Can some one. Give me an explanation and answer please thank you

From the given information provided, the first 5 nonzero terms of the power series are 1.5 + 13.5x + 60.75x² + 183.375x³ + 1018.1595x⁴.

To find the power series for the given indefinite integral, we can first find the antiderivative of the integrand using substitution. Let u = 9x, du = 9dx, then:

∫(e⁹ˣ - 1) / 6x dx = (1/6) ∫([tex]e^u[/tex] - 1) / u du

We can then expand the integrand into a power series using the Maclaurin series for [tex]e^u[/tex] and ln(1+u):

(1/6) ∫([tex]e^u[/tex] - 1) / u du = (1/6) ∫[Σ(uⁿ/n!) - Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1))] du

= (1/6) [Σ(uⁿ/n! × du) + Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1) × du)]

= (1/6) [Σ(uⁿ/n! × 9dx) + Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1) × 9dx)]

= (3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) - (1/6) Σ(-1)ⁿ (9⁽ⁿ⁺⁾ xⁿ / (n+1))

We can now simplify and group terms to obtain the power series centered at x=0:

(3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) - (1/6) Σ(-1)ⁿ (9⁽ⁿ⁺¹⁾ xⁿ / (n+1))

= (3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) + (1/6) Σ((-1)ⁿ × (-9)⁽ⁿ⁺¹⁾ × xⁿ / (n+1))

To find the first 5 nonzero terms, we can plug in n=0 through n=4 and evaluate each term:

n=0: (3/2) × 1 = 1.5

n=1: (3/2) × 9x = 13.5x

n=2: (3/2) × 81x² / 2 - (1/6) × 81x² / 3 = 60.75x²

n=3: (3/2) × 729x³ / 6 + (1/6) × 729x³ / 4 = 183.375x³

n=4: (3/2) * 6561x⁴ / 24 - (1/6) * 6561x⁴ / 5 = 1018.1595x⁴

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The correct conclusion that can be drawn from the plot is that the plant population had a significantly lower mean root length after the major drought occurred.

Explanation:

A frequency polygon is a graphical representation of a frequency distribution using line segments connected to points that indicate the midpoint of each class interval.

The horizontal axis shows the measurement variable, while the vertical axis shows the number of occurrences of the variable for each bin. The midpoint of each bin is used to represent the distribution of data that falls within that bin's range.

Since the values of adjacent bins overlap, the lines are connected. The points are connected by straight lines in a frequency polygon.

In this case, the conclusion that can be drawn from the plot is that the plant population had a significantly lower mean root length after the major drought occurred.

The peak of the frequency polygon has shifted to the left, indicating that the majority of plants have a shorter root length. The decrease in the mean root length of the plant population is due to the impact of the major drought on the island.

As a result, no plant reproduction took place, indicating a decrease in the plant population.

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The probability that at least 5 have eliminated jobs during the last year is  0.002965.

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

n = 9

p = probability of businesses have eliminated jobs = 0.13

X = Number of  businesses have eliminated jobs ~

Binomial( n= 9 , p = 0.13)

[tex]P(X \geq 5)[/tex]

[tex]P(X \geq 5) = 1-P( X < 5)[/tex]

[tex]P(X \geq 5) = 1-P( X \leq 4)[/tex]

Use following Excel command:

=1-BINOM.DIST(x, n, p, cumulative)

=1-BINOM.DIST(4,9,0.13,TRUE)

=0.0029649

=0.002965

Thus

[tex]\mathbf{{P(X \geq 5) =0.002965}}[/tex].

Therefore, probability that at least 5 have eliminated jobs during the last year is  0.002965.

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Complete question';

Job Elimination in the past year, 13% of businesses have eliminated jobs. If 9 businesses are selected at random, find the probability that at least 5 have eliminated jobs during the last year. Round the answer to at least four decimal places P(at least 5 have eliminated jobs during the last year) X

to enclose the circular garden, we need 163.64 meters of fencing. This means that if we were to wrap a measuring tape or any other material around the perimeter of the garden, it would need to be 163.64 meters long to cover the entire circumference of the circle.

To determine the amount of fencing required to enclose a circular garden with a radius of 26 meters, we need to calculate the circumference of the circle. The circumference is the distance around the perimeter of the circle, which can be calculated using the formula:

Circumference = 2 x π x radius

where π is the mathematical constant approximately equal to 3.14, and the radius is the distance from the center of the circle to any point on its perimeter.

