if 5 books are picked at random from a shelf containing 8 novels, 3 books of poems, and a dictionary, what is the probability that

Answer:

csc(t) = -3/2

Step-by-step explanation:

Given sin(-t) = 2/3, we can find the value of csc(t) as follows:

sin(-t) = 2/3

sin(t) = -2/3 (since the sine function is an odd function)

Since csc(t) = 1/sin(t), we have:

csc(t) = 1/sin(t) = 1/(-2/3) = -3/2

Answer:

[tex]\displaystyle \csc(t)=-\frac{3}{2}[/tex]

Step-by-step explanation:

[tex]\displaystyle \sin(-t)=\frac{2}{3}\\\\\sin(t)=-\frac{2}{3}\\ \\\frac{1}{\sin(t)}=\frac{1}{-\frac{2}{3}}\\\\\\\csc(t)=-\frac{3}{2}[/tex]

The second step can be done because sin(-t) is an odd function.

The distance of the rope to the base of the flagpole is 27.05 ft.

A rope is tied from the top of a flag pole to the ground. If the rope is 28 ft long and makes a 15 degree angle with the ground, the distance of the rope to the base of the flag pole can be calculated as follows:

The situation forms a right angle triangle.

Hence,

using trigonometric ratios,

cos 15° = adjacent / hypotenuse

cos 15° = x / 28

cross multiply

Therefore,

x = 28 cos 15

x = 28 × 0.96592582628

x =  27.0459231361

x = 27.05 ft

Therefore,

distance of the flagpole to the base of the ground  = 27.05 ft

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The difference in height between Sarah and Tayjen kite is 1060 cm (10.6 m)

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

1 m = 100 cm

Sara's kite flew 48 meters in the air. Hence:

Height of Sarah kite = 48 m = 48 m * 100 cm per m = 4800 cm

Tayjen's kite flew 5,860 centimeters in the air. Therefore:

Difference in height = 5860 - 4800 = 1060 cm = 1060 cm * 1 m per 100 cm = 10.6 m

The difference in height is 1060 cm (10.6 m)

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To design a pool that would fit inside Mr. Taylor's backyard, you would need to know the dimensions of the available space.

You would also need to take into account any landscaping, slopes, and other features of the backyard that could impact the design and construction of the pool.

Once you have the necessary information about the backyard, you can start designing a pool that would be accessible and realistic. Here are some tips and guidelines for designing a pool.

Choose a shape and size that fits the available space and is functional. Rectangular or oval shapes are typically the most common and practical, but other shapes can be used as well.

Consider the depth of the pool. For safety reasons, the depth should be at least 4 feet at the shallow end and 8 feet at the deep end. You may also want to consider adding a gradual slope in the pool to make it easier for people to enter and exit.

Choose the material for the pool. Concrete, fiberglass, and vinyl are common materials used for pools. Each material has its own advantages and disadvantages, so research the options and choose the one that is best for your design and budget.

Consider adding features such as a diving board, slide, or waterfall to make the pool more enjoyable and attractive.

Calculate the amount of water it will take to fill the pool. This will depend on the size and depth of the pool. To get an estimate, you can use online pool volume calculators or consult with a pool contractor.

Once you have a design for the pool and know how much water it will take to fill, you can determine if it is feasible and within Mr. Taylor's budget.

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The number of seconds does the firework hit the ground is 3 seconds

From the information given, we have the quadratic function;

y = -16x² + 32x + 48

To determine the value of x , let's reduce the expression, we get;

-2x² + 4x + 6

Now, let's factorize the terms

Multiply the coefficient by the constant and find the pair factors

-2x² + 6x - 2x + 6

Factorize in pairs, we get;

-2x(x -3) - 2(x -3)

Then, we have the expressions

-2x - 2 = 0

solve for x

x = -1

x - 3 = 0

x = 3

Hence, the value is 3 seconds

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Answer:

3

Step-by-step explanation:

i took the test

a) The distribution is roughly symmetric and bimodal. b) The histogram has two modes, which may be due to the different shoe size scales used for men and women in the U.S. but not in Europe.

