5 Work out the volume of this prism. Write your answer
a in cm³
b in mm³.
20cm
120cm
30cm
10 cm

Answer:

Since Q is a center of gravity, we can apply these formulas

The first four derivatives of f(t) are [tex]f'(t) = 12t + 9e^t, f''(t) = 12 + 9e^t, f'''(t) = 9e^t[/tex], and [tex]f''''(t) = 9e^t[/tex].

The given function is [tex]f(t) = 6t^2+ 9e^t[/tex].

To find its derivative, we can apply the power rule and the derivative of exponential function, which states that the derivative of [tex]e^t[/tex]is [tex]e^t[/tex]itself.

Thus, we get [tex]f'(t) = 12t + 9e^t[/tex].

Applying the power rule again, we get [tex]f''(t) = 12 + 9e^t[/tex].

Taking the derivative one more time, we get [tex]f'''(t) = 9e^t[/tex].

Finally, taking the fourth derivative, we get [tex]f''''(t) = 9e^t[/tex].

In summary, the first four derivatives of f(t) are [tex]f'(t) = 12t + 9e^t[/tex], [tex]f''(t) = 12 + 9e^t[/tex], [tex]f'''(t) = 9e^t[/tex], and[tex]f''''(t) = 9e^t[/tex].

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human hair to grow 20 inches, considering the length of hair is proportional to the number of months it has grown.

First, let's establish the proportionality constant, which is the average rate at which human hair grows. On average, human hair grows approximately 0.5 inches per month.

Now, let's find out how many months it takes for hair to grow 20 inches. We can set up a proportion equation as follows:

Length of hair (in inches) / Number of months = Proportionality constant
Let "x" be the number of months it takes for hair to grow 20 inches. We can write the equation as:
20 inches / x months = 0.5 inches/month

To solve for x, we can multiply both sides by x months, which gives us:
20 inches = 0.5 inches/month * x months
Now, we can divide both sides by 0.5 inches/month:

x months = 20 inches / 0.5 inches/month
x months = 40 months

So, it takes 40 months for human hair to grow 20 inches, considering the length of hair is proportional to the number of months it has grown.

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The stairs can be broken up into three rectangular prisms

The concrete that will be needed to form the stairs is 9.72 m ^3

To get the volume of concrete

Since they are 3

2.7 / 3

= 0.9

1.5 / 3

= 0.5

0.5 + 0.5

= 1

each width is 3.6m

The volume of each = 0.9 x 1.5 x 3.6 = 4.86

Volume 2 = 0.9 x 1.0 x 3.6 = 3.24

Volume 3 = 0.9 x 0.5 x 3.6 = 1.62

amount of concrete = 1.62 + 3.24 + 4.86

= 9.72 m ^3

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It will take approximately 15.27 years for your investment to reach $5,000 at a growth rate of 4.55% per year.

Using the compound interest calculation, we can determine how long it will take for your investment to grow to $5,000 at a growth rate of 4.55% per year:

[tex]A = P(\frac{1 + r}{n} )^(^n^t^)[/tex]

Where:

A = the final amount ($5,000)

P = the initial deposit ($2,500)

r = the interest rate (4.55%)

n = the number of times interest is compounded per year (assuming yearly compounding, n=1)

t = the number of years

Plugging in the values, we get:

[tex]\$5,000 = \$2,500(\frac{1 + 0.0455}{1} )^(^1^t^)[/tex]

Simplifying, we get:

[tex]2 = (1.0455)^t[/tex]

Taking the natural logarithm of both sides, we get:

ln(2) = t ln(1.0455)

Solving for t, we get:

t = ln(2) / ln(1.0455) = 15.27 years

Therefore, it will take approximately 15.27 years for your investment to reach $5,000 at a growth rate of 4.55% per year.

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The choice which best describes the measure of center of these data is (d) Rome data center is "best-described" by median and  data center of "New-York" is "best-described" by mean.