So, in this case, the circumference of the circular garden can be calculated as follows:

Circumference = 2 x 3.14 x 26 m

= 163.64 m

Therefore, to enclose the circular garden, we need 163.64 meters of fencing. This means that if we were to wrap a measuring tape or any other material around the perimeter of the garden, it would need to be 163.64 meters long to cover the entire circumference of the circle.

It's worth noting that the formula for calculating the circumference of a circle can be used to find the amount of fencing required for any circular enclosure, such as a circular pond or a circular pool.

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Around noon, when the forecast temperature is about 4 degrees Celsius higher than the measured temperature, the difference is at its greatest.

The strength and direction of the linear connection between two variables are measured by the correlation coefficient. Its value goes from -1 to 1, and it is represented by the symbol "r". A perfect negative correlation, or r = -1, implies that as one variable rises, the other variable falls in an exact predictable manner. There is no linear relationship between the two variables if r = 0, which implies there is no correlation between the two variables. When r = 1, there is a perfect positive correlation, meaning that when one measure rises, the other rises in an exact predictable manner.

given

The maximum temperature for a specific day is shown in the provided image alongside the predicted maximum temperature.

The blue line depicts the expected maximum temperature, while the red line depicts the actual maximum temperature.

We can see that throughout the day, the forecast temperature is typically greater than the actual temperature.

Around noon, when the forecast temperature is about 4 degrees Celsius higher than the measured temperature, the difference is at its greatest.

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The probability of class failure is 7%. If 56 students take a class, the expected number of students who will fail the class is 4.

We will use the above formula to find the expected value of class failure. Let x be the number of students expected to fail the class.

Expected value = Probability x Total number of trials

The probability of class failure is 7%, so the probability of passing the class is 100% - 7% = 93%. The total number of trials is the total number of students taking the class, which is 56. Putting these values into the formula gives us:

Expected value = 7% x 56
Expected value = 0.07 x 56
Expected value = 3.92

We cannot have a fraction of a student, so we can round this number up to get the expected number of students who will fail the class.

Therefore, the expected number of students who will fail the class is 4.

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As a result, the following equation can be used to determine t, or how many minutes it took to fill the tub with w liters of water: t = (w - 0.2) / 0.4

Slope is a unit used to describe how steep or slope a line is. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on the line is what is referred to as the slope. In other words, the slope of the line going through the two points (x1, y1) and (x2, y2), which are on a line, is given by: Slope is equal to y2 - y1 / x2 - x1. Positive, negative, zero, or undefinable slopes are all possible.

given

With the slope and y-intercept in hand, we can now write the line's equation:

y = 0.4x + 0.2

Given a value for y, we wish to find a solution to this equation for x. In this instance, we're looking for t, or how many minutes it took to fill the tub with w liters of water. We can solve for x by substituting w for y:

w = 0.4t + 0.2

0.4t = w - 0.2

t = (w - 0.2) / 0.4

As a result, the following equation can be used to determine t, or how many minutes it took to fill the tub with w liters of water: t = (w - 0.2) / 0.4.

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In this instance, the buoy forms the right corner of a triangle made up of the two ships and the buoy. To the closest tenth, the distance between the two ships is roughly  [tex]24.1[/tex] km.

To find the distance between the two ships, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs

(the sides that form the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).

In this case, the two ships and the buoy form a right triangle, with the buoy at the right angle.

Let d be the distance between the two ships, x be the distance of the northern ship to the buoy and y be the distance of the eastern ship to the buoy. Then we have:

[tex]d^2 = x^2 + y^2[/tex]

Substituting the given values, we get:

[tex]d^2 = (20 km)^2 + (13.5 km)^2[/tex]

[tex]d^2 = 400 km^2 + 182.25 km^2[/tex]

[tex]d^2 = 582.25 km^2[/tex]

[tex]d ≈ 24.1 km[/tex]

Therefore, the distance between the two ships is approximately 24.1 km, rounded to the nearest tenth.

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The surface area of the cylinder with radius 5 inches and rectangle with height 4 inches is equal to 282.6 square inches.

Radius of the base = 5 inches

Height of the rectangle = 4 inches

Surface area of a cylinder

= area of the top and bottom circular faces + the area of the curved surface.

Here,

Rectangle represents the curved surface of the cylinder, with a height of 4 inches and a length equal to the circumference of the base.

Circumference of the base is equal to,

Circumference

= 2πr

= 2 x 3.14 x 5

= 31.4 inches (approx.)

