an actuary has discovered that policyholders are five times as likely to file two clams as to file four claims. if the number of claims filed has a poisson distribution, what is the variance of the number of claims filed?

If the probability an American will die from falling is 0.41%, the probability a American will not die from falling is 100% - 0.41% = 99.59%.

Answer: 99.59%.

Answer:

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Step-by-step explanation:

The equation m = 12 + 2Y1 gives the slope of the line through the points P1=(-1.5, Y1) and P2=(-2, -6)

To find a point's coordinates in a coordinate system, you perform the opposite. Starting at the point, move vertically up or down until you reach the x-axis. Your x-coordinate is shown there. Afterwards, you'll be able to get a better understanding of how to use it.

It is assumed that the formula you supplied would be used to determine the slope (m) of the line connecting the two specified points, P1 and P2.

We may use the following formula to find the slope (m) of the line passing through the coordinates P1=(X1, Y1) and P2=(X2, Y2):m = (Y2 - Y1) / (X2 - X1) (X2 - X1)

Using the values provided:

P1 = (-1.5, Y1) (-1.5, Y1)

P2 = (-2, -6) (-2, -6)

These values can be used as substitutes in the formula:

m = (-6 - Y1) / (-2 - (-1.5))

Making the denominator simpler:

m = (-6 - Y1) / (-2 + 1.5)

m = (-6 - Y1) / (-0.5)

m = 12 + 2Y1

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Question:

Formula: m=;

X₂-X1

P₁ = (X₁, Y₁) P₂ = (X2, Y₂)

1) P₁=(-1.5) and P₂=(-2,-6)

How to solve this exercise of linear equations of two points.

Cindy will take 0.25 hours or 15 minutes to travel a distance of 2 miles at a constant speed of 8 miles per hour.

The formula for time is: time = distance / speed where "distance" is the distance traveled by an object, and "speed" is the rate at which the object is moving.This formula can be used to calculate the time taken by an object to travel a certain distance at a constant speed, or to calculate the speed or distance if the other two variables are known.

The formula for speed is: speed = distance / time where "distance" is the distance traveled by an object and "time" is the duration of travel.This formula can be used to calculate the speed of an object if the distance it has traveled and the time it took to travel that distance are known. It can also be used to calculate the distance traveled by an object if its speed and the time it traveled at that speed are known.

In the given question,

We can use the formula:

time = distance / speed

where "distance" is the distance traveled and "speed" is the speed at which Cindy is riding her bike.

Substituting the given values, we get:

time = 2 miles / 8 miles per hour

Simplifying, we get:time = 0.25 hours.

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Answer: 1000 x 1.05^n

Step-by-step explanation:

1.05 is the increase experienced each year and n is the number of years.

Answer:

The population of bees is increasing by 5% each year since 2010. Let P(n) be the population of bees in the nth year since 2010.

The explicit formula for the bee population can be found using the formula for compound interest:

P(n) = P(0) * (1 + r)^n

where P(0) is the initial population in 2010, r is the annual growth rate, and n is the number of years since 2010.

Substituting the given values, we have:

P(n) = 1000 * (1 + 0.05)^n

Simplifying the expression, we get:

P(n) = 1000 * 1.05^n

Therefore, the explicit formula that models the bee population for n years since 2010 is P(n) = 1000 * 1.05^n.

The variables that the organizer can consider removing from the regression model are the Number of male visitors and Number of performance.

Based on the regression table provided, we can answer this question. The following is the regression table:Regression output table for night street fair variableNameCoefficientStandard Errort-StatP-ValueConstantb0.340.1402.430.023Number of male visitorsb10.6130.51320.750.462Number of female visitorsb10.9070.57918.830.000Number of retail standsb0.1160.0452.570.016Number of food (and beverage) standsb0.3160.0575.500.000Number of performanceb0.1460.1071.360.184The null hypothesis is rejected if p-value < 0.1; that is, there is a significant difference between the independent and dependent variables. The p-value of the Number of male visitors, the Number of female visitors, the Number of retail stands, the Number of food (and beverage) stands, and the Number of performances variables are 0.462, 0.000, 0.016, 0.000, and 0.184, respectively. As a result, the variables that are significant at the 10% level are the Number of female visitors, the Number of retail stands, and the Number of food (and beverage) stands. Therefore, the organizer should consider removing the Number of male visitors and Number of performance variables from the regression model. The variables that the organizer can consider removing from the regression model are the Number of male visitors and Number of performance.

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Therefore, the total amount of money utilized on fuel in June 2022 is R11 095,60.