In the table provided below, we see that the "IQR" for Rome is relatively large compared to the IQR for New York, which suggests that that there may be some skewness in the distribution of the Rome data. So, the median would be a better-measure of center than the mean.

On the other hand, the IQR for "New-York" is relatively small, which indicates that the data is more symmetric and the mean would be a better measure of center.

Therefore, the correct answer is (d).

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The given question is incomplete, the complete question is

The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy, or New York, New York:

                    High   Low    Q1     Q3    IQR    Median    Mean    σ

Rome              18       1         3       7        4         6.5          6.4    4.3

New York       14       1        4.5    8.5     4          5.5          6.1     3.2

Which of the choices below best describes how to measure the center of these data?

(a) Both centers are best described by the mean.

(b) Both centers are best described by the median.

(c) The Rome data center is best described by the mean. The New York data center is best described by the median.

(d) The Rome data center is best described by the median. The New York data center is best described by the mean.

The equations that will find the distance between the lions and giraffes include the following:

B. 11² + 16² = c².

D. 11(2) + 16(2) = 2.

In Mathematics and Science, distance can be defined as the amount of ground that is travelled by a physical object or body over a particular period of time and speed, irrespective of its direction, starting point or ending point.

Mathematically, the distance traveled by both the lions and giraffes when they are positioned one (1) unit apart can be calculated by using this equation:

11² + 16² = c²

Additionally, the distance traveled by both the lions and giraffes when they are positioned two (2) unit apart can be calculated by using this equation:

11(2) + 16(2) = c

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Answer:

A = P(1 + r/n)^(nt)

Where:

A = the future balance

P = the present balance ($1430.00)

r = the annual interest rate (2% or 0.02)

n = the number of times the interest is compounded per year (since it's compounded annually, n = 1)

t = the number of years (8 years in this case)

Plugging in the values into the formula:

A = 1430(1 + 0.02/1)^(1*8)

Simplifying the equation:

A = 1430(1.02)^8

Using a calculator or performing the calculations manually:

A ≈ 1430(1.171661)

A ≈ 1674.02

the balance after 8 years will be approximately $1674.02.

The equation relates the sound level, in decibels (dB), of a noise with an intensity of I to the smallest sound intensity that can be heard by the human ear, which is approximately 1 x 10^-12 watts/meter2.

Using this equation and the given maximum intensity of a car horn (0.01 watts/meter2), we can find the maximum sound level in decibels:

Sound level = 10 log (0.01/1 x 10^-12)
Sound level = 10 log (1 x 10^10)
Sound level = 100 dB

Therefore, the value that is closest to the maximum sound level in decibels of a car horn is 100 dB.

The formula that shows the dependence of the edge length a on the volume V of a cube is a = ∛V

In other words, to find the edge length of a cube, we take the cube root of its volume. This formula is derived from the formula for the volume of a cube, which is:

V = a³

Here, a is the length of each edge of the cube. Solving this equation for a, we get:

a = ∛V

This formula can be used to find the length of one edge of a cube when its volume is known. Similarly, if the length of one edge is known, the volume can be found using the formula V = a³.

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The correct statement regarding the maximum values of the quadratic functions is given as follows:

Function 1 has the larger maximum at (4, 1).

The standard definition of a quadratic function is given as follows:

y = ax² + bx + c.

The x-coordinate of the vertex of a quadratic function is given as follows:

x = -b/2a.

Hence, for each function, the x-coordinate of the vertex is given as follows:

Each function has a negative leading coefficient, hence the vertex represents a maximum value, and the y-coordinate is given as follows:

1 > -14, hence the correct statement is given as follows:

Function 1 has the larger maximum at (4, 1).

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John will be able to buy the 10 baseball bats for his team with some money left over is -$6.50 and David will be able to buy the 3 pairs of running shoes for his kids with some money left over is $12.30.

