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The derivate of f(y) is -9y^6 - 33y^4 + 84y^2.

To differentiate the given function f(y), we will use the product rule and the chain rule of differentiation. Let's break down the function into two parts:

f(y) = (1 y^2 - 9 y^4) * (y + 3y^3)

Using the product rule, we can differentiate each part separately:

f'(y) = (1 y^2 - 9 y^4)' * (y + 3y^3) + (1 y^2 - 9 y^4) * (y + 3y^3)'

The derivative of the first part is:

(1 y^2 - 9 y^4)' = 2y - 36y^3

Now we need to differentiate the second part using the chain rule. Let's call the inner function u:

u = y + 3y^3

Using the power rule, the derivative of u with respect to y is:

u' = 1 + 9y^2

Now we can substitute these values back into our original equation:

f'(y) = (2y - 36y^3) * (y + 3y^3) + (1 y^2 - 9 y^4) * (1 + 9y^2)

Simplifying further:

f'(y) = 2y^2 + 6y^4 - 36y^4 - 108y^6 + y^2 + 9y^4 - 9y^6 + 81y^2

Combining like terms:

f'(y) = -9y^6 - 33y^4 + 84y^2

Therefore, the derivative of f(y) is -9y^6 - 33y^4 + 84y^2.

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Therefore, the dimensions of triangle ABC and the angles opposite to these sides are:

a ≈ 6.85 units

b = 13 units

c ≈ 9.39 units

A ≈ 40 degrees

B = 97 degrees

C = 43 degrees

A triangle is a geometrical shape that has three sides and three angles. It is formed by connecting three non-collinear points in a plane with straight line segments. The three sides may have different lengths, and the three angles may have different measures. The sum of the angles in a triangle is always 180 degrees. Triangles are used in many fields of mathematics, as well as in science, engineering, and everyday life. They can be classified by their side lengths and angle measures, and there are various formulas and theorems that apply to triangles.

Here,

We can use the Law of Sines to find the missing measures of the triangle.

Recall that the Law of Sines states that for any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides opposite to the angles A, B, and C, respectively.

Given that b=13 units, and angle B=97 degrees, we can set up the proportion:

13/sin(97) = c/sin(43)

Solving for c, we get:

c = (13*sin(43))/sin(97) ≈ 9.39

Now, to find the remaining angle and side, we can use the fact that the angles of a triangle sum up to 180 degrees. We know that angle C is 43 degrees, so we can find angle A as:

A = 180 - 97 - 43 = 40 degrees

And we can find side a using the Law of Sines:

a/sin(40) = 13/sin(97)

Solving for a, we get:

a = (13*sin(40))/sin(97) ≈ 6.85

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The area of the rectangle is 105 square cm

Represent the dimensions of the rectangle with x and y

So, the length of the square would be:

Length = x - 2

Width = y + 6

The areas are then calculated as:

Rectangle = xy

Square = (x -2)(y + 6)

The relationship between the areas is:

(x -2)(y + 6) = 64 + xy

Expand

xy + 6x - 2y - 12 = 64 + xy

This gives

6x - 2y - 12 = 64

Add 12 to both sides

6x - 2y= 76

Divide through by 2

3x - y = 38

By trial by error, we have:

x = 15 and y = 7

The rectangle area is then calculated as:

Rectangle = xy

This gives

Rectangle = 15 * 7

Evaluate

Rectangle = 105

Hence, the area of the rectangle is 105 square cm

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The height of Marlon is 42.5 inches with a mean of 40 inches and being taller than 70% of the boys.

Given, Heights of four-year-olds are Normally distributed, with a mean of 40 inches and a standard deviation of 3 inches. At his four-year checkup, Marlon’s height is measured as taller than 70% of boys his age.

