39.99+0.45x=44.99+0.4x​

Answer:

3times

Step-by-step explanation:

Baking Process: repeatedly rolling out and folding the dough to make layers

Soon Yi starts with a layer of dough = 2millimeters

Each time Soon Yi rolls and folds the dough, the thickness increases by 8 % = 1 + 8 %

When time = 1

Thickness = 2(1 + 8 %) = 2(1+0.08)

= 2(1.08) = 2.16

For time = n

Thickness = 2(1 + 8 %)^n = 2(1.08)^n

When thickness ≥ 2.5mm, n= ?

2.5 = 2(1.08)^n

2.5/2 = (1.08)^n

1.25 = (1.08)^n

Since the numbers are close (1.25 and 1.08), we can compute by multiplying 1.08 by itself till we get 2.5.

1.08 ×1.08× 1.08 = 1.259712

(1.08)³ is a bit above 1.25

2(1.08)³ satisfies the thickness of at least 2.5mm

Let's check our answer using the formula:

When n = 3

2(1.08)³ = 2 × 1.259712 = 2.519424

This satisfies the thickness of at least 2.5mm

Therefore, the smallest number of times Soon Yi will have to roll and fold the dough so that the resulting dough is at least 2.5 mm = 3

option C is the correct answer. sin β = 15 / 17

Given data

Right angled triangle has sides

opposite = 15

adjacent = 8

Hypotenuse = 17

sin β = opposite / hypotenuse

substituting the values gives

sin β = 15 / 17

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Answer:

1. 27.5 in.^2

2. 360 in.^2

Step-by-step explanation:

1.

A = bh/2

A = (4 + 7)(5)/2

A = 27.5 in.^2

2.

A = bh/2

A = (35 + 13)(15)/2

A = 360 in.^2

Answer:

first we deal with the parentheses.

3x + 28 - 8x = 69

3x - 8x  = 41

-5x = 41

x = -8.2

ep-by-step explanation:

Answer:

x = -8

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

plug in the number 9

-2(9)= -18

-18+3= -15

Answer:

0.06 (0.06061538462)

Answer:

56

Step-by-step explanation:

In perimeter, The cost to frame Joy's math certificate in a fancy frame is $138.00.

The dimensions of Joy's math certificate are 10 inches tall and 13 inches wide.

Joy wants to frame it in a fancy frame that costs $3.00 per inch.

To determine the total cost of framing the certificate, we need to find its perimeter and then multiply that by the cost per inch.

The perimeter of the certificate is:

Perimeter = 2 × (height + width)

Substituting the given values, we get:

Perimeter = 2 × (10 + 13)Perimeter = 46 inches

Therefore, the total cost of framing Joy's math certificate is:

Total cost = Perimeter × Cost per inch

Total cost = 46 × 3.00Total cost = $138.00

Thus, the cost to frame Joy's math certificate in a fancy frame is $138.00.

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Answer:

B. RZ =R BZ

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisectors of both sides. Therefore, CZ and SZ are perpendicular bisectors of AB and ST, respectively.

Option B is true because point R lies on the perpendicular bisector of AB, and therefore RZ = RB.

Answer: vv

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisector of the sides ST and AR.

Therefore, we can draw perpendiculars from point Z to the sides ST and AR, which intersect them at points T' and R', respectively.

Now, let's examine the options:

A. SZ & TZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distance from Z to S and T could be different.

B. RZ = RB: This is true, as point Z lies on the perpendicular bisector of AR, and is therefore equidistant from R and B.

C. CTZ = ASZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of AR, and the distances from Z to C and A could be different.

D. ASZ = ZSB: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distances from Z to A and B could be different.

Therefore, the only statement that must be true is option B: RZ = RB.

The tangent in the unit circle is equal to 0.334.

Since, We know that;

In trigonometry, unit circles are representations of a circle with radius 1 and centered at the origin of a Cartesian plane commonly use to estimate and understand angles and trigonometric functions related to them.

Here, Angles are generated by line segments whose coordinates are of the form (x, y), where x is the position of the terminal point along the x-axis and y is the position of the terminal point along the y-axis.

In addition, the tangent of the angle generated in a unit angle is defined by the following equation:

tan θ = y / x     (1)

If we know that x = - 0.9483 and y = - 0.3173, then the tangent of the angle generated in the unit circle is:

tan θ = (- 0.3173)/(- 0.9483)

tan θ = 0.334

Thus, The tangent in the unit circle is equal to 0.334.

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By substituting the limits of integration and solving the definite integral, the volume of the solid is approximately 3.57 cubic units.

What is integration ?

