The measure of an angle is forty-nine times the measure of its supplementary angle. What is the measure of each angle?

Answer:

Dividend: 3 1/2

Divisor: 1 3/4

To solve this problem, we can convert both mixed numbers to improper fractions:

Dividend: 7/2

Divisor: 7/4

Then we can divide the two fractions:

(7/2) ÷ (7/4) = (7/2) x (4/7) = 2

So the quotient is 2, which is a whole number. Therefore, the division problem 3 1/2 ÷ 1 3/4 = 2 has been solved.

An expression which can be used to determine the total cost of the project if the project is not completed by the due date is: D) x - 0.15x.

In Mathematics, a mathematical expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Since the cost of the streetcar project is x dollars and the cost of the project is reduced by 15% if the project is not completed by the due date, a mathematical expression which can be used to determine the total cost of the project;

Total cost = x - 15% of x

Total cost = x - (15/100 × x)

Total cost = x - (0.15 × x)

Total cost = x - 0.15x

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Answer:

14+3*x = 10-6*x

Step-by-step explanation:fourteen more means 14+ 3 times a number means 3 multiplied by a number x is the number of your choice and 10 less means 10 - and 6 times the number means 6*x

Answer: Y = 7/2x -5

Step-by-step explanation:

slope intercept equation:

y = mx + b

plug in what you are given

y = (7/2)x (-5)

m<A, which is 48 degree.

The values of mL and mJ are 55 and 61 degrees, respectively.

Since vertical angles are equal in magnitude and are created by intersecting two lines, they are known as the opposing angles.

what are the explanation of the problems?

1.Angles in the vertical plane coincide. They are equal in size, thus this indicates. Calculate x x = 4x - 24 by putting them on an equal footing. In the equation, deduct x from both sides.

o = 3x - 24 On both sides, add 24.

24 = 3x Divide both sides by 3

Multiply both sides by 3 

8 to get x 

m<A, which is 8.

4x-24

=3*8+24=24+24=48 degree

2.We can thus write,

The angles L and Z are vertical.

∠L = 2x + 9 and,

∠Z = 3x - 14.

Given that both angles are vertical,

∠L = ∠Z

2x + 9 = 3x - 14

Continuing to solve

3x - 2x = 9 + 14

x = 23

The value of L is therefore,

= 2(23)+9

= 46+9

= 55°

Angle L has a value of 55°.

2. Y and J are equal because they are both vertical angles.

∠Y = 7x + 12

∠J = 10x - 9

∠Y = ∠J

7x + 12 = 10x - 9

Continuing to solve

3x = 21

x = 7

So, the value of ∠J is, = 10(7) - 9 = 70 - 9 = 61°

The value of ∠J is 61°.

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Answer:

\(sin^2x\)

Step-by-step explanation:

To simplify the expression (1 - cos x)(1 + cos x), we can use the difference of squares identity, which states that \(a^2 - b^2 = (a + b)(a - b).\)

Let's apply this identity to the given expression:

\((1 - cos x)(1 + cos x) = 1^2 - (cos x)^2\)

Now, we can simplify further by using the trigonometric identity \(cos^2(x) + sin^2(x) = 1.\) By rearranging this identity, we have \(cos^2(x) = 1 - sin^2(x).\)

Substituting this into our expression, we get:

\(1^2 - (cos x)^2 = 1 - (1 - sin^2(x))\)

Simplifying further:

\(1 - (1 - sin^2(x)) = 1 - 1 + sin^2(x)\)

Finally, we get the simplified expression:

\((1 - cos x)(1 + cos x) = sin^2(x)\)

To simplify the expression \(\sf\:(1-\cos x)(1+\cos x)\\\), follow these steps:

Step 1: Apply the distributive property.

\(\longrightarrow\sf\:(1-\cos x)(1+\cos x) = 1 \cdot 1 + 1 \cdot \\\)\(\sf\: \cos x -\cos x \cdot 1 - \cos x \cdot \cos x\\\)

Step 2: Simplify the terms.

\(\longrightarrow\sf\:1 + \cos x - \cos x - \cos^2 x\\\)

Step 3: Combine like terms.

\(\longrightarrow\sf\:1 - \cos^2 x\\\)

Step 4: Apply the identity \(\sf\:\cos^2 x = 1 - \sin^2 x\\\).

\(\sf\:1 - (1 - \sin^2 x)\\\)

Step 5: Simplify further.