The mean = 40 inches

standard deviation = 3 inches

Marlon is taller than 70% of the boys

so the height of Marlon is,

70/100×(40 + 3)

= 42.5 inches

So, the height of Marlon is 42.5 inches

Hence, the height of Marlon is 42.5 inches

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Answer:

i d k the answer soory about that

Step-by-step explanation:

just for points

Answer: 0.86

Step-by-step explanation:

Probability of wining AND scoring 5 or more runs / probability of winning the game

​

0.43/0.5 = 0.86 is the final answer

Answer: 0.865

Step-by-step explanation:

a) \(\sigma^2\) is an unbiased estimator of \(\sigma2\). b) the mean squared error of \(\sigma^2\) when n=3 is \(\frac{4}{3} \sigma^4\).

(a) We must demonstrate that \(E(\sigma^2) = \sigma2\) in order to demonstrate that \(\sigma^2\) is an unbiased estimator of \(\sigma2\).

We have:

\(E(\sigma^{2}) = E(n^{-1} \Sigma i=1^n (X_i - \mu)^2)\)

\(= n^{-1} \Sigma i=1^n E((X_i - \mu)^2)\)

\(= n^{-1} \Sigma i=1^n Var(X_i)\)

\(= n^{-1} \Sigma i=1^n \sigma^2\) (since population variance is \(\sigma^2\))

\(= \sigma^2\)

Hence, \(\sigma^2\) is a fair estimator of \(\sigma2\).

(b) We have:

\(MSE(\sigma^2) = E[(\sigma^2 - \sigma2)^2]\)

\(= E[ (n^{-1} \Sigma i=1^n (X_i - \mu)^2 - \sigma2)^2 ]\)

=\(E[ (n^{-1} \Sigma i=1^n (X_i - \mu)^2)^2 - 2n^{-1} \Sigma i = 1^n (X_i - \mu)^2)\sigma2 + \sigma4]\)

\(= E[ (n^{-2} \Sigmai=1^n \Sigmaj=1^n (X_i - \mu)^2(X_j - \mu)^2) - 2(n^{-1} \SIgma i=1^n (X_i - \mu)^2)\sigma2 + \sigma4]\) (using the expansion of square)

Given that the population has a known mean \(\mu\) and variance \(\sigma^2\) and is normally distributed, we may simplify this statement as follows:

\(MSE(\sigma^2) = n^{-2} \Sigma i=1^n \Sigma j=1^n E[(X_i - \mu)^2(X_j - \mu)^2] - 2\sigma2(n^{-1} \Sigmai=1^n E[(X_i - \mu)^2]) + \sigma^4\)

\(= n^{-2} \Sigma i=1^n \Sigma j=1^n Cov(X_i - \mu, X_j - \mu) + \sigma^4\) (using the definition of covariance)

\(= n^{-2} \Sigma i=1^n \Sigma j=1^n E(X_iX_j) - \mu^2 + \sigma^4 (since, Cov(X_i - \mu, X_j - \mu) = E[(X_i - \mu)(X_j - \mu)] = E(X_iX_j) - \mu^2)\)

\(= n^{-2} \Sigma i=1^n \Sigma j=1^n (\sigma^2\delta_{ij} + \mu^2 - \mu^2) + \sigma^4\) (using the fact that the population is normally distributed with known mean and variance)

\(= n^{-1} \Sigma i=1^n \sigma^4 + \sigma^4\)

\(= \frac{(n+1)\sigma^4}{n}\)

Hence, the \(\frac{(3+1)\sigma^4}{3} = \frac{4}{3} \sigma^4\) is the mean squared error of \(\sigma^2\) when n=3.

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Answer: 4

Step-by-step explanation: Divide 28 by 7

Answer:

2root of 15

Step-by-step explanation:

Answer:

2a\(\sqrt{15a}\)

Step-by-step explanation:

The tangent line has the largest slope at x = 3√2 and x = -3√2 on the curve y = 1 + 60x³ − 2x⁵.

First, let's find the derivative of the given function y = 1 + 60x³ − 2x⁵ using the power rule for differentiation:

dy/dx = 0 + 3(60)x² - 5(2)x⁴

= 180x² - 10x⁴

To find the critical points, we set the derivative equal to zero and solve for x:

180x² - 10x⁴ = 0

Factoring out common terms, we get:

10x²(18 - x²) = 0

Setting each factor equal to zero, we have:

10x² = 0 or 18 - x² = 0

From the first equation, we find x = 0.

