Consider w1 = 4 + 2i and w2 = –1 – 3i. Which graph represents the sum w1 + w2? On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line goes from (0, 0) to point (3, negative 5). On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line goes from (0, 0) to point (3, negative 1). On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line goes from (0, 0) to point (5, 5). On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line goes from (0, 0) to point (5, 1).

Expressions (i) and (v) are equivalent to the original expression [tex]162x^2 - 72.[/tex]

In mathematics, an expression is a combination of numbers, variables, and operators that represents a value or a quantity. It can consist of constants, variables, arithmetic operators, and other mathematical functions or operations.

The expression [tex]162x^2 - 72[/tex] can be factored using the difference of squares formula: [tex]a^2 - b^2 = (a+b)(a-b)[/tex].

First, we can factor out 18 from the expression:

[tex]162x^2 - 72 = 18(9x^2 - 4)[/tex]

Now, we can apply the difference of squares formula by setting a = 3x and b = 2:

[tex]9x^2 - 4 = (3x)^2 - 2^2 = (3x + 2)(3x - 2)[/tex]

Substituting this back into the original expression, we get:

[tex]162x^2 - 72 = 18(9x^2 - 4) = 18(3x + 2)(3x - 2)[/tex]

Therefore, expressions (i) and (v) are equivalent to the original expression [tex]162x^2 - 72[/tex].

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Replacing stoplights with roundabouts does not significantly reduce the rate of accidents at intersections based on the given data.

Based on the statistical analysis, replacing stoplights with roundabouts does not significantly reduce the rate of accidents at intersections.

To test this hypothesis, we will use a paired t-test, which compares the means of two sets of paired data. The null hypothesis is that there is no significant difference between the mean accident rates before and after installing roundabouts, while the alternative hypothesis is that the mean accident rate after installing roundabouts is significantly lower than before.

Here are the steps to conduct the paired t-test:

Using the given data, the differences between the accident rates before and after installing roundabouts are:

-0.6, 0.2, 0.6, -0.1, 0

The mean of the differences is 0.02, and the standard deviation is 0.43. There are 5 paired observations, so the degrees of freedom are 4.

Using the formula, we get:

t = 0.02 / (0.43 / √(5)) = 0.14

The critical t-value at a 0.05 level of significance and 4 degrees of freedom is 2.776 from a t-distribution table.

Since the calculated t-value (0.14) is less than the critical t-value (2.776), we fail to reject the null hypothesis. Therefore, we can conclude that replacing stoplights with roundabouts does not significantly reduce the rate of accidents at intersections based on the given data.

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The upper control limit for the p-chart is 0.111, and the lower control limit is 0.003.

To calculate the upper and lower control limits for a p-chart, we need to use the following formula:

UCL = p' + 3√(p'(1-p')/n)

LCL = p' - 3√(p'(1-p')/n)

Where p' is the mean proportion of defective pots, n is the sample size (in this case, 120), and UCL and LCL are the upper and lower control limits, respectively.

Given that the proportion of defective pots is believed to be 0.05, we can calculate the mean proportion of defective pots as:

p' = 0.05

Substituting this value in the above formula, we get:

UCL = 0.05 + 3√(0.05(1-0.05)/120) = 0.111

LCL = 0.05 - 3√(0.05(1-0.05)/120) = 0.003

Any sample proportion of defective pots falling outside these limits would be considered statistically significant and warrant further investigation to identify the root cause of the defects in the production process.

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Complete question is:

A random sample of 120 cast aluminum pots is taken from a production line once every day. the number of defective pots is counted. the proportion of defective pots has been closely examined in the past and is believed to be 0.05. what are the upper and lower control limits for the p' chart.

Answer:

460.46

Step-by-step explanation:

If a fence costs $2.99 per foot, the cost of the feence will be 154(2.99) = $460.46

How to find the area of the circular flour

The formula for finding the area of a circle is expressed as:

A = πr²

r is the radius of the circle

Given that r = 7 feet

A = π(7)²

A = 49 * 22/7

A = 22 * 7

A = 154 square feet

If a fence costs $2.99 per foot, the cost of the fence will be 154(2.99) = $460.46

The first point to plot on the mean control chart would be at 1.9 at control chart with both limits.

1. There are four measurements in each sample, as shown in the table.

2. To plot the first point on the mean control chart, we need to calculate the mean of the first sample. Adding up the four measurements from the 10:00 am sample (2.0 + 1.8 + 2.0 + 1.8) gives a total of 7.6. Dividing by the number of measurements in the sample (4) gives a mean of 1.9. Since the mean is within the control limits of 1.8 and 2.2, the first point on the chart would be plotted at 1.9.
1. To determine how many measurements are in each sample, we simply count the number of measurements provided for each time.

