A random sample of 1000 people was taken. Four hundred fifty of the people in the sample favored Candidate A. The 95% confidence interval for the true proportion of people who favors Candidate a isa. 0.419 to 0.481 b. 0.40 to 0.50 0.45 to 0.55 d. 1.645 to 1.96

The simplification of the given expression, [tex]\sqrt{\frac{2^{x+2} + 2^{x}}{2^{x-3}} + 9}[/tex], is 7

From the question, we are to simplify the given expression

The given expression is

[tex]\sqrt{\frac{2^{x+2} + 2^{x}}{2^{x-3}} + 9}[/tex]

The expression can be simplified as follows:

[tex]\sqrt{\frac{2^{x+2} + 2^{x}}{2^{x-3}} + 9}[/tex]

[tex]\sqrt{\frac{2^{x} \times 2^{2} + 2^{x}}{2^{x} \div 2^{3}} + 9}[/tex]

[tex]\sqrt{\frac{2^{x} (2^{2} + 1)}{2^{x} \times \frac{1}{2^{3}}} + 9}[/tex]

[tex]\sqrt{\frac{(2^{2} + 1)}{ \frac{1}{2^{3}}} + 9}[/tex]

[tex]\sqrt{\frac{(4 + 1)}{ \frac{1}{8}} + 9}[/tex]

[tex]\sqrt{\frac{(5)}{ \frac{1}{8}} + 9}[/tex]

[tex]\sqrt{(5) \div \frac{1}{8} + 9}[/tex]

[tex]\sqrt{(5) \times \frac{8}{1} + 9}[/tex]

[tex]\sqrt{5 \times 8+ 9}[/tex]

[tex]\sqrt{40+ 9}[/tex]

[tex]\sqrt{49}[/tex]

= 7

Hence, the simplified expression is 7

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To solve for the probability of a temperature of 98.5 or lower, we need to find the z-score for 98.5 using the formula z = (x - mu) / sigma, where x is the temperature, mu is the mean, and sigma is the standard deviation.

z = (98.5 - 98.6) / 0.8 = -0.125

Using a standard normal distribution table or calculator, we can find the probability of z being less than or equal to -0.125, which is 0.4502. Therefore, the probability of a temperature of 98.5 or lower for a randomly selected healthy person is 0.4502.

No, a temperature of 98.5 is not an unlikely occurrence for a single individual, given that the distribution of human body temperatures is approximately normal with a mean of 98.6 and a standard deviation of 0.8. The probability of a temperature of 98.5 or lower is about 0.45, which means that there is a reasonable chance that a healthy person could have this temperature.

Thus, to solve for the probability of an average temperature of 3.5 or lower for 135 healthy people, we need to use the central limit theorem, which states that the distribution of sample means will be approximately normal with a mean of the population mean and a standard deviation of the population standard deviation divided by the square root of the sample size.

The standard error of the mean (SEM) is calculated as SEM = sigma/sqrt (n), where sigma is the population standard deviation and n is the sample size.

SEM = 0.8 / sqrt(135) = 0.068

The z-score for an average temperature of 3.5 is calculated as z = (3.5 - 98.6) / 0.068 = -1375.74

Using a standard normal distribution table or calculator, we can find the probability of z being less than or equal to -1375.74, which is essentially 0. Therefore, the probability of an average temperature of 3.5 or lower for 135 healthy people is almost 0.
To answer your questions, we will use the normal distribution properties of human body temperatures.

(1) To find the probability that the temperature for a randomly selected healthy person is 98.5 or lower, we need to calculate the z-score:

z = (X - μ) / σ
z = (98.5 - 98.6) / 0.8
z = -0.1 / 0.8
z = -0.125

Now, we can look up the probability in a standard normal distribution table or use a calculator to find the area to the left of z = -0.125. The probability is approximately 0.4505 (rounded to four decimal places).

(2) A temperature of 98.5 is not an unlikely occurrence for a single individual, given that the true average temperature of healthy people is 98.6. The probability of having a temperature of 98.5 or lower is 0.4505, which is not very small, so this is not an unlikely event.

(3) To find the probability that the average temperature for a sample of 135 healthy people is 98.5 or lower, we first need to find the standard error (SE) of the sample mean:

SE = σ / √n
SE = 0.8 / √135
SE ≈ 0.0688

Next, we calculate the z-score for the sample mean:

z = (X - μ) / SE
z = (98.5 - 98.6) / 0.0688
z ≈ -1.451

Now, we look up the probability in a standard normal distribution table or use a calculator to find the area to the left of z = -1.451. The probability is approximately 0.0735 (rounded to four decimal places).