The histogram of European shoe sizes of 269 male and female college students converted from their reported US shoe sizes is not visible based on the information provided, but the questions are clear.

a) The shape of the distribution is not visible, but it is mentioned that it is "roughly symmetric and bimodal".

b) There are two modes in the histogram. This could be because shoe sizes in the United States are defined differently for men and women, but not in Europe. As a result, the histogram of the distribution of European shoe sizes for both men and women may show two distinct peaks.

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By factorizing the polynomials, the HCF of the expressions 3(x-y)^2 and 12x^2(x^2+y^2+2xy) is 3.

HCF or Highest Common Factor is the greatest number which divides each of the two or more numbers. HCF is also called the Greatest Common Measure (GCM) and Greatest Common Divisor(GCD).

To obtain the HCF of algebraic expression, take the common of all the prime factors of two polynomials.

We first factorize the given algebraic expressions:

3(x - y)^2 = 3 × (x - y) × (x - y)

12x^2(x^2+y^2+2xy) = 12x^2(x + y)^2

12x^2(x + y)^2 = 2 × 2 × 3 × x × x ×  (x + y) × (x + y)

so, the highest common factor between the both expressions is 3.

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Answer:

100 dispenses

Step-by-step explanation:

To check the answer:

Gumballs: 200 - (1*100) = 100

Explanation: 200 gumballs - (1 gumball * 100 dispenses) = 100 gumballs left.

Chocolate Candies: 900 - (8*100) = 100

Explanation: 900 candies - (8 candies * 100 dispenses) = 100 candies left.

Answer:

  100

Step-by-step explanation:

Given a candy machine with 200 gumballs dispensed 1 at a time, and another with 900 chocolates dispensed 8 at a time, you want to know how many dispenses from each will result in equal counts left in the machines.

The number of remaining gumballs after d dispenses is ...

  g = 200 -d

The number of remaining chocolates after d dispenses is ...

  c = 900 -8d

The number remaining in each machine will be equal when ...

  g = c

  200 -d = 900 -8d . . . . . substitute the above expressions

  7d = 700 . . . . . . . . . . add 8d -200

  d = 100 . . . . . . . . . divide by 7

100 dispenses from each machine will make the number of candies in the machines equal.

Given the equation AB = BC, we want to find B, assuming that A, B, and C are square matrices and B is invertible. We can conclude that B is invertible.

To do this, we will use the fact that if A is invertible, then we can multiply both sides of the equation by its inverse to isolate B:

AB = BC

[tex]A^-1 AB = A^-1 BC[/tex]

B = A^-1 BC

Here, A^-1 is the inverse of A, and it satisfies the equation[tex]A A^-1 = A^-1 A[/tex]= I, where I is the identity matrix. By multiplying both sides of the equation [tex]AB = BC by A^-1[/tex], we obtain the expression for B.

Now, let's consider the invertibility of B. If A and B are invertible, then the product AB is also invertible. This is because the product of two invertible matrices is invertible, and its inverse is given by the formula [tex](AB)^-1 = B^-1A^-1[/tex]. In this case, since[tex]B = A^-1 BC,[/tex] we can conclude that B is invertible.

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706.5 in³

The volume of a shape describes the amount of space a shape takes up.

Volume Formula

For a cylinder, the volume formula is V = πr²h. In this formula, V represents the total volume. Additionally, π represents the constant pi, which is approximately 3.14. The variable r represents the radius. Remember that radius is the distance from the center of the circle to the edge. Finally, h is the height of the cylinder.

Solving for Volume

The diagram shows that the radius is 5in. We know this because the distance from the center to the edge of the circle is 5in. Additionally, the height is 9in. Now, we can plug these values into the formula.