Based on the given information, we can calculate the total cost for each customer after factoring in the sales tax and discounts.

For John:
The cost of 10 baseball bats without any discounts or tax would be 10 * $25 = $250.
Since baseball bats are 5% off, John will get a discount of 0.05 * $250 = $12.50.
So, the cost of 10 baseball bats after discount is $250 - $12.50 = $237.50.
Adding 8% sales tax to this amount, the total cost for John will be $237.50 + (0.08 * $237.50) = $256.50.

For David:
The cost of 3 pairs of running shoes without any discounts or tax would be 3 * $50 = $150.
Since running shoes are 15% off, David will get a discount of 0.15 * $150 = $22.50.
So, the cost of 3 pairs of running shoes after discount is $150 - $22.50 = $127.50.
Adding 8% sales tax to this amount, the total cost for David will be $127.50 + (0.08 * $127.50) = $137.70.

Therefore, John will be able to buy the 10 baseball bats for his team with some money left over ($250 - $256.50 = -$6.50) and David will be able to buy the 3 pairs of running shoes for his kids with some money left over ($150 - $137.70 = $12.30).

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Answer:

12

Step-by-step explanation:

20-(5+(9-6)) = 20-(5+(3)) = 20-(8) = 12.

Alternatively, rewrite the question without parenthesis.

20-(5+(9-6)) = 20-(5+9-6) = 20-5-9+6 = 12.

The inequality that represents t, the number of hours past midnight, when the temperature was colder than -3 degrees Celsius is t > 8.

When the temperature drops at a steady rate of 1 degree Celsius per hour, it will take 8 hours to reach -3 degrees Celsius from the initial temperature of 5 degrees Celsius.

Therefore, any time past 8 hours after midnight will result in a temperature colder than -3 degrees Celsius.

Thus, the inequality t > 8 represents the number of hours past midnight when the temperature was colder than -3 degrees Celsius.

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The Pythagorean Theorem is used to prove that triangle FGH is a right triangle at angle F.

Similar triangles are triangles that share these two features listed as follows:

Considering the equivalent side lengths, the proportional relationship for the side lengths in this problem is given as follows:

4/4.8 = FH/3.6 = 5/6.

Hence the length FH is given as follows:

4/4.8 = FH/3.6

FH = 3.6 x 4/4.8

FH = 3.

If the Pythagorean Theorem is respected, the triangle is a right triangle, hence:

3² + 4² = 5²

9 + 16 = 25

25 = 25. -> right trianglge.

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Answer:

Step-by-step explanation:

A= 1/2 b h    b=6   h=2.5

= 7.5

Answer:

7.5 inches squared

Step-by-step explanation:

If only distances are provided, there are two methods to find the area of a triangle.  Which method to use depends on which lengths are provided:

Method 1: Base * Height

For any triangle, a line segment from one vertex that terminates perpendicularly to the leg across from it is considered a "height," and the leg that the "height" intersects is "base".  If both quantities are known, then the area of the triangle is base times height divided by 2 (sometimes stated as 1/2 times base times height).

In an equation format: [tex]Area_{triangle}=\frac{1}{2}base*height[/tex], often abbreviated as [tex]A_{triangle}=\frac{1}{2}bh[/tex]

For this example, the base at the bottom "6 in" has a corresponding height of "2.5 in", so

[tex]A_{triangle}=\frac{1}{2}(2.5~\text{in})(6~\text{in})[/tex]

[tex]A_{triangle}=7.5\text{ in}^2[/tex]

Method 2: Heron's Formula

If you are not provided any of the heights, but only the three legs of the triangle, Heron's formula provides a method of finding the area of the triangle.  It is significantly more complicated, and should only be used if one doesn't have one of the heights given.

Heron's formula gives the area of a triangle using the following formula:[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex] where a, b, and c, are the side lengths of the triangle, and "s" is the "semi-perimeter" (one half of the perimeter) of the triangle: [tex]s=\dfrac{a+b+c}{2}[/tex]

To be consistent, let's let a=3 in, b=5 in, and c=6 in.