\(\longrightarrow\sf\:1 - 1 + \sin^2 x\\\)

Step 6: Final result.

\(\sf\red\bigstar{\boxed{\sin^2 x}}\\\)

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

23 feet

Step-by-step explanation:

According to the scenario, computation of the given data are s follows,

Total rope = 46 feet

Number of person = 2

So, we can calculate the amount of rope each person get by using following formula,

Each person quantity = Total rope ÷ Number of person

By putting the value in the formula, we get

Each person quantity = 46 feet ÷ 2

= 23 feet

Hence, each person gets 23 feet of rope.

Answer:

choice 1) 312 cm²

Step-by-step explanation:

area = (16 x 12) + (10 x 12) = 312 cm²

Answer:

312

Step-by-step explanation:

triangle：

10x12/2=60

two triangle：

60x2=120

rectangle：

16x12=192

add up：

120+192=312

Answer:

The solution to the recurrence relation is given by an = 2^(n+1) - 1.

Step-by-step explanation:

(a) To solve the recurrence relation an = an-2 + 4, with initial conditions a1 = 3 and a2 = 5, we'll consider two cases: one for when n is even and one for when n is odd.

For n even:

Substituting n = 2k (where k is a positive integer) into the recurrence relation, we get:

a2k = a2k-2 + 4

Now let's write out a few terms to observe the pattern:

a2 = a0 + 4

a4 = a2 + 4

a6 = a4 + 4

...

We notice that a2k = a0 + 4k for even values of k.

Using the initial condition a2 = 5, we can find a0:

a2 = a0 + 4(1)

5 = a0 + 4

a0 = 1

Therefore, for even values of n, the solution is given by an = 1 + 4k.

For n odd:

Substituting n = 2k + 1 (where k is a non-negative integer) into the recurrence relation, we get:

a2k+1 = a2k-1 + 4

Again, let's write out a few terms to observe the pattern:

a3 = a1 + 4

a5 = a3 + 4

a7 = a5 + 4

...

We see that a2k+1 = a1 + 4k for odd values of k.

Using the initial condition a1 = 3, we find:

a3 = a1 + 4(1)

a3 = 3 + 4

a3 = 7

Therefore, for odd values of n, the solution is given by an = 3 + 4k.

(b) To solve the recurrence relation an = 2an-1 + 1, with initial condition a1 = 1, we'll find a general expression for an.

Let's write out a few terms to observe the pattern:

a2 = 2a1 + 1

a3 = 2a2 + 1

a4 = 2a3 + 1

...

We can see that each term is one more than twice the previous term.

By substituting repeatedly, we can express an in terms of a1:

an = 2(2(2(...2(a1) + 1)...)) + 1

= 2^n * a1 + (2^n - 1)

Using the initial condition a1 = 1, we have:

an = 2^n * 1 + (2^n - 1)

= 2^n + 2^n - 1

= 2 * 2^n - 1

Therefore, the solution to the recurrence relation is given by an = 2^(n+1) - 1.

Answer:

the 4th one

Step-by-step explanation:

(a) Linear differential equation of second order

(b) Linear differential equation of second order

(c) Linear differential equation of fourth order

(d) Non-linear differential equation of first order

(e) Non-linear differential equation of second order

(f) Linear differential equation of third order

(g) (a) and (d) are initial value problems

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The volume enclosed by the two curves when revolved about the x-axis is \(\(\frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\).\) To find the volume when the area enclosed by the graphs of \(\(y = x^2\)\)and \(\(y = \frac{3}{x^3}\)\) is revolved about the x-axis, we can use the method of cylindrical shells.

First, let's find the points of intersection between the two curves by setting them equal to each other:

\(\[x^2 = \frac{3}{x^3}\]\)

To simplify this equation, we can multiply both sides by \(\(x^3\)\):

\(\[x^5 = 3\]\)

Now, taking the fifth root of both sides:

\(\[x = \sqrt[5]{3}\]\)

So the two curves intersect at \(\(x = \sqrt[5]{3}\)\).

To calculate the volume area enclosed by the graphs of \(\(y = x^2\)\)and \(\(y = \frac{3}{x^3}\)\) is revolved about the x-axis, we need to integrate the circumference of each cylindrical shell multiplied by its height. The height of each shell is the difference in the y-values of the two curves, and the circumference is\(\(2\pi x\)\).