For this calculation, I used 3.14 for π. The unrounded volume in terms of pi is 225π.

The volume of the cylinder is 706.5 in³.

The tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

What is Circle?

A circle is a two-dimensional geometric shape that is defined as the set of all points in a plane that are a fixed distance away from a given point, called the center of the circle. This distance is known as the radius of the circle.

A circle can also be defined as the locus of a point that moves in a plane in such a way that its distance from a fixed point is constant. The constant distance is the radius of the circle.

The minute hand on a clock makes a full rotation in 60 minutes, which means it travels the circumference of a circle with a radius of 23 cm in 60 minutes. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.

Therefore, the circumference of the circle traced by the tip of the minute hand is:

C = 2πr = 2 × 3.14 × 23 cm ≈ 144.44 cm

To find out how far the minute hand travels in 11 minutes, we need to calculate what fraction of the circumference it covers in that time. Since 11 minutes is about 18.3% of an hour (60 minutes), the minute hand travels 18.3% of the circumference of the circle in that time:

Distance traveled = 0.183 × 144.44 cm ≈ 26.4 cm

Therefore, the tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

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The rectangular prism's volume can be represented by a cube whose dimensions are 6 inches.

A right rectangular prism is what?

The right rectangular prism has two simultaneous end panels that are orthogonal to each of the bases, two adjacent lateral faces, and four rectangle-shaped lateral faces. The faces of an oblique prism, a non-right oblong prism, are parallelograms. Alternative name for a right rectangular prism is a cuboid.

To begin, determine the rectangular prism's volume. To calculate this, multiply the length by the breadth by the height, which equals 9 ×4 ×6. 216 cubic inches make up this.

The side length of a cube with a 216 cubic inch capacity must now be determined. The recipe for A cube's volume is equal to its side length raised to the third power (cubed). You are now attempting to determine where s³= 216 This can also be expressed as s = ∛216.

The only thing left to do is to discover the number that, when multiplied by itself three times, equals 216, or its cubic root. It is quite easy to determine that 6× 6× 6, sometimes known as 6 cubed, equals 216. This indicates that the cube's side length is 6 inches.

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The vertical intercept for the table showing the relationship for Jada's grandparents starting a savings account for her is starting savings amount in the account of $ 600.

The vertical intercept in a graph is the point where a line intersects the vertical axis of the coordinate plane. It represents the value of the dependent variable (y) when the independent variable (x) is equal to zero.

The vertical intercept would therefore be first amount in the savings account by Jada's grandparents which is the $ 600.  This is the amount when x = 0 or rather when x was the starting year of 2006.

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The correct option is C, P - value is 0.0718.

A sample proportion in statistics is a measurement of the proportion or percentage of a sample that demonstrates an important characteristic or quality. It is computed by dividing the sample's overall population by the proportion of participants who exhibit the characteristic.

For instance, if a sample of 100 individuals is chosen to estimate the percentage of people who love chocolate ice cream, and 30 of those individuals state that they do, the sample proportion would be 0.3 or 30%, as 30 out of 100 individuals state that they do.

We must first compute the test statistic in order to determine the P-value for Aurelia's test. The test statistic has a typical normal distribution when the null hypothesis is true.

The sample proportion of heads is:

p' = 43/100 = 0.43

The test statistic is:

[tex]z = \frac{(p' - p)}{ \sqrt{(p(1-p) / n)}}[/tex]

where p is the hypothesized proportion under the null hypothesis, and n is the sample size.

Substituting the given values, we get:

[tex]z = \frac{(0.43 - 0.5)}{/ {sqrt(0.5 \times 0.5 / 100)}} = -1.8[/tex]

Since this is a two-sided test, we need to find the area under the standard normal distribution curve in both tails of the distribution that is more extreme than the observed test statistic.