Calculating the semi-perimeter of the given triangle first:

[tex]s=\dfrac{a+b+c}{2}=\dfrac{(3~\text{in})+(5~\text{in})+(6~\text{in})}{2}=\dfrac{14~\text{in}}{2}=7~\text{in}[/tex]

Calculating the area:

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]

[tex]A=\sqrt{(7~\text{in})((7~\text{in})-(3~\text{in}))((7~\text{in})-(5~\text{in}))((7~\text{in})-(6~\text{in}))}[/tex]

[tex]A=\sqrt{(7~\text{in})(4~\text{in)(2~\text{in})(1~\text{in})}[/tex]

[tex]A=\sqrt{56~\text{in}^4}[/tex]

[tex]A=7.48331477355...~\text{in}^2[/tex]

[tex]A\approx7.5~\text{in}^2[/tex]

Side note:  The 2.5 inches that they gave you in the problem isn't exactly 2.5 inches.  They rounded to one decimal place there.

The height of the CN tower which is 320m away from the Mr.Thayer is 555.85 meters.

Please look at the attached diagram for a clear explanation,

From the diagram point A represents, the Mr.Thayer's eyes, point B represents Mr.Thayer's foot, point C represents the base of the CN tower along with point E represents the top of the tower.

From the following diagram lets find out the height of the tower,

In right-angled triangle ADE, Tan theta = opposite/adjacent

So, Tan (60°) = DE/AD

√3 = DE/320m

DE = 320m x √3

DE= 554.25m

DE represents the height of the CN tower from the eyes of Mr.Thayer.

To find out the total height of the CN tower, the height of Mr.Thayer + the height of the CN tower from Mr. Thayer's eyes = 554.25m + 1.6m = 555.85m.

From the above explanation, we can conclude that the height of the CN tower from the base = 555.85m.

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Answer:

Top

Step-by-step explanation:

The closer the data points come to forming a straight line when plotted, the higher the correlation between the two variables, or the stronger the relationship. Therefore, the top option has the most closest lines to a linear function.

(Ex. 1) Y=4x-2

This example shows the corresponding possibilities of a linear regression because of the way the line is represented as graphed, making a straight line as similar to the top option

(Ex. 2) f(x) = x^2-5+15

This example dialates to a similar option like the third option, which isnt linear regression because of it being a quadratic function.

In a nut shell, all data plotted on the graph that are formed closer together and corresponds to a linear equation is a linear regression

The equation that represents the statement is

50 = x/3 and x is 150

A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.

Word problem are brain teaser that allows people to think properly. The first step is to represent the unknown by a letter.

Representing the number by x

therefore:

The product of 5 and 10 is 5 × 10

5 × 10 = 1/3 × x

50 = x/3

therefore the equation is 50 = x/3 and the value of x is 150.

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Answer:

1. First simplify the left-hand side of the equation using the trigonometric                      identity

sin(2t)cos(t) - cos(2t)sin(t) = sin(2t - t) = sin(t)

2. That way the equation becomes sin(t) = 0.

3. The solutions to this equation are t = kπ for all integers k.

4. Therefore, the general solution to the original equation is:

                   t = kπ or t = π/2 + kπ, where k is an integer.

Answer: attach an image

Step-by-step explanation:

To find the principal, we can use the formula for simple interest:

I = P*r*t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

We need to convert 82 days to years by dividing it by 365 (the number of days in a year):

t = 82/365

t = 0.2247

Now we can plug in the values we know and solve for P:

67.14 = P*0.0625*0.2247

P = 67.14/(0.0625*0.2247)

P = 1900

Therefore, the principal is $1900.

(a) Boris performed better on the aptitude test, since its z-score was higher.

(b) Callie performed better on the knowledge test.