Area of the curved surface of the cylinder is ,

Curved surface area

= Length x Height

= 31.4 inches x 4 inches

= 125.6 square inches

Area of each circular face of the cylinder is ,

Circular face area

= πr²

= 3.14 x 5²

= 78.5 square inches

Substitute the value to get total surface area of the cylinder we have,

Total surface area of the cylinder

= 2 x Circular face area + Curved surface area

= 2 x 78.5 square inches + 125.6 square inches

= 282.6 square inches (approx.)

Therefore, the surface area of the cylinder is approximately equal to 282.6 square inches.

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Answer:

x-14=52|+14

x=52+14

x=66 candies

Step-by-step explanation: If Anna gives 14 candies to her sister, she remains with 52. How many candies does Anna have ?

Welch's t-test is a modified version of the t-test for independent means. Welch's t-test is an important statistical test that compares the mean of two groups that have different variances and is utilized when the assumptions of the t-test for independent means are violated.

However, unlike the standard t-test for independent means, Welch's t-test does not rely on the assumption that the variances of the two groups are equal. Instead, Welch's t-test relies on a more flexible assumption, that is, the assumption of unequal variances.

Welch's t-test's basic assumptions include the following:Independent samples: The sample sizes should be equal or almost equal in size. Normality: The two groups must have normally distributed populations. Even though Welch's t-test is more flexible than the standard t-test for independent means, the test is most accurate when the distributional assumptions are met.

It should be remembered that it is more conservative when the distributional assumptions are violated.

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Harold therefore walks an average distance of 10 metres when moving from one location to another.

All the points in a plane that are equally spaced from a fixed point known as the centre make up a circle, which is a geometric form. The radius of a circle is the separation between any two points on the circle and its centre. A circle's diameter is defined as a line segment whose endpoints are on the circle and which goes through the centre of the circle. Circles are helpful in many areas of mathematics and science due to a number of significant characteristics.

given

A circle with a dimension of 100 metres has a circumference of d, where d is the diameter. As a result, this circle's diameter is:

C = d = (100) = 100 m

Harold will walk from one spot to the next after completing 1/6

of the circle's circumference because the circle's circumference has six points that are all equally spaced apart. As a result, Harold travels the following distance between each location:

Distance equals 1/6 * C * 1/6 * 100 * (50/3) metres.

b) The average of the distances between each location, which we just discovered to be (50/3) metres, represents the average distance that Harold covers when moving from one place to another. The circle has six evenly distributed points, so the average distance travelled by Harold is:

(Total distance travelled) / Mean distance (Number of segments)

Total distance travelled equals the distance between two adjacent locations on the circle, which is C/2, or (1/2) 100 metres, or 50 metres.

Segment count equals number of marks - 1 (i.e., 6 - 1 = 5).

The average distance Harold travels while strolling is as follows:

Typical distance is calculated as (Total distance travelled) / (Number of segments), which equals (50) / 5 = 10 metres.

Harold therefore walks an average distance of 10 metres when moving from one location to another.

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⇒To be able to answer this question to find how many hours Brooke played his flute for 5 days we ought to first convert the 5 days to hours.

⇒There are 24 hours in a day this means that in 5 days we have =24×5

=120 hours.

⇒We have 120 hours in 5 days , it is said that Brooke played her flute [tex]\frac{3}{4}[/tex],

Meaning she played the flute [tex]\frac{3}{4}[/tex] hours of 120 hours which is equal

[tex]\frac{3}{4} *\frac{120}{1}\\=90[/tex]

For 5 days Brooke played her flute 90 hours

⇒The next step is to convert the 2 days to hours which is equivalent to 24×2

=48 hours are in 2 days, it is said Brooke played the flute [tex]\frac{1}{2}[/tex] hours of 2 days. This simply is equivalent to

[tex]\frac{1}{2} *\frac{48}{1} \\=24[/tex]

⇒For 2 days Brooke played the flute 24 hours,

The total number of hours she played it all is =Number of hours she played it in 5 days+ Number of hours she played it in 2 days.

=90+24

=114

⇒In total of these 7 days she played the flute for 114 hours

Explanation:

A strain of Mycobacterium tuberculosis that is deficient in nonhomologous end joining repair should be more sensitive to damage by X-rays.

Nonhomologous end joining is a DNA repair mechanism that can join two DNA fragments with little or no homology between them. X-rays, which are high-energy electromagnetic waves, can cause damage to DNA by breaking the strands of the double helix.

This damage can be repaired by mechanisms like nonhomologous end joining, so a strain of Mycobacterium tuberculosis that is deficient in this repair mechanism would be more sensitive to damage by X-rays.

UV radiation, glycosylase, and depurination are not directly related to nonhomologous end joining repair and would not have the same effect.