Integration is a fundamental concept in calculus that deals with the problem of finding the total change in a quantity over a given interval. It is the reverse process of differentiation, which deals with finding the rate of change of a quantity.

We can think of slicing the solid into thin horizontal slices, each parallel to the y = 0 plane. The cross-section of each slice with the elliptic cylinder will be an ellipse. The area of each ellipse can be calculated using the formula for the area of an ellipse, which is πab, where a and b are the semi-major and semi-minor axes of the ellipse.

The semi-major axis of the ellipse is 2, and the semi-minor axis is √(4 - 4x^2) = √(4(1 - x^2)) = 2√(1 - x^2). So the area of each slice is A(x) = π(2)(2√(1 - x^2)) = 4π√(1 - x^2)

The height of each slice is dy = dz = dx, since the slices are parallel to the y = 0 plane and the height of each slice is equal to the change in y or z between two consecutive slices.

So, the volume of the solid is ,

∫ (4π√(1-x^2)) dx from x = -1/2 to x = 1/2

By substituting the limits of integration and solving the definite integral, the volume of the solid is approximately 3.57 cubic units.

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Given:

The function is

\(f(x)=4x-8\)

To find:

The input of the function when the output is 20.

Solution:

We have,

\(f(x)=4x-8\)

Here, x is input and f(x) is output.

Put f(x)=20 in the given function to find the input of the function when the output is 20.

\(20=4x-8\)

\(20+8=4x\)

\(28=4x\)

Divide both sides by 4.

\(\dfrac{28}{4}=x\)

\(7=x\)

Therefore, the required input value is 7.

The value of the pooled-variance t STAT test statistic for testing H0:μ1=μ2 is approximately 2.8378

Assuming that you have a sample of n1 = 9 with the sample mean X1 = 50, and a sample standard deviation of S1 = 7, and you have an independent sample of n2 = 13 from another population with a sample mean of X2 = 32 and the sample standard deviation S2 = 8. The first thing to do is to find out if the variance of both samples is equal.

Null Hypothesis:

H0:σ12 = σ22 (variances are equal)

Alternative Hypothesis: Ha: σ12 ≠ σ22 (variances are not equal)

Calculations:

F = S12 / S22 = 7² / 8² = 0.61

Critical Values: We are doing a two-tailed test, thus α = 0.05 / 2 = 0.025 and the degree of freedom is v1 = 8 and v2 = 12, hence F0.025,8,12 = 0.344, and F0.975,8,12 = 3.140

Therefore, we reject the null hypothesis H0 and conclude that variances are not equal. Instead, we use a pooled variance which is given by:

Sp² = [(n1-1)S12 + (n2-1)S22]/(n1+n2-2)

= [(9-1)7² + (13-1)8²]/(9+13-2)

= [96(49)+156(64)]/20(22)

= 2382/440= 5.41

Using this pooled variance, the pooled-variance t STAT test statistic can now be calculated using the following formula:

t STAT = (X1 - X2) / Sp * sqrt (1/n1 + 1/n2)t STAT = (50 - 32) / sqrt(5.41) * sqrt (1/9 + 1/13)tSTAT = 2.8378

Therefore, The value of the pooled-variance t STAT test statistic for testing H0:μ1=μ2 is approximately 2.8378 (rounded to 4 decimal places).

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Answer:

n ≤ 7

Step-by-step explanation:

n-3 ≤ 4

n - 3 + 3 ≤ 4 + 3  ==> add 3 on both sides to isolate the variable n

n ≤ 7

Your answer was almost right, although n can also be less than 7 as well.

Let X be exponential with a rate of lambda and let Y = [X] + 1. Substituting it, we get

P(Y = k) = e ^ (-λ(k-1))(1 - p). Therefore, P(Y = k) = (1 - p)pk-1.

We need to show that Y is geometric with a parameter of p = 1 - e ^ (-lambda).

To solve the problem, we have to show that P(Y = k) = (1 - p)pk-1 for all k ≥ 1.P(Y = k) = P([X] + 1 = k)

We know that [X] ≤ X < [X] + 1.

Substituting Y = [X] + 1,

we get [Y - 1] ≤ X < Y - 1. ⇒ Y - 1 ≤ X < Y

It follows that

P(Y = k) = P([X] + 1 = k)

= P(Y - 1 ≤ X < Y)

= P(X ≥ k - 1, X < k)

= P(X < k) - P(X < k - 1)P(X < k)

= 1 - e ^ (-λk)P(X < k - 1)

= 1 - e ^ (-λ(k-1))

Therefore, P(Y = k) = (1 - e ^ (-λk)) - (1 - e ^ (-λ(k-1)))

= e ^ (-λ(k-1))(1 - e ^ (-λ))

We know that p = 1 - e ^ (-λ).