(c) The z-score for the aptitude test was still higher than the z-score for the knowledge test, so Boris performed better on the aptitude test.

(a) To determine which test Boris performed better on, we need to compare his z-scores for the knowledge test and the aptitude test.

For the knowledge test, his z-score is calculated as:

z = (55 - 60) / 3 = -1.67

For the aptitude test, his z-score is:

z = (106 - 110) / 6.8 = -0.59

Since the z-score for the aptitude test is higher than the z-score for the knowledge test, Boris performed better on the aptitude test.

(b) To determine which test Callie performed better on, we need to compare her z-scores for the knowledge test and the aptitude test.

For the knowledge test, her z-score is:

z = (67 - 60) / 3 = 2.33

For the aptitude test, her z-score is:

z = (119 - 110) / 6.8 = 1.32

Since the z-score for the knowledge test is higher than the z-score for the aptitude test, Callie performed better on the knowledge test.

(c) Boris' z-score on the logic test (-0.43) is unrelated to his performance on the knowledge and aptitude tests, so it does not change the answer to which test he performed better on. The z-score for the aptitude test was still higher than the z-score for the knowledge test, so Boris performed better on the aptitude test.

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Answer:

x = (-2 + 3) * (4-(-8))

Step-by-step explanation:

An interest rate of approximately 2.40% per annum, compounded annually, is required to double an investment in 29 years.

Let "r" be the annual interest rate, then the investment will double after 29 years if (1 + r)^29 = 2. Solving this equation, we get r ≈ 0.0240 or 2.40% (rounded to two decimal places) as the required annual interest rate. This means that if the investment is compounded annually at this rate, it will double after 29 years.

Alternatively, we can use the formula for compound interest, A = P(1 + r/n)^(nt), where A is the future value, P is the present value, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

We want to find the interest rate, r, that will double the investment, so we can set A = 2P, t = 29, n = 1 (compounded annually), and solve for r. This gives us r ≈ 0.0240 or 2.40%.

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The only possible value of k is k = 336675.

Suppose, for the sake of contradiction, that k is a prime such that k(k+2013) is a perfect square. Let's denote the perfect square as m^2, where m is a positive integer. Then we can write:

k(k+2013) = m^2

Expanding the left-hand side, we get:

k^2 + 2013k = m^2

Moving all the terms to one side, we get:

k^2 - m^2 + 2013k = 0

Using the difference of squares, we can factor this as:

(k - m)(k + m) + 2013k = 0

Since k is a prime, it must be greater than 1. Thus, k + m and k - m are both integers greater than 1 whose product is divisible by k. This means that at least one of them is divisible by k. Since k is prime, this can only happen if either k + m or km is equal to k. Thus, we have two cases to consider:

Case 1: k + m = k, which implies m = 0. But m is a positive integer, so this is impossible.

Case 2: k - m = k, which implies m = 0. But again, m is a positive integer, so this is impossible.

Therefore, our assumption that k is prime leads to a contradiction, and we conclude that k cannot be prime.

To find the correct value of k, note that k and k+2013 share a common factor of 3. Thus, we can write k = 3n and k+2013 = 3m for some integers n and m. Substituting these expressions into the equation k(k+2013) = m^2 and simplifying, we get:

3n(3n+2013) = m^2

n(3n+2013/3) = m^2/3

n(n+671) = m^2/3

Since n and n+671 are relatively prime, both n and n+671 must be perfect squares. Let's write n = p^2 and n+671 = q^2 for some integers p and q. Then we have:

q^2 - p^2 = 671

Using the difference of squares again, we can factor this as:

(q + p)(q - p) = 671

Since 671 is a prime, its only factors are 1 and 671. Therefore, we have two possibilities:

q + p = 671, q - p = 1, which implies q = 336, p = 335, n = p^2 = 112225, k = 3n = 336675

q + p = 671, q - p = 671, which implies q = 336 + 335 = 671, p = 0, which is not a valid solution since n cannot be negative.

k = 336675. is the best possible answer.