10:00 am: 4 measurements (2.0, 1.8, 2.0, 1.8)
10:15 am: 4 measurements (2.0, 2.0, 2.0, 2.0)
10:30 am: 4 measurements (1.8, 1.9, 2.1, 2.2)
10:45 am: 4 measurements (2.1, 2.1, 1.9, 1.9)
11:00 am: 4 measurements (1.6, 2.0, 2.2, 1.7)

Each sample contains 4 measurements.

2. To plot the first point on a mean control chart, we need to calculate the mean of the first sample (10:00 am).

Mean = (2.0 + 1.8 + 2.0 + 1.8) / 4
Mean = 7.6 / 4
Mean = 1.9

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1. There are 4 measurements in each sample.

2. The first point to plot on the mean control chart would be 1.9, corresponding to the 10:00 am sample.

To determine the number of measurements in each sample, simply count the number of values for each time point.
10:00 am: 4 measurements (2.0, 1.8, 2.0, 1.8)
10:15 am: 4 measurements (2.0, 2.0, 2.0, 2.0)
10:30 am: 4 measurements (1.8, 1.9, 2.1, 2.2)
10:45 am: 4 measurements (2.1, 2.1, 1.9, 1.9)
11:00 am: 4 measurements (1.6, 2.0, 2.2, 1.7)
There are 4 measurements in each sample.
To plot the first point on the mean control chart, calculate the mean of the first sample (10:00 am).
Mean = (2.0 + 1.8 + 2.0 + 1.8) / 4 = 7.6 / 4 = 1.9.

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The product of 7 and 4 is 28, which is equal to the number of tiles in the product area.

Therefore, this configuration represents the factors of the quadratic expression [tex]x^2 + 9x + 8.[/tex]

To represent the factors of the quadratic expression x^2 + 9x + 8 using algebra tiles, we need to arrange the tiles into two rectangular areas representing the two factors, and the total number of tiles in the product area should be equal to the product of the number of tiles in each factor area.

Based on the information given, we can arrange the tiles as follows:

Factor 1 area: 7 tiles, with 1 x-tile and 6 blank tiles (represented by underscores):

Copy code

x

_

_

_

_

_

_

Factor 2 area: 4 tiles, with 1 x-tile and 3 blank tiles (represented by underscores):

Copy code

x

_

_

_

Product area: 28 tiles, with 1 x^2-tile, 9 x-tiles, 9 negative tiles (represented by red tiles), and 9 blank tiles (represented by underscores):

Copy code

x^2   -     -     -

x     x     x     x

_     _     _     _

_     _     _     _

_     _     _     _

_     _     _     _

_     _     _     _

To check that this configuration represents the given quadratic expression, we can count the number of tiles in each area and verify that the product of the two factors equals the number of tiles in the product area:

Factor 1 area: 7 tiles

Factor 2 area: 4 tiles

Product area: 28 tiles.

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The exponential function that represents the number of new participants as a function of the day number is:

f(x) = 12 * 4ˣ

What is the exponential function?

An exponential function is a mathematical function of the form:

f(x) = aˣ

where "a" is a constant called the base, and "x" is a variable. Exponential functions can be defined for any base "a", but the most common base is the mathematical constant "e" (approximately 2.71828), known as the natural exponential function.

Let's assume that each person who receives a selfie and accepts the challenge sends selfies to 4 new friends the next day.

Then, the number of new participants on Day 1 will be the number of friends that Aliyah, Kim, and Reese each sent selfies to, which is 4 friends each, or a total of 12 new participants.

On Day 2, the 12 new participants each send selfies to 4 new friends, resulting in 4*12 = 48 new participants.

On Day 3, the 48 new participants each send selfies to 4 new friends, resulting in 4*48 = 192 new participants.

We can see that the number of new participants is growing exponentially, with each new day resulting in a larger number of new participants than the previous day.

To write an exponential function that represents the number of new participants as a function of the day number, we can use the general form of an exponential function:

f(x) = a * bˣ

where a is the initial value (the number of new participants on Day 1), b is the growth factor (the factor by which the number of new participants increases each day), and x is the day number.

In this case, we know that a = 12 (the initial number of new participants) and b = 4 (the factor by which the number of new participants increases each day, since each participant sends selfies to 4 new friends).

Therefore, the exponential function that represents the number of new participants as a function of the day number is:

f(x) = 12 * 4ˣ

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Answer:

$13.25 .