Substituting it, we get P(Y = k) = e ^ (-λ(k-1))(1 - p)

Therefore, P(Y = k) = (1 - p)pk-1.

Hence proved.

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The equation of the trend line is given as follows:

y = 1.33x + 20.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

Two points on the line in this problem are given as follows:

(0, 20) and (15, 40).

When x = 0, y = 20, hence the intercept b is given as follows:

b = 20.

When x increases by 15, y increases by 20, hence the slope m is given as follows:

m = 20/15

m = 1.33.

Hence the function is given as follows:

y = 1.33x + 20.

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Answer:

8 and 25

Step-by-step explanation:

We can set up an equation to help solve this problem.

Let x represent the smaller number

x+(x+17)=33

2x+17=33

2x=16

x=8

The smaller number is 8

Add 17 to 8

The larger number is 25

Answer:

Smaller number:8 larger number:25

Step-by-step explanation:

25-8=17

25+8=33

You can also set up an equation to help things be easier.

The Laplace transform of the given function is,

L{f(t)} = (8/s) - 4e^{-3s/2}/s - 6e^{-2s}/s

Given function is f(t) = {8 12 1 Jo, 0 ≤ t < 3/2, 3/2 ≤ t < 2, 2 ≤ t < ∞ respectively.

We have to find Laplace transform of the given function.

For first interval 0 ≤ t < 3/2,

f(t) = 8u(t) - 8u(t-3/2)

For second interval 3/2 ≤ t < 2,

f(t) = 12u(t-3/2) - 12u(t-2)

For third interval 2 ≤ t < ∞,

f(t) = Jo(u(t-2))

Hence, we can write the Laplace transform of the given function as,

L{f(t)} = L{8u(t) - 8u(t-3/2)} + L{12u(t-3/2) - 12u(t-2)} + L{Jo(u(t-2))}

Where, L is Laplace transform.

Let's calculate each Laplace transform stepwise,

1. L{8u(t) - 8u(t-3/2)}L{8u(t)} = 8/L{u(t)}L{u(t)}

= 1/sL{u(t-3/2)}

= e^{-3s/2}/s

Therefore,

L{8u(t) - 8u(t-3/2)} = 8[1/s - e^{-3s/2}/s]

2. L{12u(t-3/2) - 12u(t-2)}L{12u(t-3/2)}

= 12e^{-3s/2}/sL{12u(t-2)}

= 12e^{-2s}/s

Therefore,

L{12u(t-3/2) - 12u(t-2)} = 12[e^{-3s/2}/s - e^{-2s}/s]

3. L{Jo(u(t-2))}L{Jo(u(t-2))} = ∫_{0}^{∞}δ(t-2)e^{-st}dtL{Jo(u(t-2))}

= e^{-2s}

Hence, the Laplace transform of the given function is,

L{f(t)} = 8[1/s - e^{-3s/2}/s] + 12[e^{-3s/2}/s - e^{-2s}/s] + e^{-2s}

= (8/s) - 4e^{-3s/2}/s - 6e^{-2s}/s

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Answer:

25

Step-by-step explanation:

The kinetic energy of a ball with a mass of 2 kg that is rolling at a velocity of 5 m/s is 5 Joules

From the question, we are to determine the kinetic energy of the ball

From the given equation for the velocity,

\(v = \sqrt{\frac{2K}{m} }\)

We will make K the subject of the equation

 \(v = \sqrt{\frac{2K}{m} }\)

Take the squares of both sides

\(v^{2} ={\frac{2K}{m} }\)

Multiply both sides by m

\(mv^{2} ={\frac{2K}{m} } \times m\)

\(mv^{2} =2K\)

∴ \(K = \frac{1}{2} mv^{2}\)

Now, for the kinetic energy of a ball with a mass of 2 kilograms that is rolling at a velocity of 5 meters/second

That is,

m = 2 kg

and v = 5 m/s

Putting the parameters into the equation, we get

\(K = \frac{1}{2} \times 2 \times 5^{2}\)

K = 25 J

Hence, the kinetic energy of a ball with a mass of 2 kg that is rolling at a velocity of 5 m/s is 5 Joules

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Here is the complete question:

Select the correct answer from each drop-down menu. The velocity, v, in meters/second, of an object with a mass of m, in kilograms, and kinetic energy of K, in joules, is given by this equation.

\(v = \sqrt{\frac{2K}{m} }\)

Use the equation to complete this statement. The kinetic energy of a ball with a mass of 2 kilograms that is rolling at a velocity of 5 meters/second is joules.