Percent is a way of expressing a quantity as a fraction of 100. It is denoted by the symbol %, which means "per hundred". Percentages are often used to represent proportions or ratios in various fields, including finance, science, and statistics. For example, an interest rate of 5% means that for every hundred dollars borrowed or invested, five dollars of interest will be charged or earned.

Here,

(a) To calculate the total distance covered by the water tanker in March 2022, we need to find the distance travelled per day and multiply it by the number of days in March.

Distance travelled per day = 2 × 18 = 36 km (since it's a return trip)

Number of weekdays in March = 31 - 4 (Saturdays) = 27

Total distance covered = distance per day × number of weekdays

= 36 km/day × 27 days

= 972 km

(b) To determine the quantity of fuel utilized by the water tanker in March 2022, we need to divide the total distance covered by the average fuel consumption rate.

Fuel consumption rate = 5 km/ℓ

Total distance covered = 972 km

Fuel utilized = total distance covered / fuel consumption rate

= 972 km / 5 km/ℓ

= 194.4 ℓ

(c) To determine the total amount of money utilized on fuel for the water tanker in March 2022, we need to multiply the fuel quantity by the fuel price.

Fuel price in March 2022 = R16,28/ℓ

Fuel utilized = 194.4 ℓ

Total cost of fuel = fuel price × fuel quantity

= R16,28/ℓ × 194.4 ℓ

= R3 163,39

Therefore, the total amount of money utilized on fuel for the water tanker in March 2022 is R3 163,39.

(d) To determine the total amount of money utilized on fuel in June 2022, we need to repeat the above calculation using the June fuel price.

Fuel price in June 2022 = R24,14/ℓ

Fuel capacity = 460 ℓ

Total cost of fuel = fuel price × fuel capacity

= R24,14/ℓ × 460 ℓ

= R11 095,60

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Complete question:

Records of the number of water tankers that were supplied to the construction site appear in the calender on ANNEXURE A. The water source is at a distance of about 18 km (return trip) from the construction site. The water tanker has a fuel capacity of 460 litres.. The rate of fuel consumption of the Mercedes water tanker averages 5 km/ℓ. The prices of fuel per litre in March and June 2022 appear below. JUNE 2022 FUEL PRICES \begin{tabular}{|l|l|} \hline DIESEL & COST \\ \hline 50ppm & R24,14 \\ \hline \end{tabular} Source: 4.1 (a) Calculate the total distance that the water tanker has covered in March (2) 2022. (b) Hence, determine the quantity of fuel that was utilized by the water tanker in March 2022. (c) Determine the total amount of money that was utilized on fuel for the water tanker in March 2022. (2) 4.2 Determine the total amount of money that was utilized on fuel in June 2022.

The power of the test to detect an average increase in height of 1 inch could be increased by d. giving the drug to 25 randomly selected students instead of 50.

The power of a test is the probability of correctly rejecting the null hypothesis when it is false. In this case, the null hypothesis is that the drug does not cause people to grow taller, and the alternative hypothesis is that the drug causes an average increase in height of 1 inch.

To increase the power of the test, we want to increase the probability of correctly rejecting the null hypothesis when it is false. One way to do this is to increase the sample size, which will reduce the standard error of the mean and increase the t-statistic, making it more likely to reject the null hypothesis.

However, in this case, we can increase the power of the test by giving the drug to a smaller sample size of 25 instead of 50. This is because the effect size of the drug is not known, and giving the drug to a larger sample size will increase the variance of the data, making it harder to detect a significant difference. By reducing the sample size, we can increase the power of the test while still maintaining a reasonable sample size.

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Answer:

x = 3

Step-by-step explanation:

Solving systems of linear equations via substitution:

[tex]2x-6y=-6[/tex]

[tex]y=1.5x-2.5[/tex]

We are already given the value of y, so to find the value of x, we need to plug in the y value in the other equation.

[tex]2x-6(1.5x-2.5)=-6[/tex]

Distribute 6

[tex]2x-9x+15=-6[/tex]

Combine our like terms

[tex]-7x+15=-6[/tex]

Subtract 15 to both sides

[tex]-7x=-21\\[/tex]

Divide by -7

[tex]x=3[/tex]

The true statements regarding the plot of normal distributions A and B are B has the larger mean, and B has the larger standard deviation; options 2 and 3.

A plot of a normal distribution is a bell-shaped curve that represents the probability distribution of a continuous random variable that follows a normal distribution.

The plot shows the frequency of occurrence of values of the variable, with the most common values near the mean and the less common values near the tails of the distribution.

