel lines.

Therefore, By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.

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A timeline that spans 541 centimeters would be equivalent to a length of 5.41 meters or approximately 17.75 feet.

What is the unit conversion?

Unit conversion is the process of converting a quantity expressed in one unit of measurement to another unit of measurement that is equivalent in value. The need for unit conversion arises because different units are used to measure the same physical quantity in different countries or regions, or in different fields of study.

Making a model of the geologic time scale with a scale of 1 centimeter equals 1 million years means that each centimeter on the timeline represents 1 million years of geologic time.

To create the model, we can start by determining the total length of the timeline we want to create.

Let's say we want to include the entire Phanerozoic Eon, which spans approximately 541 million years.
To represent this on our timeline, we would need a total length of 541 centimeters.

However, we need to keep in mind that 100 cm is equal to 1 meter, which is a little longer than 3 feet.

Therefore, a timeline that spans 541 centimeters would be equivalent to a length of 5.41 meters or approximately 17.75 feet.

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Okay, let's walk through this step-by-step:

The initial balance of the savings account: $312.50

The final balance after 9 years: $1250

Let's call the interest rate r.

We know the final balance is the initial balance times (1 + r)^9

(because of continuous compounding over 9 years)

So:

312.50 = (1 + r)^9

312.50 / (1 + r)^9 = 1250

Solving for r:

(312.50 / 1250)^(1/9) = 1 + r

0.2504 = 1 + r

0.7596 = r

Converting to a percentage:

0.7596 * 100% = 75.96%

Rounding to the nearest whole percent: 76%

So the interest rate is 76%.

Does this make sense? Let me know if you have any other questions!

Answer: The equation for the decrease in water is given by:

W = -0.414t + 129.549

To find after about how many minutes the water level would be less than or equal to 64 cups, we can set W to 64 and solve for t:

64 = -0.414t + 129.549

-65.549 = -0.414t

t = 158.1

Rounding to the nearest 10 minutes, we get:

t = 160

Therefore, after about 160 minutes, the water level would be less than or equal to 64 cups.

Regarding the values of a and b, we can see that they are not relevant to this problem since they are not given in the equation for the decrease in water. So, none of the given options is correct.

Step-by-step explanation:

(1) The value of X is equal to 4  (2) The mean age is 3. (3) The probability of randomly selecting  a child under the age of 9  is approximately 0.83.  

The formula for calculating the average of given numbers is equal to the sum of all values ​​divided by the total number of values. There are three main types of averages: mean, median, and mode. All of these techniques work slightly differently and often give slightly different typical values.

(i). Given that there are a total of 42 children on the birthday, finding the value of x:

2x + 3x (4x-1) + x + (x-2) + (x-3) = 42

11x - 6 = 42

11x = 48

x = 4

Therefore, the value of x is equal to 4.

(ii). To find the average age, we need to calculate the sum of all the ages and divide by the total number of children:

Average age = (7 x 2 + 8 x 3 + 9 x (4-1) +10 x 4 +11 x (4-2) 12 x (4-3)) / 42

 = (14 + 24 + 27 + 40 + 22 +12) / 42

 = 139/42

 = 3.31

Rounded to the nearest whole number, the average age is 3.  

(iii). The probability of randomly selecting  a child under 9 is obtained by adding  the number of children aged 7, 8 or 9 (because we want children under 9) and  dividing by the total number of children:

Number of children under 9 years  = 2x + 3x + (4x-1)

Number of children under 9 years  = 9x - 1

Number of children under 9  = 9(4)–1

Number of children under 9 years  = 35

Probability of choosing a child under 9  = number of children under 9  / total number of children

Probability of choosing a child under 9 = 35/42

The probability of choosing a child under 9 years old is ≈ 0.83

Thus, the probability of randomly selecting  a child under the age of 9  is approximately 0.83.

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