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Answer:

Dear user,

Answer to your query is provided below

The fraction of the circuit is (3/14)

Step-by-step explanation:

Explanation of the same is attached in image

Answer:

3/14

Step-by-step explanation:

Alan would need a sample size of at least 447 to construct a 95% confidence interval for the proportion of those testing positive for COVID-19 who require hospitalization with a margin of error no more than 2%, using a prior estimate of 15%.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

To find the sample size required for constructing a 95% confidence interval for the proportion of those testing positive for COVID-19 who require hospitalization with a margin of error no more than 2%, we can use the following formula:

n = [(z-score)² * p * (1-p)] / (margin of error)²

where:

n is the sample size

z-score is the critical value for a 95% confidence interval, which is 1.96

p is the prior estimate of the proportion, which is 0.15

margin of error is 0.02

Plugging in the values, we get:

n = [(1.96)² * 0.15 * (1-0.15)] / (0.02)²

n = 446.25

Rounding up to the nearest whole number, we get a required sample size of 447.

Therefore, Alan would need a sample size of at least 447 to construct a 95% confidence interval for the proportion of those testing positive for COVID-19 who require hospitalization with a margin of error no more than 2%, using a prior estimate of 15%.

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The best estimate for μ1-μ2 is -3.7, the margin of error is approximately 1.62, and the 99% confidence interval is (-5.32, -2.08).

To calculate the margin of error, we need to determine the standard error of the difference in means. The formula for the standard error is:

SE = \(\sqrt((s_1^2/n1) + (s_2^2/n2))\)

SE = \(\sqrt((1.8^2/50) + (6.2^2/50))\) ≈ 0.628

For a 99% confidence level, the critical value (z-value) is approximately 2.58.

Margin of error = 2.58 * 0.628 ≈ 1.62

Therefore, the best estimate for μ1-μ2 is -3.7, the margin of error is approximately 1.62, and the 99% confidence interval is (-5.32, -2.08).

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The partial derivative of the utility function \(U(x_1, x_2)\) with respect to \(x_1\) is \(a * x_1^{(a-1)} * x_2^{(1-a)}\), and the partial derivative with respect to \(x_2\) is \((1-a) * x_1^a * x_2^{(-a)}.\)

The utility function  \(U(x_1, x_2)\) represents a consumer's satisfaction or preference for two consumption goods, \(x_1\) and \(x_2\). The partial derivatives provide insights into how the utility function changes as we vary the quantities of the goods.

To calculate the partial derivative with respect to \(x_1\), we differentiate the utility function with respect to \(x_1\) while treating \(x_2\) as a constant. The result is \(a * x_1^{(a-1)} * x_2^{(1-a)}\). This derivative captures the impact of changes in \(x_1\) on the overall utility, taking into account the relative importance of \(x_1\)(determined by the parameter a) and the quantity of \(x_2\).

Similarly, to find the partial derivative with respect to \(x_2\), we differentiate the utility function with respect to \(x_2\) while treating \(x_1\)as a constant. The resulting derivative is \((1-a) * x_1^a * x_2^{(-a)}.\). This derivative shows how changes in \(x_2\) affect the overall utility, considering the relative weight of \(x_2\) (given by 1-a) and the quantity of \(x_1\).

In summary, the partial derivatives provide information about the sensitivity of the utility function to changes in the quantities of the consumption goods, allowing us to understand the consumer's preferences and decision-making.

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Answer:

(A)\(56.5^\circ\)

Step-by-step explanation:

From the diagram attached:

Angle 1 and Angle 6 are Co-Interior Angles.

The sum of co-interior angle is 180 degrees.

Therefore:

\(m\angle 1+ m\angle 6=180^\circ\\\\m\angle 6=123.5^\circ,$ therefore:\\m\angle 1+ 123.5^\circ=180^\circ\\m\angle 1=180^\circ-123.5^\circ\\m\angle 1=56.5^\circ\)

The measure of angle 1 is therefore 56.5 degrees.

The correct option is A.

∠6 and ∠1 are same-side interior angles, m∠6 = 123.5°, therefore m∠1 will be: A. 56.5°

Recall:

The image showing the two parallel lines that is cut by a transversal creating angles is shown in the diagram attached below.

Given:

m∠6 = 123.5°

∠6 and ∠1 are same-side interior angles.

m∠6 + m∠1 = 180°

123.5° + m∠1 = 180°

m∠1 = 180° - 123.5°

m∠1 = 56.5° (Option A)

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Answer:

The desired divisor is n = 21

Step-by-step explanation:

Let that number be n.  Then:

-15/56        -5

---------- = ---------

     n            6

Through cross-multiplication we get:

(-15/56)*6 = -5n, which reduces to:

(-15)(7) = -5n, or 3(7) = n

The desired divisor is n = 21

The correct answer is "formulate H0 and H1." This comparison helps determine whether there is sufficient evidence to reject the null hypothesis and support the alternative hypothesis.