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Answer:

303

Step-by-step explanation:

92 4/5% = 92.8%

let's call x is the value of 100%

then 92.8% of x = 281.184

or 0.928x = 281.184

x = 281.184/0.928 = 303

The equation that represent the average price of a house as a function of the year can be presented as follows;

The average of a value, such as the average price of a houses is the ratio between the sum of the prices of the houses to the number of houses.

The average cost of a family house in 1997 = $156,100

The average cost of the family house in 2010 = $254,400

The equation for the price (p) of a house as a function of the year, t where t = 0 corresponds to 1997, can be found as follows;

The slope of the equation is; (254,400 - 156,100)/(2010 - 1997) = 98300/13

98300/13 = 7561 7/13

The linear equation is therefore;
p - 156100 = (98300/13) × (t - 0)

p = (98300/13) × t + 156100

p = (7561 7/13) × t + 156100

The average price of a house today, 2023 can be found by plugging in the value, t = 2023 - 1997 = 26 in the above equation as follows;

p = (98300/13) × 26 + 156100 = 352,700

The price of a house today is $352,700

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The line of reflection of the given image is: reflection across x = -5

There are different ways of carrying out transformations and they are:

Reflection

Translation

Dilation

Rotation

Now, a line of reflection is defined as a line that lies between two identical mirror images, so the distance of any point of one figure from the line will equal the distance of the same point of the mirror image (flipped figure).

Looking at the given image, it is very clear that the line of reflection of the image is a reflection across x = -5

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Total shaded area is the sum of the areas of the two triangles is 64.5 in²

The area of each of the two triangles can be found from the formula ...

A = (1/2)bh

left triangle

A = (1/2)(9.8 in)(8.6 in) = 42.14 in²

right triangle

A = (1/2)(5.2 in)(8.6 in) = 22.36 in²

Total shaded area is the sum of the areas of the two triangles:

(42.14 +22.36) in² = 64.5 in²

Hence, total shaded area is the sum of the areas of the two triangles is 64.5 in²

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There is sufficient evidence to suggest that drivers over the age of 60 drive less on average than 24 miles per day. To answer this question, we can use a one-sample t-test. The null hypothesis is that the mean number of miles driven by drivers over 60 is equal to 24, while the alternative hypothesis is that it is less than 24.

Using the given information, we can calculate the t-statistic as follows:

t = (23.4 - 24) / (4.1 / sqrt(25)) = -1.95

The degrees of freedom for this test are 24 (n-1).

Using a t-table or calculator, we can find the critical value for a one-tailed test at a significance level of 0.05 with 24 degrees of freedom to be -1.711.

Since our calculated t-value of -1.95 is less than the critical value of -1.711, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that drivers over the age of 60 drive less on average than 24 miles per day.

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Answer:   B, C, E

Step-by-step explanation:

When multiplying or dividing - and + numbers, rules are as follows:

If the signs are the same, equals +

So for division

[tex]\frac{+}{+} =+[/tex]     and       [tex]\frac{-}{-} =+[/tex]

If signs are different, equals -

[tex]\frac{-}{+}=-[/tex]     and     [tex]\frac{+}{-} = -[/tex]

Question [tex]-(\frac{8}{2} )[/tex]    the number is negative

A. not the same because   [tex]\frac{-}{-} =+[/tex]    and your question is -

B. yes it is the same because   [tex]\frac{+}{-} = -[/tex] and your question is also -

C. yes it is the same because the parenthesis are ok to remove and it doesn't change your answer

D. not the same [tex]\frac{+}{+} =+[/tex]  and your question is -

E. yes it is the same because [tex]\frac{-}{+}=-[/tex]  and your answer is also -

The standard error is found to be 0.024, when constructing a 90% confidence interval for the true proportion of students.

The point estimate of the proportion of students (sample) who dropped an online course is:

p' = 104/520 = 0.2

The standard error of the sample proportion is:

SE = √[p'(1 - p') / n]

where n is the sample size.

SE = √[0.2(1 - 0.2) / 520] = 0.024

To construct a 90% confidence interval, we can use the formula:

CI = p' ± z × SE

where z is the desired confidence level's associated z-score. The z-score with a 90% degree of confidence is 1.645.

CI = 0.2 ± 1.645(0.024) = (0.155, 0.245)

Therefore, we can be 90% confident that the true proportion of students who will drop an online course is between 0.155 and 0.245.

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Answer:

4,000 pounds

Step-by-step explanation:

One ton is equal to 2,000 pounds.
Therefore, a boulder that weighs 2 tons would weigh:

2 tons x 2,000 pounds/ton = 4,000 pounds

So the boulder weighed 4,000 pounds.