From the second equation, we have:

18 - x² = 0

x² = 18

Taking the square root, we get:

x = ±√18

= ±3√2

So the critical points are x = 0, x = 3√2, and x = -3√2.

Now we need to evaluate the slope at these critical points. We can do this by plugging each x-value into the derivative:

When x = 0:

dy/dx = 180(0)² - 10(0)⁴ = 0

When x = 3√2:

dy/dx = 180(3√2)² - 10(3√2)⁴ = 180(18) - 10(216) = 3240 - 2160 = 1080

When x = -3√2:

dy/dx = 180(-3√2)² - 10(-3√2)⁴ = 180(18) - 10(216) = 3240 - 2160 = 1080

The slope is 0 when x = 0 and 1080 when x = 3√2 or x = -3√2.

Therefore, the tangent line has the largest slope at x = 3√2 and x = -3√2 on the curve y = 1 + 60x³ − 2x⁵.

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The complete question is as follows:

At which points on the curve y = 1 + 60x³ − 2x5⁵ does the tangent line have the largest slope?

Answer: = 6.109 × 107

Answer: 6.109 x 10^7

Step-by-step explanation: I think

The arrival rate is approximately 32.79 customers per hour.

To find the arrival rate in customers per hour, we need to convert the given information to an hourly basis.

Cars arrive at a rate of 6 cars every 11 minutes.

The average service time is 3 minutes per customer.

To calculate the arrival rate in customers per hour, we need to convert the time frame to hours and divide the number of cars by the time:

Arrival rate = (Number of cars) / (Time in hours)

Number of cars = 6 cars

Time = 11 minutes

To convert 11 minutes to hours:

11 minutes * (1 hour / 60 minutes) = 11/60 hours ≈ 0.183 hours

Arrival rate = 6 cars / 0.183 hours

Arrival rate ≈ 32.79 cars per hour

Therefore, the arrival rate is approximately 32.79 customers per hour.

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Answer:

  1.  S(1) = 1; S(n) = S(n-1) +n^2

  2. see attached

  3. neither

Step-by-step explanation:

1. The first step shows 1 square, so the first part of the recursive definition is ...

  S(1) = 1

Each successive step has n^2 squares added to the number in the previous step. So, that part of the recursive definition is ...

  S(n) = S(n-1) +n^2

__

2. See the attachment for a graph.

__

3. The recursive relation for an arithmetic function is of the form ...

  S(n) = S(n-1) +k . . . . . for k = some constant

The recursive relation for a geometric function is of the form ...

  S(n) = k·S(n-1) . . . . . . for k = some constant

The above recursive relation is not in either of these forms, so it is neither geometric nor arithmetic.

Answer:

12 toppings

Step-by-step explanation:

To do this, we need to write an equation for each place, and then, equal both equations to solve for this.

Let's call "y" the price of the pizza, and "x" the number of toppings.

At Vincents, pizza costs 6.75 + 0.75 for each topping, so the equation here would be:

y = 6.75 + 0.75x  (1)

Now, at italian pizza, a pizza costs 6.15 + 0.80 per topping, so the equation:

y = 6.15 + 0.80x  (2)

Now, we don't need to know the actual price of the pizza, we only want to know how many toppings we need to add on both places, so the pizza has the same price. We have both equations, it's time to equal both of them:

Equalling (1) and (2) we have:

6.75 + 0.75x = 6.15 + 0.80x

Now, let's solve for x:

6.75 - 6.15 = 0.80x - 0.75x

0.6 = 0.05x

x = 0.6 / 0.05

x = 12

So the number of toppings to include in the pizza so the price is the same for both places, will have to be 12 toppings.

Answer:

12 toppings and the prize will be the same.