The normal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ). The mean determines the location of the center of the distribution, while the standard deviation determines the spread or width of the distribution.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

( 9, 1/7 )

Step-by-step explanation:

I/9x- y=6/7                  equation    (1)

1/18x-2y=3/14              equation    (2)

9x(1)-18x(2)              multiply equation (1 ) by 9 and (2 ) by 18 and subtract  

                                                                                                      them                                                                                                                

we get y=1/7

then put the value of y=1/7 in ( 1 ) or (2)

1/9x-1/7=6/7 ⇒x=9

therefore  the right answer is ( 9, 1/7 )

Answer:

Ngozi is 45 years old

Step-by-step explanation:

N = 2A

AG = 1/3A

A + AG = 30

Subsitute AG with 1/3A.

A + 1/3A = 30

1 1/3 A = 30

A = 22.5

AG = 7.5

Ngozi = 45

Answer:

w = 28 miles

Step-by-step explanation:

The perimeter is the sum of the lengths of the sides.

The sum of the lengths of the sides is w + 28 + 28.

The perimeter is 84.

w + 28 + 28 must equal 84.

w + 28 + 28 = 84

Now we solve for w.

Add 28 and 28.

w + 56 = 84

Subtract 56 from both sides.

w = 28

Answer: w = 28 miles

Answer:

-----------------------------------

The y-intercept is the point where the line crosses the y-axis, which occurs when x = 0.

To find the y-intercept, substitute 0 for x in the equation y = 4x + 2:

The y-intercept is 2 and matching choice is C.

Answer:

2

Step-by-step explanation:

We need to find out the y intercept of the given equation which is y = 4x + 2 .

y intercept is a point where the graph of the equation cuts the y axis. So at y intercept x coordinate will be 0 , so plug in x = 0 , in the given equation as ;

y = 4x + 2

y = 4(0) + 2

y = 0 + 2

y = 2

Therefore the y intercept of the line is 2 . ( option C )

Answer:

Step-by-step explanation:

Regular price:$19

60 per cent of $19 is 11.4 dollars.

but if ypu are looking for how much did she pay then it is..

19-11.4=$7.6

The expected probability distribution is $4.35

We must multiply each supplied chance by the respective payout value in order to determine the expected value.

As a result, we have the payout probability distribution shown below:

0.35(1) + 2(0.2) + 5(0.1) + 8(0.2) + 10(0.15) (0.15)

= 0.35 + 0.4 + 0.5 + 1.6 + 1.5

= $4.35

When the set of possible outcomes is discrete in nature, the distribution is referred to as a discrete probability distribution. When a dice is rolled, all conceivable results, for instance, are discrete and result in a large number of outcomes. A different name for it is the probability mass function.

statistical distributions that can be used

Uniform discrete distribution The chances of each outcome are equal.

Single-trial distribution with two potential results.

A series of Bernoulli events are called the binomial distribution.

Poisson Distribution: The likelihood that a particular occurrence may or may not occur.

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The standard deviation of the sampling distribution of pCheck to see if the 10% condition is 0.44.

If a large candy machine has 45% orange candies, and an SRS of 25 candies is taken from it, then the 10% condition can be checked to see if it is met. To do this, it is necessary to calculate the sample proportion p. To calculate p, the number of orange candies in the sample (let's call it x) is divided by the total number of candies in the sample (25). Thus, p = x/25. The 10% condition is met if the value of p is less than or equal to 0.1 (10%).

Since the value of p is unknown, the number of orange candies in the sample must first be determined. To find this number, the proportion of orange candies in the entire candy machine must be used. The proportion of orange candies is 45%, or 0.45.

This means that for every 100 candies in the candy machine, 45 are orange. Since there are 25 candies in the sample, 0.45*25 = 11.25 orange candies are expected in the sample. Since this is a sample proportion, the exact value of x must be rounded to the nearest whole number. This gives a value of 11 orange candies in the sample.

Now that the value of x is known, the value of p can be calculated. This gives p = 11/25 = 0.44.

Since 0.44 is greater than 0.1 (10%), the 10% condition is not met in this case.

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0, which is less than 0.01.

Suppose that X is a uniformly distributed random variable, scaled so that it has zero mean and unit variance. (1) What is P{|X|> ox}? (2) What is P{[X] > 30x}? (3) Is X spiky? Be sure to consider both positive and negative values of X.