Answer:(94-7a)

Step-by-step explanation:

if 69 ate ur mom

The nonlinear systems can exhibit more complicated behavior, and the stability of the critical point can depend on the specific nonlinearities present in the system.

In the context of a linear autonomous system of differential equations in two dimensions, the critical point is a node if both eigenvalues have the same sign and are nonzero. Specifically, if both eigenvalues are positive, then the node is called a source, and if both eigenvalues are negative, then the node is called a sink.

Whether the node is asymptotically stable or unstable depends on the values of the eigenvalues. If both eigenvalues are negative, then the node is asymptotically stable, meaning that nearby solutions converge to the node as time goes to infinity. If both eigenvalues are positive, then the node is unstable, meaning that nearby solutions move away from the node as time goes to infinity.

If one eigenvalue is positive and the other is negative, then the critical point is a saddle, and the stability of the critical point depends on the direction of the solutions in the vicinity of the saddle.

It is important to note that these conditions for a critical point to be a node and its stability only apply to linear systems. Nonlinear systems can exhibit more complicated behavior, and the stability of the critical point can depend on the specific nonlinearities present in the system.

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The variance for the given data is 11.3.

To find the variance for the given data, follow these steps:

1. Calculate the mean of the data. To do this, add up all the numbers and divide by the total number of values. In this case, the sum is -3 (1+4-5-9+6) and there are 5 values, so the mean is -3/5 = -0.6.

2. Calculate the difference between each value and the mean. To do this, subtract the mean from each value. For example, the difference between 1 and -0.6 is 1.6.

3. Square each difference. This is important because we want to give greater weight to values that are further away from the mean. For example, (1.6)^2 = 2.56.

4. Add up all the squared differences. For this data set, the sum of the squared differences is 56.4.

5. Divide the sum of squared differences by the total number of values. In this case, 56.4 divided by 5 is 11.28.

6. Round your answer to one more decimal place than the original data. The answer is 11.3, which matches option d, 39.3, after rounding.

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These values are based on the t-distribution table and represent critical values for the given probabilities and degrees of freedom.

To answer this question, we need to use a t-table. The values we are looking for are the t-values associated with specific probabilities and degrees of freedom.

(a) t0.10, 10 = 1.372 (from the t-table, using 10 degrees of freedom and the probability of 0.10)

(b) t0.05, 10 = 1.812 (from the t-table, using 10 degrees of freedom and the probability of 0.05)

(c) t0.05, 21 = 1.721 (from the t-table, using 21 degrees of freedom and the probability of 0.05)

(d) t0.05, 60 = 1.671 (from the t-table, using 60 degrees of freedom and the probability of 0.05)

(e) t0.005, 60 = 2.660 (from the t-table, using 60 degrees of freedom and the probability of 0.005)

Note that we round all answers to three decimal places, as specified in the question. The values we have found are the t-values for the specified probabilities and degrees of freedom. These values can be used in calculations involving t-distributions.

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The graph that shows the solution to the system of equations is given by the image presented at the end of the answer.

The system of equations for this problem is defined as follows:

Replacing y = 0.5x on the second equation, the x-coordinate of the solution is given as follows:

x + 2(0.5x) = -8

x + x = -8

2x = -8

x = -4.

The y-coordinate of the solution is given as follows:

y = 0.5(-4)

y = -2.

Hence the graph will show the two lines intersecting at the point (-2,-4).

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Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

To find the probability of (a or b), we can use the formula:

P(a or b) = P(a) + P(b) - P(a and b)

Plugging in the given values:

P(a or b) = 0.21 + 0.35 - 0.12

= 0.44

Therefore, the probability of (a or b) is 0.44.

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A. For z = 0.50 = 66; B. For z = -0.25 = 57 and the probability of randomly selecting a score less than z = -0.25, you can use a standard normal (z-score) table or calculator. For z = -0.25, the probability is approximately 0.4013, meaning there's a 40.13% chance of randomly selecting a score less than z = -0.25.

To find the X value for each z-score, we use the formula:

X = u + (z * a)

where u is the mean, a is the standard deviation, and z is the z-score.

A. For z = 0.50:

X = 60 + (0.50 * 12)
X = 66

Therefore, the X value for z = 0.50 is 66.

B. For z = -0.25:

X = 60 + (-0.25 * 12)
X = 57

Therefore, the X value for z = -0.25 is 57.

To find the probability of randomly selecting a score that is less than z = -0.25, we use a z-table or a calculator that can calculate normal distribution probabilities. The probability of a score being less than z = -0.25 is the same as the area under the curve to the left of z = -0.25.