Step-by-step explanation:

In case 1 he buys 1 kg of gummy bears and 2 kg of jelly beans .

So By the given condition :-

••••This will serve as equation (1) .

In case 2 he buys 2 kg of gummy bears and 3kg of jelly beans .

So by given condition :-

•••••This will serve as equation (2) .

Solving equation (1) and (2)

From equation (1)

x=38-2y .

we obtain,

2(38-2y)+3y=62.75

76-4y+3y=62.75

y=76-62.75=13.25 .

So cost of 1 kg of jelly bean is $13.25 .

The greatest common factor of 90 and 315 when divided by the least common multiple of 5 and 15 is 45.

When we multiply all the common prime factors, we get the greatest common factor of the numbers.

These prime factors should come from the prime factorization of the numbers given. These should be in all the unique combinations possible.

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Answer:

To graph this inequality, you can start by graphing the related function y = -x^2 - 1. This is a downward-facing parabola that opens downwards and has a vertex at (0, -1).

To graph the inequality y ≥ -x^2 - 1, you need to shade the region above the graph of the parabola. This is because any point above the parabola will have a y-coordinate that is greater than or equal to the corresponding y-coordinate on the parabola.

So, to graph the inequality, you can shade the region above the parabola. You can use a dotted line to represent the boundary of the inequality, since the inequality includes the possibility of equality (y = -x^2 - 1).

I hope this helps!

The measure in degrees of the central angle in the circle graph for the people that chose red is 72 degrees.

A central angle is an angle formed by two radii (or rays) that intersect at the center of a circle. It is an angle whose vertex is at the center of the circle, and its sides are the radii that intersect the circle's circumference.

According to the given information:

To find the measure in degrees of the central angle for the people that chose red, we need to calculate the percentage of people that chose red out of the total number of people surveyed, and then convert that percentage into degrees.

Total number of people surveyed = 180 (brown) + 60 (black) + 90 (red) + 120 (blue) = 450

Percentage of people that chose red = (Number of people that chose red / Total number of people surveyed) * 100 = (90 / 450) * 100 = 20%

Now, we can convert the percentage into degrees using the formula for calculating the central angle in a circle graph:

Central angle = (Percentage / 100) * 360

Plugging in the percentage of people that chose red:

Central angle for red = (20 / 100) * 360 = 72 degrees

So, the measure in degrees of the central angle in the circle graph for the people that chose red is 72 degrees.

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Answer:

I would say convenience sampling. It's hard to tell. Sampling every other person is like systematic sampling, BUT convenience sampling would be to sample people that are easy to reach.

The area of the cement part is 24 m².

Area is the region bounded by a plane shape.

To calculate the area of the part with cement. we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area is 24 m².

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Answer: A

Explanation:

Step-by-step explanation:

where is. the. polynomial.

we get the quotient as 161 and remainder as 11.So the missing numbers are:R = 11

9, 1, 6

First divide the greater number by the smallest number and then divide the smaller number by the remainder. We continue the process until we get 0 remainder. The divisor is the HCF of the given numbers.

To divide 5,472 by a two-digit number, we can use long division method as follows:

34) 5 4 7 2( 34

   -    4 0

     ______

       1 4 7

  -    1 3 6

      _______

            1 1

Therefore, we get the quotient as 161 and remainder as 11.

So the missing numbers are:

R = 11

9, 1, 6

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The probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is 0.2461.

Option C is correct

The probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is given by the binomial probability formula:

P(X = k) = (n choose k) [tex]* p^k * (1-p)^(n-k)[/tex]

where X is the random variable representing the number of heads, n is the total number of coin flips, k is the number of heads obtained, and p is the probability of getting a head on any individual flip.

Since we are assuming that the coin is fair, p = 0.5. Let's say you flipped the coin n times and obtained k heads. Then the probability of obtaining exactly k heads with a fair coin is:

P(X = k) = (n choose k [tex]* 0.5^k * ()1-0.5)^(n-k)[/tex]

We don't know what n or k are, so we can't compute the exact probability. However, we can use the fact that the coin is fair to get an estimate. If we assume that the number of heads obtained is roughly half of the total number of flips, then k = n/2. Plugging this into the formula, we get:

[tex]P(X = n/2) = (n choose n/2) * 0.5^(n/2) * (1-0.5)^(n/2)[/tex]

Simplifying this expression, we get:

[tex]P(X = n/2) = (n choose n/2) * 0.5^n[/tex]

Now, we want to find the probability of obtaining exactly as many heads as we just obtained. Let's say we flipped the coin 10 times and obtained 5 heads. Then we want to find P(X = 5), which is:

P(X = 5) = (10 choose 5) [tex]* 0.5^5 * (1-0.5)^(10-5)[/tex] = 0.2461

Therefore, the probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is 0.2461.