Using a standard normal distribution table, we find that the area to the left of -1.8 is 0.0359. Therefore, the area in both tails is:

P-value = 2 × 0.0359 = 0.0718

So, the correct answer is:

c) 0.0718

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Answer:C

Step-by-step explanation: Kahn Academy

The range of values for the third side must be 5 < C < 13 this means that the third side must be a value greater than 5 and less than 13.

What is triangle?

A triangle is a two-dimensional geometric shape with three sides and three angles. It is a basic polygon and one of the simplest shapes in geometry. Triangles come in different types based on the length of their sides or the measure of their angles, such as equilateral triangles (all sides are equal), isosceles triangles (two sides are equal), scalene triangles (no sides are equal), right triangles (one angle measures 90 degrees), and obtuse triangles (one angle measures greater than 90 degrees).

The third side of a triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for a triangle with sides A, B, and C, we have:

                                    A + B > C

                                    B + C > A

                                    A + C > B

For the given sides of 8 and 5, the range of values for the third side can be found by considering the two inequalities:

                                    5 + C > 8

                                     8 + C > 5

Adding the two inequalities, we get:

                        13 > C

So the range of values for the third side must be:

                         5 < C < 13

This means that the third side must be a value greater than 5 and less than 13.

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From the graphs below, we can see that the solution of the given system of linear equations is (3,0.5).

What is meant by a system of linear equations?

A collection of one or more linear equations containing the same variables is known as a system of linear equations. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation is invariably a straight line equation. A group of diverse straight line equations make up a system of linear equations.

We are given two linear equations:

y = -1/2 x + 2

y = 1/2x - 1

As mentioned earlier, these are equations of two straight lines with slopes -1/2 and 1/2.

Now the solution of the equation is the intersecting point of these straight lines. We graph these equations and found the intersecting point.

Therefore, from the graphs below, the solution of the given system of linear equations is (3,0.5).

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The mode of the data set given is 63.

Statistics uses the terms mean, median, and mode to describe central tendency. They each provide information about what value in a data set is conventional or representative of the data set in their own unique ways.

The number that appears the most frequently in a piece of data is the mode. Count the occurrences of each number in the data collection. The figure with the largest total is the mode. More than one mode is acceptable. Additionally, there is no mode if all numbers appear exactly once.

Given that:

62,63,67,66,66,63,62,68,69,65,67,63,64,

By rearrangement, we have:

62, 62, 63, 63, 63, 64, 65, 66, 66, 67, 67, 68, 69

Therefore, the highest occurring number(mode) is 63.

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Answer:

First option: 37°, 11°,  132°

Step-by-step explanation:

The sum of the three interior angles of a triangle must add up to 180°

Only the first option 37°, 11° and 132° add up to 180°
37 + 11 + 132 = 48 + 132 = 180°

You don't need to add up all the other sets of angles completely. Just look at the units place

Option 2, units sum = 4 + 6 + 1 =11; does not end in a 0, ends in 1

Option 3: units sum = 1 + 0 + 2; does not end in a 0, ends in 3

Option 4: units sum = 0 + 1 + 5 ends in a 6

Answer:

X=63

Y=63

Z=72

Step-by-step explanation:

The value for angle X

X + 85 + 32 = 180°

X + 117 = 180°

X = 180° - 117°

X = 63°

Since <x and <y are vertically opposite

<X and <Y = 63°

Remember vertically opposite are the same.

The value for angle z

Z + 45 + Y = 180°

Z + 45 + 63 = 180°

Z° + 108° = 180° - 108°

Z = 72°

Therefore

Value for X = 63°

Value for Y = 63°

Value for Z = 72°

We can interpret from the results that the distribution of data might be negatively skewed.

In the given question it is mentioned that while Morgan was analyzing her data, she notices that the value of her mean is quite a bit smaller than the value of her median.

As we know that, in statistics, when the mean is smaller than the median and mode, it indicates a negatively skewed distribution.