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The approximate price per square inch of the cookie cake is $0.50

The area of a circle is given through the formulation:

A = πr^2

In which r is the radius of the circle.

for the reason that diameter of the cookie cake is 6 inches, the radius is half of of that, or three inches.

Substituting this into the formulation, we've:

A = π(3^2) = 28.26 square inches (approximate)

The value per square inch is the overall value of the cookie cake divided with the aid of its area:

value per square inch = $14.13 / 28.26 sq.in = $0.50 (approximate)

Therefore, the approximate price per square inch of the cookie cake is $0.50

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1. 53

2. can you  explain more it would really help more

The values of sides x and y of the triangle are 6.75 and 11.25 units respectively.

The square of the hypotenuse side of the right-angled triangle equals the sum of the squares of the other two sides, according to Pythagoras' Theorem. The three sides of this triangle are referred to as the perpendicular, base, and hypotenuse.

by using the Pythagorean theorem:

Equation1:  y ² =x ² + 9²

Equation2:  (12 + x) ² =1 5 ² + y ²

Putting values of equation1  in 2 we get

(12 + x) ² =1 5 ² +x ² + 9²

144 + x²+ 2×12x = 225 + x²+ 81

x=6.75

Putting value of x in equation1

y ² =6.75 ² + 9²

y=11.25

Hence, the values of x and y are

x = 6.75 unit

y =11.25 unit

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Answer:

The slope of the line passing through the points (-6,-5) and (-1,1) can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-6,-5) and (x2, y2) = (-1,1)

slope = (1 - (-5)) / (-1 - (-6)) = 6/5

Now, using point-slope form of the equation of a line, we get:

y - y1 = m(x - x1)

where m = 6/5 and (x1, y1) = (-6,-5)

y + 5 = 6/5(x + 6)

y + 5 = 6/5x + 6.72

y = 6/5x + 6.72 - 5

y = 6/5x + 1.72

Therefore, the equation of the line passing through the points (-6,-5) and (-1,1) is:

y = 6/5x + 1.72

Option (c) y=6/5x is not the correct equation of the line. The correct answer is (d) y=6/5x + 11/6.

The probability of selecting a ball that has an even number from a bag containing 13 balls numbered 1 through 13 is 6/13 or approximately 0.4615. This is because out of the 13 balls, 6 of them have even numbers.

To calculate the probability, we use the formula:

Probability = Number of Favorable Outcomes / Total Number of Outcomes

In this case, the favorable outcomes would be the number of even numbers, which is 6. The total number of outcomes would be 13 (the total number of balls in the bag). Therefore, the probability of selecting a ball that has an even number is 6/13.

Another way to look at this is to think of the probability as the ratio of favorable outcomes to total possible outcomes. In this case, the ratio is 6:13, which can be simplified to 3:6 or 1:2. Since one out of every two outcomes is favorable, the probability is 0.5, which is the same as 6/13.

To further understand the concept of probability, consider the example of a fair coin. If a fair coin is flipped, the probability of getting either heads or tails is 50%. This is because the ratio of favorable outcomes (one head and one tail) to total possible outcomes (two heads and two tails) is 1:2.

In conclusion, the probability of selecting a ball that has an even number from a bag containing 13 balls numbered 1 through 13 is 6/13 or approximately 0.4615.

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The value of the exact surface area of the cone is 360π

To find the surface area of a cone, we need to calculate the area of the circular base and the curved lateral surface.

The radius of the circular base can be found using the Pythagorean theorem:

r = √(s^2 - h^2)

where s is the slant height and h is the height.

In this case, we have:

r = √(26^2 - 24^2)

r = 10

So, the surface area is

S = πr² + πrl

This gives

S = π * 10² + π * 10 * 26

S = 360π

Hence, the exact surface area of the cone is 360π

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Answer:

18x + 12y ≤ 50

Step-by-step explanation:

Let x be the number of large popcoms and y be the number of small popcoms.

The cost of a large popcom is $18, and the cost of a small popcom is $12. The total cost of purchasing x large popcoms and y small popcoms is given by:

Total cost = 18x + 12y

The problem states that Jarvis has $50 in his wallet to pay for the popcoms. Therefore, we can write the following inequality:

18x + 12y ≤ 50

This inequality represents the situation where Jarvis and his family want to purchase popcoms, and Jarvis has $50 to spend. The inequality ensures that the total cost of the popcoms does not exceed $50.

Similarly, there are 10 choices for the first number, 9 choices for the second number, and 8 choices for the third number. Therefore, the total number of possibilities is[tex]26 × 25 × 24 × 23 × 22 × 10 × 9 × 8 = 14,776,320[/tex] possibilities.