Option C is correct

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The granite countertop would cost $783.00.

Finding the cost of granite:

To find the cost of granite find the amount of granite that can be used for the entire kitchen.  

Since the kitchen floor is in a rectangle shape find the area of the kitchen floor using the area of a rectangle. Which will equal the amount of granite used for the kitchen.  

Use the formula for the cost of the countertop, which is the product of the area, and the cost per square meter, to determine the total cost.

Here we have

A counter in Adriana's kitchen is 1 m wide and 3 m long.

Hence, the area of the countertop can be found by multiplying the length and the width:

Area of kitchen = length x width = 3 m x 1 m = 3 m²

The cost of the granite is given by $ 261.00 per square meter

The cost of the granite countertop will equal the product of the area and the cost per square meter:

Total Cost = 3 m² x $261.00/m² = $783.00

Therefore,

The granite countertop would cost $783.00.

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The population of your friend's town is 300,000 if the population of your town is about 30,000.

To solve this problem, we can use the fact that if one quantity is a fraction of another quantity, we can multiply or divide the given quantity by that fraction to find the other quantity. In this case, we know that the population of your town is 1/10th of your friend's town's population, so we can multiply your town's population by 10 to get your friend's town's population.

If the population of your town is about 30,000, and it's about 1/10 the population of your friend's town, we can calculate your friend's town's population by multiplying your town's population by 10.

So, the population of your friend's town is

30,000 x 10 = 300,000

Therefore, your friend's town has a population of about 300,000.

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Answer: 32

Step-by-step explanation:

50% of last year is divided by 2 (50/100 = 1/2). 64/2 = 32

The answer to this problem is  "The population is the total number of people who go to the mall, and the sample is the first 75 people at the mall".

When conducting a survey, it's important to carefully define the population of interest and the sample being surveyed. The population is the entire group that you want to draw conclusions about, while the sample is the group of individuals that you actually survey. In this situation, the population of interest is the total number of people who go to the mall, as this is the group that we want to make inferences about.

The sample is the first 75 people who entered the mall and were asked about their favorite restaurant in the food court. This sample was likely selected in a way that is meant to be representative of the larger population of mall-goers. However, it's worth noting that the sample is still a subset of the population, and therefore there is some risk of sampling error. For example, if the first 75 people who entered the mall were all from the same demographic group, the survey results might not be representative of the larger population.

Overall, it's important to be clear about the population and sample when conducting a survey, as this helps to ensure that the results are meaningful and accurate.

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The number of ways to arrange the letters of PENCIL when the first letter can't be N or L is option (B) 480.

The word PENCIL has 6 letters, here we have to use permutation method.  If all the letters are used, there are 6! = 720 ways to arrange them. However, the first letter can’t be N or L. This means that there are only 4 choices for the first letter (P, E, C, or I). After choosing the first letter, there are 5 letters left to arrange,

So there are 5! = 120 ways to arrange them.

Therefore, the total number of ways to arrange the letters of PENCIL when the first letter can’t be N or L is

4 x 5! = 4 x 120 = 480

Therefore, the correct option is (B) 480.

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The best prediction possible for the number of times the spinner will not land on yellow is 18.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

Assuming that the spinner is fair and all outcomes are equally likely, we can calculate the probability of the spinner not landing on yellow in one spin by adding up the probabilities of all other outcomes, which are green, blue, and red.

The probability of the spinner not landing on yellow in one spin is:

P(not yellow) = P(green) + P(blue) + P(red)

= 1/6 + 1/3 + 1/6

= 1/2

Therefore, the expected number of times the spinner will not land on yellow in 36 spins is:

E(not yellow) = 36 x P(not yellow)

= 36 x 1/2

= 18

So the best prediction possible for the number of times the spinner will not land on yellow is 18. However, it's important to note that this is just a prediction based on probabilities, and the actual number of times the spinner doesn't land on yellow in 36 spins may vary.

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Answer:

25

Step-by-step explanation:

Yes , it is appropriate to choose normal approximation to calculate the chance of winning at least 10 times out of 75 total plays of game.

Use the normal approximation,

Chance of winning at least 10 times out of 75 total plays of the game,

Conditions for using the normal distribution are met.

Binomial distribution can be approximated by the normal distribution,

The number of trials 'n' is large enough usually n > 30.

The probability of success 'p' is not too close to 0 or 1.

The trials are independent.