Let's integrate from \(\(x = 0\)\) to \(\(x = \sqrt[5]{3}\)\):

\(\[V = \int_0^{\sqrt[5]{3}} 2\pi x \left(\frac{3}{x^3} - x^2\right) \, dx\]\)

Simplifying this expression:

\(\[V = 2\pi \int_0^{\sqrt[5]{3}} \left(\frac{3}{x} - x^3\right) \, dx\]\)

Integrating each term separately:

\(\[V = 2\pi \left[3 \ln|x| - \frac{x^4}{4}\right]_0^{\sqrt[5]{3}}\]\)

Plugging in the limits of integration:

\(\[V = 2\pi \left[3 \ln|\sqrt[5]{3}| - \frac{\sqrt[5]{3}^4}{4}\right] - 2\pi \left[3 \ln|0| - \frac{0^4}{4}\right]\]\)

Since \(\(\ln|0|\)\)is undefined, the second term on the right side is zero:

\(\[V = 2\pi \left[3 \ln|\sqrt[5]{3}| - \frac{\sqrt[5]{3}^4}{4}\right]\]\)

Simplifying further:

\(\[V = 2\pi \left[3 \ln 3^{\frac{1}{5}} - \frac{3}{4} \cdot 3^{\frac{4}{5}}\right]\]\)

Using the properties of logarithms, we can simplify the first term:

\(\[V = 2\pi \left[3 \cdot \frac{1}{5} \ln 3 - \frac{3}{4} \cdot 3^{\frac{4}{5}}\right]\]\)

\(\[V = \frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\]\)

So the volume enclosed by the two curves when revolved about the x-axis is \(\(\frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\).\)

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When two marbles are selected at random without replacement from a box containing marbles numbered 1, 2, 3, 4, and 5, the probability distribution for the maximum value of the two marbles is uniform. Each possible maximum value (1, 2, 3, 4, or 5) has an equal probability of 1/5.

The probability distribution is the list of probabilities for each possible value of the random variable. For this problem, the random variable is the maximum value of the two marbles selected.

To find the probability distribution for the maximum of the two values on the marbles, we need to consider all possible outcomes and their corresponding probabilities.

Let's analyze each possible outcome:

This can only occur if we select the marble numbered 1 first, followed by any other marble. The probability of this is (1/5) * (4/4) = 1/5.

This can occur if we select the marble numbered 2 first, followed by either the marble numbered 1, 3, 4, or 5. The probability of this is (1/5) * (4/4) = 1/5.

This can occur if we select the marble numbered 3 first, followed by either the marble numbered 1, 2, 4, or 5. The probability of this is (1/5) * (4/4) = 1/5.

This can occur if we select the marble numbered 4 first, followed by either the marble numbered 1, 2, 3, or 5. The probability of this is (1/5) * (4/4) = 1/5.

This can occur if we select the marble numbered 5 first, followed by any other marble. The probability of this is (1/5) * (4/4) = 1/5.

Now, we can summarize the probability distribution for the maximum of the two values on the marbles:

Maximum Value Probability

       1                     1/5

       2                     1/5

       3                     1/5

       4                     1/5

       5                          1/5

Therefore, the probability distribution for the maximum of the two values on the marbles is uniform, with an equal probability of 1/5 for each possible maximum value.

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Given that: Five marbles, numbered 1, 2, 3, 4, and 5, are placed in a box. Two marbles are selected at random without replacement.

We are to find the probability distribution for the maximum of the two values on the marbles.

To find the probability distribution for the maximum of the two values on the marbles, we consider all the possible pairs that can be formed from the five marbles i.e.

(1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3,5), and (4,5).

The maximum of the two values on the marbles are: 2, 3, 4, 5, 3, 4, 5, 4, 5, and 5 respectively.

Hence the probability distribution table can be obtained as shown below:

Maximum of the two values on the marbles, x    Probability, P(x)2     1/103     2/104     3/105     4/10

Thus the probability distribution for the maximum of the two values on the marbles is shown above.

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Answer:

x = 57°

Step-by-step explanation:

23° + 100° + x = 180°

123° + x = 180°

-123         -123

x = 57°

Hope this helps!

Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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A. Distribution’s mean and standard deviation are  0.75 and 0.87 respectively.

B. The likelihood function is given by: L(π|y=1)π-π^2.

A. Assuming π = 0.50, the probability of getting y = 0 is equal to (1 - π)^y, or (1 - 0.50)^0 = 1. The probability of getting y = 1 is equal to (1 - π)^y * π, or (1 - 0.50)^1 * 0.50 = 0.50. The probability of getting y = 2 is equal to (1 - π)^y * (π)^(y-1), or (1 - 0.50)^2 * 0.50^(2-1) = 0.25.