Using a z-table, we find that the probability of a score being less than z = -0.25 is 0.4013.

Therefore, the probability of randomly selecting a score that is less than z = -0.25 is 0.4013 or approximately 40.13%.

A. For z = 0.50:
To find the X value, use the formula X = μ + (z * σ), where μ is the mean and σ is the standard deviation.
X = 60 + (0.50 * 12) = 60 + 6 = 66

B. For z = -0.25:
X = 60 + (-0.25 * 12) = 60 - 3 = 57

To find the probability of randomly selecting a score less than z = -0.25, you can use a standard normal (z-score) table or calculator. For z = -0.25, the probability is approximately 0.4013, meaning there's a 40.13% chance of randomly selecting a score less than z = -0.25.

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approximately $29.54 The average income (in dollars) over this 4-hour period. To find the average income over the 4-hour period, we need to integrate the income function I(t) = 20e^(0.5t) with respect to time (t) over the interval [0, 4] and then divide by the length of the interval (4 hours).

The average income A(t) can be calculated using the formula:

A(t) = (1/4) ∫(20e^(0.5t) dt) from 0 to 4

First, let's find the integral of 20e^(0.5t) with respect to t:

∫(20e^(0.5t) dt) = 40e^(0.5t)

Now, let's apply the definite integral from 0 to 4:

[40e^(0.5(4)) - 40e^(0.5(0))] = 40e^2 - 40

Next, divide by 4 to find the average income:

A(t) = (1/4)(40e^2 - 40) ≈ 29.54 (rounded to the nearest cent)

The average income (in dollars) over this 4-hour period is approximately $29.54.

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The requried, 120 divided by 1800 is equal to 0.06666667 or approximately 0.067 when rounded to three decimal places.

To divide 120 by 1800, we can perform the following calculation:

120 ÷ 1800 = 0.06666667

Therefore, 120 divided by 1800 is equal to 0.06666667 or approximately 0.067 when rounded to three decimal places.

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Answer:

Step-by-step explanation:

To calculate the slope between two points A (-3, 6) and B (-2, 9), we can use the formula:

slope = (change in y) / (change in x)

where "change in y" is the difference between the y-coordinates of the two points, and "change in x" is the difference between the x-coordinates of the two points.

So, let's plug in the values of the two points into the formula:

slope = (9 - 6) / (-2 - (-3))

slope = 3 / 1

slope = 3

Therefore, the slope between points A (-3, 6) and B (-2, 9) is 3.

[tex]A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{6})\qquad B(\stackrel{x_2}{-2}~,~\stackrel{y_2}{9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{9}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{-2}-\underset{x_1}{(-3)}}} \implies \cfrac{3}{-2 +3} \implies \cfrac{ 3 }{ 1 } \implies \text{\LARGE 3}[/tex]

An example of a triangle with the same area as the shaded rectangle has been attached in the folder below.

Looking at the shaded diagram, we can tell that the rectangle has a length of 4cm and a width of 2 cm. The area of a rectangle can be calculated by the formula A = L x W, This amounts to 8 cm.

The area of a triangle can be calculated by multiplying the base by the height and then dividing by two. The formula is: A = 1/2 x base x height.

However, since we know the area of the rectangle is 8cm, we can decide that the height is 4cm and base 4 cm. it becomes 4 x 4 x 1/2 = 8

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The missing side of triangle is 11.66 cm, under the condition that the given triangle is a right angled triangle and the other sides of the triangle are 10cm, 6cm respectively.

In order to evaluate the other side of the triangle, we have to rely on the principles of Pythagorean Theorem which states that in a right triangle, the sum of the square sides are equal to the square of the hypotenuse side.

Then, let us consider that x be the length of the missing side then

x² = 10² + 6²

x² = 100 + 36

x² = 136

x = √(136)

x ≈ 11.66 cm

Then, the missing side of this triangle is approximately 11.66 cm.

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The complete question is

Find the missing siside of the following right triangle in the figure





The slope for the fitted line for the Male group is 9 + 4*X1, where X1 is the value of the continuous variable for the Male group. The coefficient of Male*X1 in the equation indicates the change in slope for the Male group compared to the slope for the non-Male group.

To find the slope of the fitted line for the Male group, you need to consider the given equation:

Yhat = 100 + 9X1 + 9Male + 4Male*X1

Since Male is a 0/1 variable, we assign a value of 1 for the Male group:

Yhat = 100 + 9X1 + 9(1) + 4(1)*X1

Now, simplify the equation:

Yhat = 100 + 9X1 + 9 + 4X1

Combine the terms with the continuous variable X1:

Yhat = 100 + 9X1 + 4X1 + 9

Yhat = 100 + 13X1 + 9

The slope of the fitted line for the Male group is the coefficient of the continuous variable X1, which is 13.