Step-by-step explanation:

Let

number of toppings = a

Medium pizza at Vincent's

cost  = 6.75 + 0.75a

Medium pizza at Original Italian Pizza

cost  = 6.15 + 0.80a

For the cost to be the same

6.75 + 0.75a = 6.15 + 0.80a

collect like terms

6.75 - 6.15 = 0.80a - 0.75a

0.6  = 0.05a

divide both sides by 0.05

a = 0.6/0.05

a = 12  

12 toppings and the prize will be the same.

1. The square of odd number will give odd number and adding 1 will give even number.

2. The Square of even number will give even number and subtracting 1 will give odd

Odd numbers are those numbers that cannot be divided into two equal parts, whereas even numbers are those numbers that can be divided into two equal parts. Examples of even numbers include any number of multiple of 2, like 2, 4, 6, 8 ,10.. e.t.c

Examples of odd number include adding even numbers by 1. i.e 2+1, 4+1, 6+1, 8+1, 10+1... e.tc which are, 3, 5, 7, 9 , 11.. e.t.c

The square of odd number will give odd number and the square of even number will give even number.

If x is odd in x²+1 , let's take 3 samples of odd numbers, 3, 9, 11

therefore 3²+1 = 9+1 = 10

9² +1 = 81 +1 = 82

11² +1 = 121+1 = 122

therefore x² +1 will give even number if x is odd

If x is even in x²-1 , let's take 3 samples of even numbers. 2, 8, 10

2²-1 = 4-1 = 3

8²-1 = 64-1 = 63

10²-1 = 100-1 = 99

therefore x²-1 will be odd when x is even

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Therefore ,as a result, ABC is equivalent with XYZ, which is the answer to the triangle problem that was presented.

Given its three sides and three vertices, a triangular is a polygon. This geometric shape is fundamental. Triangle ABC is a triangle that has the points A, B, and C as its corners. In geometric shapes, when four pieces are not collinear, a single plane and triangle are obtained. Polygons include triangles since they have three sides and a top right corner.

Here.

Therefore,

∠ A = ∠X because ABC is identical with XYZ.

∠B and ∠Y have the same meaning.

∠Z equals ∠C, and

Line ab has the same value as xy.

Line bc and yz are interchangeable.

Line ac corresponds to xz.

Cpct was employed to find a solution.

Triangle segments that are congruent are matched.

As a result, ABC is symmetrical with XYZ is the answer to the presented triangle problem.

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Complete question is: Are triangles ABC and XYZ similar?

The algorithm is designed to find out whether the child wins or loses in a game where two players take turns to pick balls. The algorithm takes the number of balls remaining in the box as input and returns True if the child wins, otherwise False.

The algorithm assumes that both players play optimally. The algorithm works by recursively picking balls from the box and checking whether the child or the game owner wins the game.

This is a recursive problem where each player plays optimally. There are two players in the game. The child will pick the balls first and then the game owner takes turns. Both will pick the balls optimally in order to win.

In each turn, k balls can be picked from the box. The winner is the one who picks the last ball. If the child picks the last ball, they win otherwise the game owner wins.

The algorithm is as follows:

Algorithm - Pick Balls

1. Define a recursive function called PickBalls(n). The function takes one parameter as input, which is the number of balls remaining in the box.

2. Check if the number of balls remaining is less than or equal to k. If yes, then return True as the game has ended and the child has won.

3. If the number of balls is greater than k, then pick k balls from the box.

4. If the child picks the last ball, then return True.

5. If the child does not pick the last ball, then the game owner picks the balls recursively.

6. If the game owner picks the last ball, then return False. Otherwise, return True.

Explanation: We are designing a recursive algorithm to find out whether the child will win or lose in a game where two players take turns to pick balls. The algorithm takes the number of balls remaining in the box as input and returns True if the child wins, otherwise False. We are assuming that both players play optimally. The algorithm works as follows:

If the number of balls remaining in the box is less than or equal to k, then the child can pick all the balls and win the game. Therefore, the function returns True.