For a uniformly distributed random variable with mean 0 and variance 1, P{|X|> ox} is equal to 0.5. (2) For a uniformly distributed random variable with mean 0 and variance 1, P{[X] > 30x} is equal to 0. (3) X is not spiky since P{|X| > 30x}

0.000045, which is greater than 0.01.
Suppose that Y is a Laplacian random variable with a pdf given by: fy(u) 2 e 2 -Au-hel, -  Oy}? (2) What is P{İY| > 30y}? (3) Is Y spiky? Be sure to consider both positive and negative values of Y.
Answer: (1) For a Laplacian random variable with mean 0 and variance 1, P{|Y|> oy} is equal to 0.5. (2) For a Laplacian random variable with mean 0 and variance 1, P{[Y] > 30y} is equal to 0.000045. (3) Y is spiky since P{|Y| > 30y}

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Assuming each spider has 8 legs, it would take 877,256 legs to make 109,657 spiders

Answer:

If a polygon is dilated by a scale factor of k, then its area is multiplied by k².

a. When k = 4, the area of the image is 10 × 4² = 160 square units.

b. When k = 1.5, the area of the image is 10 × 1.5² = 22.5 square units.

c. When k = 1, the area of the image is 10 × 1² = 10 square units. (The image is the same size as the original.)

d. When k = 1/3, the area of the image is 10 × (1/3)² = 10/9 square units.

Step-by-step explanation:

the total time Joe spends traveling on the train is 16 hours 40 minutes. Therefore, the correct answer is option E.

The time Joe spends traveling on the train can be found using the formula:

time = distance / speed

For the trip to Georgetown, the distance is 350 miles and the speed is 42 miles per hour, so the time spent traveling there is:

time to Georgetown = 350 / 42 = 8.33 hours

For the return trip, Joe travels the same distance of 350 miles at the same speed of 42 miles per hour. Therefore, the time spent traveling back is also 8.33 hours.

The total time Joe spends traveling on the train is the sum of the time for the trip to Georgetown and the time for the return trip:

total time = time to Georgetown + time from Georgetown

total time = 8.33 + 8.33

total time = 16.66 hours

Rounding to the nearest 10 minutes, the total time Joe spends traveling on the train is 16 hours 40 minutes. Therefore, the correct answer is option E.

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16 four digit positive integers x are there with the property that x and 3x have only even digits.

There are 16 such four-digit positive integers x.

At first we have to find the four-digit positive integers x with the property that both x and 3x have only even digits, we need to consider the possible digits that x can have.

Since both x and 3x must have only even digits, the digits of x can only be 0, 2, 4, 6, or 8.

Let, the possible cases for the first digit of x:

If the first digit of x is 0:

In this case, x would be a three-digit number (e.g., 012, 024, 036, etc.). Now, if we multiply any three-digit number by 3, the resulting number will always have at least one odd digit.

we get, this case does not satisfy the condition.

If the first digit of x is 2 or 8:

In this case, the last digit of 3x will be 6 or 4, respectively. But since 6 is not an even digit and 4 is not a valid digit for x, this case is not possible either.

If the first digit of x is 4 or 6:

In this case, the last digit of 3x will be 2 or 8, respectively.

These are valid digits for x.

Now, we need to make sure that the second digit of x and 3x are also even.

The only even digits that can be used as the second digit are 0 and 8 (because 2 and 6 are already used as the first digit).

So, there are two possible cases for the first digit of x: 4 or 6.

Now, we have two choices for the second digit of x (0 or 8).

For each of these combinations, we have two choices for the third digit of x (0 or 8).

Finally, we have two choices for the fourth digit of x (0 or 8).

So, we get the total number of four-digit positive integers x with the property that both x and 3x have only even digits is:

Number of choices = 2 (choices for the first digit) * 2 (choices for the second digit) * 2 (choices for the third digit) * 2 (choices for the fourth digit) = 2⁴ = 16.

Therefore, there are 16 such four-digit positive integers x.

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Answer:

The second figure.

Step-by-step explanation:

The first figure's perimeter is:

70 in + 42 in + 56 in = 168 inches.

And the second figure's perimeter is:

42 in + 33 in + 33 in + 64 in = 172 inches.

Therefore, Figure 1 < Figure 2.

The height that the T-short lands on the bleachers is x = 0.65.

The quadratic equation may be solved by adding and subtracting the same number within the parenthesis to get a perfect square trinomial, which is how the quadratic formula is obtained. A version of the equation that can be solved using the square root function is the result of this method.

Given that it can be used to solve any quadratic equation regardless of the values of the variables a, b, and c, the quadratic formula is an effective tool for solving quadratic equations.