A negatively skewed distribution or left skewed distribution is a type of distribution in which more values are concentrated on the right side of the distribution graph while the left side of the graph is longer.

Hence, we can interpret from these information that the distribution of data of Morgan are negatively skewed.

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Answer:

After substituting -4 for "a" and 16 for "b", the equation can be simplified and solved.

-The equation 2 (2x - 11) + 6 = -4x + 16

Expanding the equation on the left-hand side, we get:

4x - 22 + 6 = -4x + 16

Simplifying, we get:

10 = -10x + 32

Subtracting 32 from both sides, we get:

-22 = -10x

Dividing both sides by -10, we get:

x = 2.2

This means that there is exactly one solution, which is x = 2.2. So, statement 3 is true.

-The equation 4x - 8 (x - 2) = -4x + 16

Expanding the equation on the left-hand side, we get:

4x - 8x + 16 = -4x + 16

Combining like terms, we get:

-4x + 16 = -4x + 16

This equation is true for all values of x, so there are infinitely many solutions. So, statement 2 is true.

-The equation 10 + x + 2 - 6x = -4x + 16

Expanding the equation on the left-hand side, we get:

10 + x + 2 - 6x = -4x + 16

Combining like terms, we get:

-5x + 12 = -4x + 16

Adding 4x to both sides, we get:

-x + 12 = 16

Adding x to both sides, we get:

12 = 16

This equation is not true for any values of x, so there are no solutions. So, statement 1 is true.

-The equation 9x +3 - 13x + 6 = -4x + 16

Expanding the equation on the left-hand side, we get:

9x + 3 - 13x + 6 = -4x + 16

Combining like terms, we get:

-4x + 9 = -4x + 16

Adding 4x to both sides, we get:

9 = 12

This equation is not true for any values of x, so there are no solutions. So, statement 1 is true.

Therefore, the true statements are:

-The equation 2 (2x - 11) + 6 = ax + b has no solution.

-The equation 4x - 8 (x - 2) = ax + b has infinitely many solutions.

-The equation -5 (4x-6) 14 = ax + b has exactly one solution.

the angle BAD is 75 degrees and  we used the properties of angles in a circle and the tangent-secant theorem to find angle BAD .

To work out angle BAD, we need to use the properties of angles in a circle and the tangent-secant theorem. Here are the steps to solve the problem:

Identify the relevant angles First, we need to draw a diagram to visualize the problem. We have a circle with center O, points A, B, C, and D on the circumference, and tangent ED. Angle ODB is given as 25 degrees. We need to find angle BAD. We can label the angles in the diagram as follows:

Angle AOB = 2x (angle at the center is twice the angle at the circumference)

Angle BCD = x (angles in the same segment are equal)

Angle OBD = 90 degrees (tangent and radius are perpendicular)

Angle OED = 90 degrees (tangent and radius are perpendicular)

Angle ABD = y (we need to find this angle)

Angle BAD = z (we need to find this angle)

Use the sum of angles in a triangle

We notice that triangle ABD is a right triangle, with right angle at B. Therefore, angles ABD and BAD are complementary. That is, ABD + BAD = 90 degrees. Use the tangent-secant theorem

We can use the tangent-secant theorem to find the value of angle ABD. The tangent-secant theorem states that if a tangent and a secant intersect at a point on a circle, then the angle between the tangent and the secant is equal to the half the difference of the intercepted arcs. In our diagram, ED is a tangent, and BD is a secant. Therefore, angle ODB = 25 degrees is half the difference of the intercepted arcs AD and AB. That is, angle ABD = (2x - x)/2 = x/2.

Solve for x

To find x, we can use the fact that the angles in a triangle add up to 180 degrees. Therefore, x + 2x + 90 = 180 (sum of angles in triangle AOB). Solving for x, we get x = 30 degrees.

Find angle ABD and angle BAD

Using the result from step 3, we get ABD = x/2 = 15 degrees. Using the result from step 2, we get BAD = 90 - ABD = 75 degrees.