If the number of balls remaining in the box is greater than k, then the child picks k balls from the box. If the child picks the last ball, then they win the game. Therefore, the function returns True.

If the child does not pick the last ball, then the game owner picks the balls recursively. If the game owner picks the last ball, then they win the game. Therefore, the function returns False. If the game owner does not pick the last ball, then the child picks again and the process repeats itself. If the child eventually picks the last ball, then they win the game. Therefore, the function returns True.

Conclusion: The algorithm is designed to find out whether the child wins or loses in a game where two players take turns to pick balls. The algorithm takes the number of balls remaining in the box as input and returns True if the child wins, otherwise False. The algorithm assumes that both players play optimally. The algorithm works by recursively picking balls from the box and checking whether the child or the game owner wins the game.

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a). The difference between the two population means is estimated at a location to be 2.7.

b). 49 different possible outcomes make up the t distribution. The margin of error at 95% confidence is 1.7.

c). The range of the difference between the two population means' 95% confidence interval is (0.0, 5.4).

d). The (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

The variability or spread in a set of data is commonly measured by the standard deviation. The deviation between the values in the data set and the mean, or average, value, is measured. A low standard deviation, for instance, denotes a tendency for data values to be close to the mean, whereas a high standard deviation denotes a larger range of data values.

Using the equation \(x_1-x_2\), we can determine the point estimate of the difference between the two population means. In this instance, we calculate the point estimate as 2.7 by taking the mean of Sample

\(1(x_1=22.8)\) and deducting it from the mean of Sample \(2(x_2=20.1)\).

With the use of the equation \(df=n_1+n_2-2\), it is possible to determine the degrees of freedom for the t distribution. In this instance, the degrees of freedom are 49 because \(n_1\) = 20 and \(n_2\) = 30.

We must apply the formula to determine the margin of error at 95% confidence \(ME=t*\sqrt[s]{n}\).

The sample standard deviation (s) is equal to the average of \(s_1\) and \(s_2\) (3.4), the t value with 95% confidence is 1.67, and n is equal to the

average of \(n_1\) and \(n_2\) (25). When these values are entered into the formula, we get \(ME=1.67*\sqrt[3.4]{25}=1.7\).

Finally, we apply the procedure to determine the 95% confidence interval for the difference between the two population means \(CI=x_1-x_2+/-ME\).

The confidence interval's bottom limit in this instance is \(x_1-x_2-ME2.7-1.7=0.0\) and the upper limit is \(x_1+x_2+ME=2.7+1.7=5.4\).

As a result, the (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

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Answer:

Mizuki is here to help!

115200 \(ft^3\) is the volume of the building.

Step-by-step explanation:

120 x 20 x 48 =

2400 x 48 =

115200

The currents in the circuit are:

To find the currents I and I₂ in the given circuit, we can use Ohm's Law and apply Kirchhoff's laws.

Let's analyze the circuit step by step:

Start by calculating the total resistance (R_total) in the circuit.

R_total = 1Ω + 72Ω + 3Ω + 1Ω

= 77Ω

Apply Ohm's Law to find the total current (I_total) flowing in the circuit.

I_total = V_total / R_total

= 9V / 77Ω

Now, let's analyze the currents in each branch of the circuit:

The current I₁ through the 1Ω resistor can be found using Ohm's Law:

I₁ = V / R = 9V / 1Ω

The current I₂ through the 72Ω resistor can be found using Ohm's Law:

I₂ = V / R = 9V / 72Ω

The current I₃ through the 3Ω resistor can be found using Ohm's Law:

I₃ = V / R = 9V / 3Ω

Finally, we need to determine the current I flowing in the circuit.

Since the 1Ω resistors are in parallel, the current splits between them.

We can use Kirchhoff's current law to find I:

I = I₁ + I₃

Therefore, the currents in the circuit are:

I = I₁ + I₃ = (9V / 1Ω) + (9V / 3Ω)

I₂ = 9V / 72Ω

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Answer:

its C

Step-by-step explanation:

Hey there!