The mean of the distribution is equal to the sum of all possible values of y multiplied by their respective probabilities, or (0 * 1) + (1 * 0.50) + (2 * 0.25) = 0.75.

The standard deviation of the distribution is equal to the square root of the sum of all possible values of y squared multiplied by their respective probabilities, or \(\sqrt{((0^2 * 1) + (1^2 * 0.50) + (2^2 * 0.25))}\) = 0.87.

B. . The likelihood function is a function of π that gives the probability of observing y=1 given a particular value of π. The likelihood function is given by:

L(π|y=1)=2π(1-π)=π-π^2.

The graph of the likelihood function is a parabola that opens downward. The maximum of the likelihood function occurs at the value of π that makes L(π|y=1) a maximum, which is the maximum likelihood estimate (MLE) of π. The MLE is the value of π that maximizes the likelihood function and is given by ˆ=π.

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To find a reasonable estimate for the total time of the album, we can add the times of the shortest and longest songs and divide by 2 to find the average time per song, and then multiply by the total number of songs on the album.

The shortest song on the album is 1 minute and 14 seconds, which is equivalent to 74 seconds.

The longest song on the album is 5 minutes and 54 seconds, which is equivalent to 354 seconds.

Therefore, the average time per song is:

(74 + 354) / 2 = 214 seconds

And the total time of the album is approximately:

13 songs x 214 seconds/song = 2,782 seconds

Converting this to minutes and seconds, we get:

2,782 seconds = 46 minutes and 22 seconds

So a reasonable estimate for the total time of the album is about 46 minutes and 22 seconds.

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The paint cans and the spaces serve as examples of equivalent ratios. 5.5 cans of paint will be required to cover 2200 sq. unit.

Two ratios that have the same values are said to be equivalent. The same number can be used to multiply or divide both sums to get an equivalent ratio. The method is the same as determining equivalent fractions. When two or more ratios are reduced to their most basic form, they have the same value. Examples of equivalent ratios are 1:2, 2:4, and 4:8. In their most basic form, all three ratios have the same value, which is 1:2. They are in proportion if two ratios are equal. Equations in algebra are said to be equivalent if their solutions or roots are equal. When the same amount or expression is added to or removed from both sides of an equation, the result is the same.

To paint a 2200 square unit space, 5.5 cans are required.

The given parameter is:

Cans: Area\(=1:400\)

Express as fraction

Cans/Area\(=1/400\)

Multiply both sides by Area

Cans\(=\frac{1}{400}*Area\)

When the area is 2200, we have:

Cans\(=\frac{1}{400}*2200\)

Cans\(=5.5\)

5.5 cans are therefore required to paint a 2200 units square space.

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By applying dilatation and congruency theorem, it can be concluded that the distance between points R and R' is 3 units (option A).

Dilation is a transformation of a geometric shape, either becoming larger or smaller, without changing the original shape using a certain scale factor.

Two shapes are said to be congruent if a pair of corresponding sides have the same ratio and the corresponding angles have the same measure.

From the problem we obtained the following information:

QR is dilated to create Q'R' ⇒ QR // Q'R'

The dilatation factor is 1.5 ⇒ Q'R'/QR = 1.5

Now we look at the ΔTRQ and ΔTR'Q':

QR // Q'R'

∠TRQ = ∠TR'Q'

So ΔTRQ is congruent to ΔTR'Q' and TR'/TR = Q'R'/QR

Now we can calculate y using this equation:

   TR'/TR = Q'R'/QR

(6 + y) / 6 = 1.5

      6 + y = 9

            y = 3

Thus, the distance between points R and R' is 3 units.

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Answer:

4 43/50

Hope this help <3

Answer:

243 / 50

Step-by-step explanation:

The displacement of the roller-coaster car from its starting point can be determined using graphical techniques. The main answer is that the displacement is approximately 157.5 ft in magnitude and in the direction opposite to the car's initial motion.

To explain further, we can break down the motion into horizontal and vertical components. The car initially moves 200 ft horizontally, which means its horizontal displacement is 200 ft. Then, it rises 135 ft at an angle of 30.0° above the horizontal. This vertical displacement can be calculated as 135 ft * sin(30.0°) = 67.5 ft upward.