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Based on the observed outcome, it is therefore very or highly unlikely that Romain's probability is equal to that of the other brothers, and thus  it is possible that Romain is cheating.

Beneath the assumption that each brother has an break even with chance of getting picked in each draw, the likelihood of Romain not getting picked indeed once out of 12 times is:

P(Romain not picked) = (2/3)¹²

                                  = 0.0077

This is one that is less than 1%, which suggests that the observed result is made up of a likelihood less than 1% beneath the given speculation. Therefore, we need to reject the hypothesis that each brother has an equal chance of getting picked in all of the draw.

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See text below

Alexandre has two brothers: Hugo and Romain. Every day Romain draws a name out of a hat to randomly select one of the three brothers to wash the dishes. Alexandre suspected that Romain is cheating, so he kept track of the draws, and found that out of 12 draws, Romain didn't get picked even once. 1 Let's test the hypothesis that each brother has an equal chance of of getting picked in each draw versus 3 the alternative that Romain's probability is lower. Assuming the hypothesis is correct, what is the probability of Romain not getting picked even once out of 12 times? Round your answer, if necessary, to the nearest tenth of a percent. Let's agree that if the observed outcome has a probability less than 1% under the tested hypothesis, we will reject the hypothesis. What should we conclude regarding the hypothesis? Choose 1 answer: We cannot reject the hypothesis. B We should reject the hypothesis.

A cube is a three dimensional figure with six square faces that are all congruent, meaning they are identical in shape and size.

Each face of the cube is perpendicular to the adjacent faces, forming right angles where they meet. The cube is a highly symmetrical shape, with all edges and angles equal in length and measure respectively. Its regularity and symmetry make it a popular shape in mathematics and engineering, often used as a model for buildings, containers, and other structures.

The cube's unique properties also make it an ideal shape for games, puzzles, and art, showcasing its versatility and significance in various fields.

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The answer of addition is 94.

The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three.

To add 8 and 78, we can start by adding the ones place digits, which are 8 and 7.

8 + 7 = 15

Since 15 is greater than 10, we need to regroup 10 ones as 1 ten and carry it over to the tens place. We can represent this with place value blocks by moving a rod of 10 ones from the ones place to the tens place.

So we have:

 8

+78

---

```

 8

+78

---

 16 (write 6 in the ones place and carry 1 to the tens place)

```

Now we can add the tens place digits, which are 1 (carried over) and 8:

1 + 8 = 9

So the final result is:

 8

+78

-----

86

Therefore, 8 plus 78, plus 7 is:

```

 8

+78

+ 7

---

 94

```

So the answer of addition is 94.

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I'm sorry, but I cannot answer your question without a net or a description of the solid figure. Can you please provide more information or context?

The following is the value of x and mBD: x = 83/6 and mBD⌢ = 83°.

Given circle E (⊙E) with diameter AC, we have the following information:

1. m∠CED = (3x)°
2. m∠BEC = (3x + 2)°
3. m∠AEB = (6x + 7)°

Since AC is the diameter of the circle, the inscribed angle ∠AEB is subtended by the diameter and thus forms a semicircle. In a semicircle, the inscribed angle is always a right angle. Therefore, m∠AEB = 90°. We can now set up the equation:

(6x + 7)° = 90°

Solving for x:
6x = 83
x = 83/6

Now, we need to find the measure of arc BD (mBD⌢). We can do this by finding the measure of angle BEC, as the measure of an inscribed angle is half the measure of its intercepted arc.

m∠BEC = (3x + 2)° = (3(83/6) + 2)° = (83/2)°

Since the measure of an inscribed angle is half the measure of its intercepted arc:

mBD⌢ = 2(m∠BEC) = 2(83/2)° = 83°

So, x = 83/6 and mBD⌢ = 83°.

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