Fundamental Counting Principle and how to count with and without replacement.The Fundamental Counting Principle (FCP) states that if there are m ways to perform an event and n ways to perform a second event, then there are m × n ways to perform both events. For example, suppose there are 2 shirts, 3 pants, and 4 pairs of shoes in your closet. Using the FCP, you can calculate the number of outfit combinations: 2 × 3 × 4 = 24.If you are allowed to use characters more than once (with replacement), the number of different possibilities for a password can be calculated by multiplying the number of choices for each character type. There are 26 lowercase letters, so there are 26 choices for the first letter, 26 choices for the second letter, and so on. Similarly, there are 10 digits, so there are 10 choices for each number.

Therefore, the total number of possibilities is [tex]26 × 26 × 26 × 26 × 26 × 10 × 10 × 10 = 26^5 × 10^3 = 11,881,376,000[/tex] possibilities.If you may only use each letter or number one time, then you cannot repeat any choices. Therefore, the number of possibilities is reduced. There are 26 choices for the first letter, 25 choices for the second letter (since one has already been used), and so on.

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At an airport restaurant, the cost of one hamburger is $2.50.

Two sodas and four hamburgers cost $12.00, and an order of four sodas and two hamburgers costs $9.00.

To know the cost of each soda and hamburger, we need to use the equation (x and y)

Use x for soda, and use y for hamburger

Two sodas and four hamburgers cost $12.00

Then, (2 x x) + (4 x y) = 12

2x + 4y = 12

We need to divide the numbers by 2, as follows:

x + 2y = 6

four sodas and two hamburgers cost $9.00

(4 x x) + (2 x y) = 9

4x + 2y = 9

We have to substitute the "x", as follows:

4 (6-2y) + 2y = 9

24 - 8y + 2y = 9

24 - 6y = 9

24 - 9 = 6y

15 = 6y

y = 2.5

Therefore, the cost of one hamburger is $2.50.

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Option C is the correct answer. The increase in the sale of hot chocolate is correlated to, but not caused by, the sale of coffee.

What is correlation?

Correlation is a statistical measure that shows how closely two or more variables are linked to one another. It is a measurement of the strength and direction of the linear connection between two variables, in other words.

Based on the information provided, it can be concluded that there is a correlation between the sale of hot chocolate and the sale of coffee.

Option A can't be considered because it conflicts with the material provided.

Option B indicates a causal relationship that cannot be proven merely on the basis of the observed correlation between the sales of hot chocolate and coffee.

Option D is untrue as well because a correlation has been found.

Therefore, option C is the valid conclusion that can be drawn from the given information, stating that the increase in the sale of hot chocolate is correlated to, but not necessarily caused by, the sale of coffee.

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Each number occupies 7.7 inches² of  the dartboard.

In geοmetry, area is the amοunt οf space a flat shape, like a pοlygοn, circle οr ellipse, takes up οn a plane. The area οf a shape is always measured in square units. Tο find the area οf simple shapes like a square οr the area οf a rectangle, yοu οnly need its width, w, and length, l (οr base, b). The area is length times width:

First we need the area of the dartboard

Area = πr²

here r = d/2 = 14/2 = 7

Area of dartboard = πr²

[tex]$ \rm = \frac{22}{7 } \times 7 \times 7[/tex]

= 22 × 7

= 154 inches²

Now, its is said that each number occupies 1/20 of the board,

Then area of each number =  154 ×  1/20

                                             = 7.7 inches²

Thus, Each number occupies 7.7 inches² of  the dartboard.

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The winner of the election got 26320 votes.

Let's first find the total number of votes cast in the election. We know that 2/3 fraction of the electors voted for the first candidate and 1/4 of the electors voted for the second candidate. Therefore, the remaining 1/12 of the electors voted for the third candidate. So, we have:

2/3 + 1/4 + 1/12 = 8/12 + 3/12 + 1/12 = 12/12 = 1

This means that all the electors voted, and the total number of votes cast is equal to the total number of electors.

Now, let's find the number of votes the third candidate got, which is 1/12 of the total number of votes. We know that this is equal to 3290. So, we have

1/12 x Total Number of Votes = 3290

Multiplying both sides by 12, we get:

Total Number of Votes = 3290 x 12 = 39480

Now, we can find the number of votes the first candidate got, which is 2/3 of the total number of votes. We have:

2/3 x Total Number of Votes = 2/3 x 39480 = 26320 votes

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