Therefore, the angle BAD is 75 degrees. In summary, we used the properties of angles in a circle and the tangent-secant theorem to find angle BAD. We noticed that ABD and BAD are complementary, and we used the tangent-secant theorem to find ABD. Then, we solved for x using the fact that the angles in a triangle add up to 180 degrees. Finally, we used the results from steps 2 and 3 to find BAD.

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The length of the shortest leg of T is approximately 18.33 units. We are given that the length of the altitude drawn to the hypotenuse (h) is 8, and the length of the hypotenuse (c) is 20.

We can start by using the area formula for a triangle:

Area = 1/2 * base * height

In this case, the base is the length of the hypotenuse (c), and the height is the length of the altitude (h). So we have:

Area = 1/2 * c * h

Substituting the given values, we get:

Area = 1/2 * 20 * 8 = 80

We also know that T is a right triangle, so we can use the Pythagorean theorem:

a^2 + b^2 = c^2

Substituting the given values, we get:

a^2 + b^2 = 20^2

a^2 + b^2 = 400

We can now solve for b by substituting a in terms of h (using the formula for the area of a triangle) and simplifying:

Area = 1/2 * base * height

80 = 1/2 * 20 * h

h = 8

a = (2 * Area) / c

a = (2 * 80) / 20

a = 8

Substituting a and h in the Pythagorean theorem equation, we get:

8^2 + b^2 = 20^2

64 + b^2 = 400

b^2 = 336

b = sqrt(336)

b ≈ 18.33

Therefore, the length of the shortest leg of T is approximately 18.33 units.

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Answer:

Step-by-step explanation:

Perimeter is equal to 2 times length and 2 times the width.

This problem says the length is twice the width.

Let's use 2w for the length:

Here's the equation:

2L + 2W = 156

Substitute 2W for the length,

2(2W) + 2W = 156

4W + 2W = 156

6W = 156

6W/6 = 156/6

w = 26

so length is 2 times 26 = 56 Length = 56 m

Answer:12

Step-by-step explanation:

8 times 3 equals 24.24 subtract36 get 12

Let's first assign variables to the numbers given.

We're given:

Plug the second equation into the first one and solve for y:

[tex]x+y=367\\(y+95)+y=367\\2y+95=367\\2y=272\\y=136[/tex]

Therefore, they sold 136 chocolate cones.

They sold 136 chocolate ice cream cones.

The amount Maggie will need in savings when she retires is $1,204,519.62 and  her payment be if she had 1.2 million is $4522.40

In investment, an annuity is a series of payments made at equal intervals

a) To calculate the amount Maggie will need in savings when she retires

Pm= {1 + r/j)pm - 1

Pm = (1+6.2%/12)4500 - 1

Pm (1+0.0052)4500 -1

Pm= (1.0052)4499

Simplifying to have

Pm = $4522.40

b) To  calculate much could her payment be if she had 1.2 million dollars in her account but her interest dropped to 5.5

Pm= {1 + r/j)pm - 1 +d

Where d is the savings

Pm = (1+5.5%/12)4500 - 1 + 1.2m

Pm= (1+5.5%/12) 4499 + 1.2m

PM = (1.0046)4499 + 1,200,000

Pm = 1,204,519.62

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The reliability of the machine can be estimated to be 0.9833, calculated as (1000 - 1) / 1000 + (600 - 5) / 600.  we can take the average of the two reliability estimates, giving us a reliability of 0.9833.

The reliability of a machine can be estimated by taking the ratio of machines that did not fail to the total number of machines operated in a given period. In this case, the reliability of the machine from Factory A can be estimated to be 0.99 (1000 - 1 / 1000). The reliability of the machine from Factory B can be estimated to be 0.9833 (600 - 5 / 600). To estimate the reliability of the machine based on both factories, we can take the average of the two reliability estimates, giving us a reliability of 0.9833.

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