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The probability that a value selected at random from this distribution is greater than 31 is essentially 1.

Since the mean of the normal distribution is 31 and the standard deviation is 3, we know that the distribution is centered around 31 and the values are spread out within a range of approximately 3 units on either side of the mean. To find the probability that a value selected at random from this distribution is greater than 31, we need to look at the area under the curve to the right of 31.

Using a z-score table or a calculator, we can find that the z-score for 31 in this distribution is 0. This means that 31 is exactly at the mean of the distribution. To find the area under the curve to the right of 31, we need to find the area between 31 and positive infinity in terms of standard deviations from the mean.

Since the standard deviation is 3, we can find the distance between 31 and positive infinity in terms of standard deviations by dividing by 3:

(infinity - 31) / 3 = infinity/3 - 31/3 = infinity - 10.33

This tells us that the area under the curve to the right of 31 is the same as the area to the right of 10.33 standard deviations above the mean. However, since the normal distribution is continuous and extends infinitely in both directions, the area to the right of any finite value is essentially 1 (i.e. the probability of selecting a value greater than any specific value is essentially 100%).

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X is the variable that we have assigned the agriculture column of swiss to. Running this code would give us the interquartile range of x.

a. To calculate the sample median of x, we can use the median function in R. So, the code would be:
median(x)
where x is the variable that we have assigned the agriculture column of swiss to. Running this code would give us the sample median of x.
b. To find the .34 quantile of x, we can use the quantile function in R. The code would be:
quantile(x, 0.34)
where x is the variable that we have assigned the agriculture column of swiss to, and 0.34 represents the desired quantile. Running this code would give us the value of the .34 quantile of x.
c. To calculate the interquartile range of x, we can use the IQR function in R. The code would be:
IQR(x)
where x is the variable that we have assigned the agriculture column of swiss to. Running this code would give us the interquartile range of x.

The "fertility", "Switzerland", and "x <- swiss $ agriculture" terms.
a. To calculate the sample median of x (the agriculture column in the Swiss dataset), use the following R command:
median_x <- median(swiss$agriculture)
b. To find the 34th percentile (0.34 quantile) of x using the R quantile function, use the following R command:
quantile_x <- quantile(swiss$agriculture, probs = 0.34)

c. To calculate the interquartile range of x (the agriculture column in the Swiss dataset) using R, use the following R commands:
Q1 <- quantile(swiss$agriculture, probs = 0.25)
Q3 <- quantile(swiss$agriculture, probs = 0.75)
IQR_x <- Q3 - Q1
This will give you the interquartile range (IQR) of the agriculture column in the Swiss dataset.

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Answer:

392.69908169872 feet3

Step-by-step explanation:

1/3πr^2h

1/3π*5^2*15

125π

392.69908169872 feet3

The cm units cancel out, leaving: Longest real-life distance = 14 * 15000 km = 210 km So, the longest real-life distance is approximately 210,000km.

To solve this problem, we need to use the concept of scale factor. The scale factor is the ratio of the corresponding lengths in the map and the real world. In this case, we know that the shortest side of the triangle in the map has a length of 7.0 cm, and its corresponding real-life distance is 105 km. Therefore, the scale factor is:

105 km / 7.0 cm = 15,000

This means that every cm in the map represents 15,000 km in real life. Now we can use this scale factor to find the lengths of the other sides of the triangle in real life:

Longest side = 14 cm x 15,000 km/cm = 210,000 km

Therefore, the longest real-life distance is 210,000 km (rounded to the nearest unit).

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The probability of the ball not landing on green and landing on an even, black slot is:
36/38 * 18/38 = 9/19

To find the probability that the metal ball does not land on green, we first need to determine the total number of non-green slots.

There are 38 slots in total, with 0 and 00 being green. This means there are 36 slots that are not green (18 red odd-numbered and 18 black even-numbered slots).

Now, we can calculate the probability of the metal ball not landing on the green by dividing the number of non-green slots (36) by the total number of slots (38).

Probability = (Number of non-green slots) / (Total number of slots)
Probability = 36/38

Now, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

Probability = (36/2) / (38/2)
Probability = 18/19
However, we need to take into account that the odd-numbered slots are red and the even-numbered slots are black. Since the question asks for the probability that the ball does not land on the green, we can focus on the even-numbered slots that are black. There are 18 even-numbered slots on the wheel, which means that the probability of the ball landing on an even, black slot is 18/38.

So, the probability that the metal ball does not land on the green is 18/19.

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