Next, the car travels 135 ft at an angle of 40.0° downward. This contributes to a vertical displacement of 135 ft * sin(40.0°) = 87.2 ft downward.

To find the total vertical displacement, we subtract the downward displacement from the upward displacement: 67.5 ft - 87.2 ft = -19.7 ft.

Finally, we can use the Pythagorean theorem to calculate the magnitude of the displacement. The horizontal displacement is 200 ft and the vertical displacement is -19.7 ft. So, the magnitude of the displacement is sqrt((200 ft)^2 + (-19.7 ft)^2) ≈ 157.5 ft.

Since the vertical displacement is negative, the displacement is in the direction opposite to the initial motion of the car.

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Answer:

The area is 12.56 units^2 (same as circumference?)

Step-by-step explanation:

Assuming pi is 3.14, the equation for the circumference is C = 2 pi r

Fill it out for the radius (r)

12.56 = 2 3.14 r

12.56 = 6.28 r

r = 2

With the radius, the equation for the area is A = pi r^2

Fill it out for the area

A = 3.14 2^2

A = 3.14 4

A = 12.56

In case of a normal distribution, the mean, median, and mode are equal . So option A is correct

What is normal distribution?

The most significant continuous probability distribution in probability theory and statistics is the normal distribution, also referred to as the gaussian distribution. On occasion, it is referred to as a bell curve.

The probability distribution of data is expressed mathematically as a normal distribution. It is symmetrical from both ends and has only one mode. The equal mean, median, and mode of the given data are highlighted by the normal distribution.

The options are b) It has two modes. c) It is asymmetrical. and d) the points of the curve meet the x-axis at z are incorrect.

Therefore, The correct option is A, the equal mean, median, and mode of the given data are highlighted by the normal distribution.

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Answer:

Only n if 2n is/3 when 2nis divide by 3

Answer:3

Step-by-step explanation:

you could only divide 2n in 3 was there so it would be three

Answer:

7:4 would be the ratio I think

Using a unitary method, we have identified that the smaller pot has more water.

To compare the amount of water in the two pots, we need to find a common unit of measurement. In this case, both pots are measured in cups, so we can simply compare the number of cups in each pot. The chef filled the larger pot with 3.7 cups of water, and the smaller pot with 7.3 cups of water.

Now, we can use a unitary method to compare the two quantities. Let's assume that one cup is our unit of measurement. To find out how many cups of water are in the smaller pot, we can divide 7.3 by 1 cup. This gives us 7.3 cups of water. To find out how many cups of water are in the larger pot, we can divide 3.7 by 1 cup. This gives us 3.7 cups of water.

As we can see, the smaller pot has more water than the larger pot.

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Answer:

4 1/2 <h

Step-by-step explanation:

Answer:

$11

Step-by-step explanation:

\(\left\begin{array}{c|ccc}&$Lose \$25&$Gain \$5&$Gain \$45\\$Stock ABC&40\%&15\%&45\%\end{array}\right\)

We want to calculate the expected gain or loss of Stock ABC with the probabilities above.

Note that loss is written in negative.

\(E$xpected Value =$ (-25 \times 40\%)+(5 \times 15\%) + (45 \times 45\%)\\=(-25 \times 0.4)+(5 \times 0.15)+(45 \times 0.45)\\=-10+0.75+20.25\\=\$11\)

Stock ABC has an expected gain of $11.

The probability that the geyser will erupt in the next hour is 0.6321 or 63.21%.

To find the probability that the geyser will erupt in the next hour, we can use the exponential distribution formula. The terms involved in this problem are:

1. Exponential distribution

2. Mean time between eruptions (72 minutes)

3. Probability

Step 1: Convert the given hour to minutes. There are 60 minutes in an hour.

Step 2: Calculate the parameter for the exponential distribution. Since the mean time between eruptions is 72 minutes, the parameter (λ) is equal to the reciprocal of the mean, which is 1/72.

Step 3: Use the cumulative distribution function (CDF) formula for the exponential distribution to find the probability of the geyser erupting within the next 60 minutes.

\(CDF(x) = 1 - e^{(-λx)}\)

Step 4: Plug in the values into the formula:

\(CDF(60) = 1 - e^{(-1/72 * 60)}\)

Step 5: Calculate the result:

\(CDF(60) ≈ 1 - e^{(-60/72)} ≈ 1 - e^{(-5/6) }≈ 0.6321\)

So, the probability that the geyser will erupt in the next hour is approximately 0.6321 or 63.21%.

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