When testing a hypothesis, the first step is to clearly define the null hypothesis (H0) and the alternative hypothesis (H1). The null hypothesis represents the assumption of no effect or no difference, while the alternative hypothesis represents the hypothesis you are trying to support, which typically suggests the presence of an effect or a difference.

After formulating the hypotheses, the subsequent steps in hypothesis testing are as follows:

Collect data and calculate test statistics: Gather relevant data through observations, experiments, or surveys. Then, analyze the data and calculate the appropriate test statistic based on the nature of the hypothesis being tested. The test statistic depends on the specific hypothesis test being used.

Select an appropriate test: Choose a statistical test that is most suitable for the type of data and the research question at hand. The selection of the test depends on factors such as the nature of the data (continuous or categorical), the number of groups being compared, and the assumptions associated with the test.

Choose the level of significance: Determine the desired level of significance (alpha level) for the hypothesis test. The level of significance represents the maximum probability of incorrectly rejecting the null hypothesis. Commonly used alpha levels are 0.05 (5%) or 0.01 (1%), but it can vary depending on the context and the consequences of making Type I errors.

After completing these steps, further analysis involves comparing the calculated test statistic to the critical value or p-value associated with the chosen level of significance. This comparison helps determine whether there is sufficient evidence to reject the null hypothesis and support the alternative hypothesis.

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Answer:

11) 6

12) 3

Step-by-step explanation:

2 log 2 8

so 2(log2 8)

Base 2 so 2^x=8 so 3.

2*3 is 6.

log a a cubed

base a so a^ x = a^3

x=3

so 3.

Hope this helps ;D

Answer:

6 and 3

Step-by-step explanation:

Using the rules of logarithms

log\(x^{n}\) ⇔ n log x

\(log_{b}\) x = n ⇒ x = \(b^{n}\)

\(log_{a}\) a = 1

(11)

let 2 \(log_{2}\)8 = n , then

\(log_{2}\) 8² = n

\(log_{2}\) 64 = n

\(log_{2}\) \(2^{6}\) = n

\(2^{6}\) = \(2^{n}\)

Since bases on both sides are equal, equate the exponents, that is

n = 6

(12)

\(log_{a}\) a³

= 3 \(log_{a}\) a

= 3 × 1

= 3

There are 324 different dessert menus possible for the week, considering the restriction that there must be cake on Friday and no dessert can be repeated two days in a row.

To determine the number of different dessert menus for the week, we can approach the problem systematically.

Since there are four options for dessert each day (cake, pie, ice cream, or pudding), and the same dessert may not be served two days in a row, we need to consider the dessert choices for each day of the week.

Let's start with the restriction that there must be cake on Friday due to a birthday. We have three options for dessert on the other six days (excluding Friday) because we cannot repeat the dessert from the previous day.

To count the number of dessert menus, we can consider the choices for each day of the week starting from Sunday:

1. Sunday: There are four options for dessert since no dessert has been served yet.

2. Monday: There are three options left since we cannot repeat Sunday's dessert.

3. Tuesday: There are three options available, excluding Monday's dessert.

4. Wednesday: There are three options remaining, excluding Tuesday's dessert.

5. Thursday: There are three options available, excluding Wednesday's dessert.

6. Friday: There must be cake, so only one option is available.

To find the total number of dessert menus, we multiply the number of options for each day:

4 options × 3 options × 3 options × 3 options × 3 options × 1 option = 324 dessert menus

Therefore, there are 324 different dessert menus possible for the week, considering the restriction that there must be cake on Friday and no dessert can be repeated two days in a row.

Each dessert menu represents a unique combination of desserts for each day of the week, satisfying the given conditions.

In conclusion, the dessert chef has 324 different dessert menu options for the week, ensuring a variety of desserts and fulfilling the requirement of having cake on Friday.

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If a line parallel to one side of a triangle contacts the other two sides of the triangle, the line proportionally splits these two sides. If DE = BC, then ADDB=AEEC.

If a line parallel to one side of a triangle contacts the other two sides, the two sides are proportionately divided.

The formula for a proportional equation is y = kx. The letters y and x denote the variables in the equation. The letter k represents the proportionality constant, which is fixed.

Because matching angles produce the AA similarity shortcut, when a line is drawn parallel to one side of a triangle, two similar triangles are generated. Because the triangles are comparable, the parallel line segments are proportionate segments.

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