Here,

n = 75 trials and p = 0.15 probability of winning.

To check if the normal approximation is appropriate,

Calculate the mean and standard deviation of the binomial distribution,

mean = n × p

         = 75 × 0.15

         = 11.25

Standard deviation

= √(n × p × (1 - p))

= √(75 × 0.15 × 0.85)

= 3.09

Mean is 11.25 and the standard deviation is 2.44.

The condition for independence is satisfied since each play is independent of the others.

If the other two conditions are met,

Check if np and n(1-p) are both greater than or equal to 10,

np = 75 × 0.15

    = 11.25

n(1-p) = 75 × 0.85

         = 63.75

Both np and n(1-p) are greater than or equal to 10,

So the conditions for using the normal approximation are satisfied.

Therefore, it is appropriate to use the normal approximation to find the chance of winning at least 10 times out of 75 total plays of the game.

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The money Jodi will have after selling her shares will be B. $5160.00

What is meant by selling?

Selling typically refers to the exchange of goods or assets for money or other valuable consideration. It is the process of transferring ownership of a product or item from the seller to the buyer in return for an agreed-upon price or value.

What is meant by shares?

Shares refer to units of ownership in a company or corporation. When a company sells shares, it is raising funds from investors who then become shareholders and have a claim on the company's profits and assets.

According to the given information

Jody bought 20 shares of Amazon at $121.00, which costs her 20 x $121.00 = $2420.00.

One year later, she bought 20 more shares at $127.00, which costs her 20 x $127.00 = $2540.00.

The total cost of buying all the shares is $2420.00 + $2540.00 = $4960.00.

Jody sold all her shares two years later at $133.00 per share, which gives her 40 x $133.00 = $5320.00.

Her total profit is $5320.00 - $4960.00 = $360.00.

After deducting the broker's fees, Jody will have $360.00 - $80.00 = $280.00.

Therefore, the correct answer is option B. $5160.00.

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The expression used  to calculate the surface area of the rectangular prism is given by option b. 2×6 + 2×10 + 2×15.

Let us consider 'l' be the length of the rectangular prism.

'w' be the width of the rectangular prism .

'h' be the height of the rectangular prism.

From the attached figure we have,

Length of the rectangular prism l = 3 units

Width of the rectangular prism w = 2 units

Height of the rectangular prism h = 5 units

Surface of the rectangular prism = 2(lw + wh + hl )

Substitute the values in the formula we get,

⇒Surface of the rectangular prism = 2 (3×2 + 2×5 + 5×3 )

⇒Surface of the rectangular prism = 2 ( 6 + 10 + 15)

⇒Surface of the rectangular prism = 2×6 + 2×10 + 2×15

Therefore, the surface area of the rectangular prism with given dimensions is equal to option b. 2×6 + 2×10 + 2×15.

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The above question is incomplete, the complete question is:

Which expression can be used to find the surface area of the following rectangular prism?

Attached figure.

The paired t-test results suggest that there is no significant improvement in students' learning after the new unit on factoring, based on a 90% confidence level.

To determine if there has been an improvement in students' learning after a new unit on factoring, we can perform a paired t-test on the pre-test and post-test scores of the five randomly selected students.

The differences between the pre-test and post-test scores for each student are: 3, 3, 4, 8, 0.

The mean of the differences is 3.6, and the sample standard deviation is 2.39.

The t-value for a 90% confidence interval with 4 degrees of freedom is 2.776. Since the calculated t-value of 2.68 (calculated as the mean of the differences divided by the standard error of the mean of the differences) is less than the critical t-value of 2.776, we fail to reject the null hypothesis that there is no improvement in students' learning.

Therefore, there is not enough evidence to conclude that the new unit on factoring has helped students learn based on the sample data.

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A description of the distribution of the values of a random variable and their associated probabilities is called a probability distribution. The correct answer is a.

A probability distribution is a mathematical function that describes the possible values of a random variable and the likelihood of each value occurring. It provides a complete description of the probabilities of all possible outcomes of a random experiment or event.

Probability distributions can be classified into two types: discrete probability distributions and continuous probability distributions. Discrete probability distributions are used when the possible outcomes of a random variable are countable or finite, such as the number of heads in a coin toss.

Continuous probability distributions, on the other hand, are used when the possible outcomes of a random variable are infinite, such as the time it takes for a person to complete a task.

Probability distributions are used in various fields, such as statistics, finance, engineering, and science, to model and analyze random phenomena and make predictions about future events. They are an essential tool for understanding uncertainty and making informed decisions based on probabilistic outcomes.

The correct answer is a.

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