4x - 9 = 15

ADD 9 to BOTH SIDES

4x - 9 + 9 = 15 + 9

CANCEL out: -9 + 9 because it gives you 0

KEEP: 15 + 9 because it help solve for the x-value.

NEW EQUATION: 4x = 15 + 9

SIMPLIFY IT!

4x = 24

DIVIDE 4 to BOTH SIDES

4x/4 = 24/4

CANCEL out: 4/4 because it gives you 1

KEEP: 24/4 because it gives you the answer of the x-value

NEW EQUATION: x = 24/4

SIMPLIFY IT!

x = 6

Therefore, your answer is: x = 6 (Option D.)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Hello!

30 - 25 = 5

so + 5kg

+ 5kg = + 5kg/25kg = + 5/25 = + 0.2 = + 20/100 = + 20%

Answer:

8x^2 - 4x - 5

See the steps below for better explanation:

Using the linear relationship the height of the candle after 17 hours is 22.3 cm.

As it is given that the height of the candle is linear to the amount of time. The linear relationship is the relationship between two variables such that it follows a straight line.

Now, let the time be on the x-axis and the y-axis is the height of the candle. therefore, the slope of the linear relationship can be represented as,

(x₁, y₁) = (7, 23.3)

(x₂, y₂) = (23, 21.7)

Since we know the two points of the linear relationship, therefore, the slope can be written as,

m = (y₂ - y₁)/(x₂ - x₁)

m = (21.7 - 23.3)/(23 - 7)

m = -1.6/16

m = -1/10

Now, the equation of the linear relationship can be written as,

y - y₁ = m( x - x₁)

y - 23.3 = (-1/10)(x - 7)

10y - 233 = -x + 7

x + 10 y = 240          --(1)

We are asked to determine the height of the candle after 17 hours. So, put x = 17 and find y

17 + 10y = 240

10y = 223

y = 22.3

Hence, the height of the candle after 17 hours is 22.3cm.

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The original price was: $5.00 found by using percentage.

What is percentage increase?

Percentage increase of a quantity refers to the increase in the quantity by the given percent.

For a quantity, say A, is being manufactured at a rate 'x' per year. If we say that there is an 80% increase in the manufacturing of A, the new manufacturing rate of A will be given by:

x(initial rate) + \(\frac{80x}{100}\) (increase in the rate) = final rate

Let x be the original price of the yo-yo.

We are given that upon a 20% increase, the new price became $6.00.

According to the question, \(x+\frac{20x}{100} = 6\)

\(\Rightarrow\)1.2x = 6

\(\Rightarrow\) x = \(\frac{6}{1.2}\) = 5

Thus, the original price of the yo-yo was $5.00.

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To find the center-line of the conic section conjugated to the direction with slope -1, we isolate the terms involving xy and yz in the given equation. The equation is transformed to express y in terms of x and z, resulting in the equation y = 1. This equation represents the center-line with a slope of -1. To find the center-line of the conic section conjugated to the direction with slope -1, we need to consider the terms involving xy and yz in the given equation.

The given equation is: \[ x^2 + 2xy + 7y^2 - 5xz - 17yz + 6z^2 = 0 \]

To isolate the terms involving xy and yz, we rewrite the equation as follows:

\[ (x^2 + 2xy + y^2) + 6y^2 + (z^2 - 5xz - 10yz + 17yz) = 0 \]

Now, we can factor the terms involving xy and yz:

\[ (x + y)^2 + 6y^2 + z(z - 5x - 10y + 17y) = 0 \]

Simplifying further:

\[ (x + y)^2 + 6y^2 + z(z - 5x + 7y) = 0 \]

Since we want to find the center-line conjugated to the direction with slope -1, we set the expression inside the parentheses equal to 0:

\[ z - 5x + 7y = 0 \]

To find the equation of the center-line, we need to express one variable in terms of the others. Let's solve for y:

\[ y = \frac{5x - z}{7} \]

Therefore, the equation of the center-line is \( y = 1 \), where the slope of the line is -1.

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