The equation of the path of T-shirt is y = -18x² + 4x and that of the height of bleachers is 3y=2x−14 or y = 2/3x - 14/3

To find the height of the T-shirt landing we find the intersection of the two equations as follows:

-18x² + 4x = (2x - 14)/3

-54x² + 12x = 2x - 14

54x² - 10x - 14 = 0

27x² - 5x - 7 = 0

Using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Substitute the values;

x = (-(-5) ± √((-5)² - 4(27)(-7))) / 2(27)

x = (5 ± √(925)) / 54

x = (5 ± 5√37) / 54

x = (5 + 5√37) / 54 = 0.65 and

x = (5 - 5√37) / 54 = -0.47

Hence, the height that the T-short lands on the bleachers is x = 0.65.

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[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =42\\ r=2.8 \end{cases}\implies s=\cfrac{(42)\pi (2.8)}{180}\implies s=\cfrac{49\pi }{75}\implies s\approx 2.05 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{Perimeter of the sector} }{2.8~~ + ~~2.8~~ + ~~2.05} ~~ \approx ~~ \text{\LARGE 7.65}[/tex]

let's recall that the sector's perimeter includes the arc plust the radii.

No, the statements are not equivalent as the statement "a > b" simply means that "a" is greater than "b" and there exists a number "c" such that when added to "b", it equals "a". This does not necessarily mean that "a" is greater than "b".

The statements "a>b" and "there is the number c, so that a=b+c" are not equivalent. The statement "a>b" simply means that "a" is greater than "b," while the statement "there is the number c, so that a=b+c" means that "a" can be expressed as the sum of "b" and another number "c."

These statements are not equivalent because even if "a" is greater than "b," it may not be possible to express "a" as the sum of "b" and another number "c."

Additionally, even if "a" can be expressed as the sum of "b" and another number "c," it may not necessarily be true that "a" is greater than "b."

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The required pair of corresponding angles in the given situation is (A) ∠HIK and ∠EFI.

In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and resemblance.

In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.

Angles that are equal in size and are found on the same side as the transversal line are called corresponding angles.

Either both are acute or both are obtuse.

By creating an F shape, we can typically identify comparable angles.

So, now after reading the description we know exactly what are corresponding angles.

Now, we can easily tell that the pair of corresponding is:

∠HIK and ∠EFI

Therefore, the required pair of corresponding angles in the given situation is (A) ∠HIK and ∠EFI.

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When the area is constant, the proportionality constant, 48, reflects the sum of the base and height.

When two quantities grow and shrink at the same rate, they are directly proportional. The proportionality constant k is defined as k=y/x when y and x are two numbers that are directly proportional to one another.

Using the formula for the area of a rectangle, we can determine the missing data in the table:

Area = base x height

The missing values can be located as follows using the values listed in the table:

Base (b) Height (h) Area

24 2 48

3 8 24

8 3 24

4 6 24

We can apply the inverse variation formula to find the constant of proportionality:

y = k/x

This equation can be changed in order to account for k:

k = xy

Using any pair of values from the table, we can find k as follows:

k = xy = 24(2) = 48

Hence, 48 is the proportionality constant. It is possible to verify that this value applies to all of the value pairs in the table:

For the first pair (b=24, h=2), we have xy = 24 x 2 = 48, which is the constant of proportionality.

For the second pair (b=3, h=8), we have xy = 3 x 8 = 24, which is the area.

For the third pair (b=8, h=3), we have xy = 8 x 3 = 24, which is the area.

For the fourth pair (b=4, h=6), we have xy = 4 x 6 = 24, which is the area.

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Question:

The following table shows some values ​​for the base and height of a rectangle whose area is constant. Write down the missing data.

Base (b)

Height (h)

24

2

3

8

4

4

What is the area of ​​the rectangle?

What kind of variation do you see in this table?

What is the constant of proportionality?

How did you determine the constant of proportionality?

A particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. Twenty fish are placed in a tank containing this concentration of chemical in water. Therefore

a) Probability that exactly 14 fish survive, Let x be the number of fish that survive. Using Binomial distribution, we have:[tex]P(X = x) = C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n is the total number of fish, p is the probability of survival and C(n,x) is the binomial coefficient. We have n = 20, p = 0.8 (since 20% die) and x = 14. [tex]C(20,14) * (0.8)^14 * (0.2)^6 = 38760 * 0.000016777216 * 0.0264241152 = 0.263[/tex] Therefore, the probability that exactly 14 fish survive is 0.263

b) Probability that at least 10 fish survive To find this probability, we can find the probability that 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 fish die, and subtract this probability from 1. Using the same formula as in (a), we have: [tex]P(X <= 9) = \sum  C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n = 20, p = 0.8 and x varies from 0 to 9. Using a calculator or software, we find:P(X <= 9) = 0.0169Therefore,P(X >= 10) = 1 - P(X <= 9) = 1 - 0.0169 = 0.983 Therefore, the probability that at least 10 fish survive is 0.983.

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