Decompose the following figure into separate pieces draw the pieces

The correlation coefficient between X and Y is Corr(X, Y) = 0.

To calculate the marginal distribution of X and Y, we need to integrate the joint probability density function (PDF) over the appropriate ranges.

a. Marginal distribution of X:

To find the marginal distribution of X, we integrate the joint PDF over the range of Y:

∫[0, 1] J(x, y) dy

Since the joint PDF is defined as J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1 and J(x, y) = 0 otherwise, the integral becomes:

∫[0, x] 1 dy = x, for 0 ≤ x ≤ 1

So, the marginal distribution of X is simply X(x) = x for 0 ≤ x ≤ 1.

b. Expectation of X:

The expectation (mean) of X can be calculated as the integral of x times the marginal PDF of X:

\(E(X) = ∫[0, 1] x * X(x) dx = ∫[0, 1] x^2 dx = [x^3/3] from 0 to 1 = 1/3\)

Therefore, the expectation of X is E(X) = 1/3.

c. Variance of X:

The variance of X can be calculated using the formula:

\(Var(X) = E(X^2) - (E(X))^2E(X^2) = ∫[0, 1] x^2 * X(x) dx = ∫[0, 1] x^3 dx = [x^4/4] from 0 to 1 = 1/4Var(X) = 1/4 - (1/3)^2 = 1/4 - 1/9 = 5/36\)

Therefore, the variance of X is Var(X) = 5/36.

d. Covariance of X and Y:

The covariance of X and Y can be calculated as:

Cov(X, Y) = E(XY) - E(X)E(Y)

Since the joint PDF J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1, the integral becomes:

\(E(XY) = ∫[0, 1] ∫[0, x] xy dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

\(E(X) = 1/3 (from part b)E(Y) = ∫[0, 1] ∫[0, x] y J(x, y) dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

Cov(X, Y) = 1/6 - (1/3)(1/6) = 0

Therefore, the covariance of X and Y is Cov(X, Y) = 0.

e. Correlation coefficient between X and Y:

The correlation coefficient can be calculated using the formula:

Corr(X, Y) = Cov(X, Y) / √(Var(X) * Var(Y))

Since the covariance of X and Y is 0, the correlation coefficient will also be 0.

Therefore, the correlation coefficient between X and Y is Corr(X, Y) = 0.

f. Conclusion based on the correlation coefficient:

The correlation coefficient of 0 indicates that there is no linear relationship between X and Y. In this case, the fraction of male runners (X) and the

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The equation to solve the width of rectangle created by John from 48 square centimetre tiles is w(w+2) = 48

and the greatest width in centimetres use for mosaic is 6 cm.

We have given that

John wants to create a mosaic of rectangular shape.

total area of tile(A) = 48 square centimetre

let l and w be length and width of rectangle

length of rectangle is 2 cm longer than width then length of rectangle (l) =( w+2) cm

Area oa rectangle (A) = l × w

=> (w+2) × w = 48

=> w²+ 2w = 48

which is quadratic equation , solve it

w² + 2w - 48 = 0

=> w² - 6w + 8w - 48 = 0

=> (w-6) (w+8) = 0

=> w = 6, -8

Hence, the required equation is w(w+2) = 48 and width of rectangle is 6cm.

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Answer:

Step-by-step explanation:

Let's denote the volume of the cube as V and the length of each edge as x. Given that the volume of a cube is V = x^3, we can find the rate at which the length of each edge is changing.

We're given that the rate of change of the volume is dV/dt = 56 in³/sec. We want to find the rate of change of the length of each edge, which is dx/dt, when the length of each edge is 6 inches.

First, we differentiate the volume equation with respect to time t:

V = x^3

dV/dt = d(x^3)/dt

Using the chain rule:

dV/dt = 3x^2 * (dx/dt)

Now, we know that dV/dt = 56 in³/sec and x = 6 in. Plugging these values into the equation, we get:

56 = 3 * (6)^2 * (dx/dt)

Solving for dx/dt:

56 = 108 * (dx/dt)

dx/dt = 56 / 108

dx/dt ≈ 0.5185 in/sec (rounded to four decimal places)

So, the rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.

Answer: 3.3

x.   = 1.5

220      100

The function g(x) = 4 · (0.8)ˣ translated from its parent function will be translated by a vertical stretch of 4. Then the correct option is A.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

The equation is given below.

g(x) = 4 · (0.8)ˣ

In the equation, 4 represents the vertical stretch of the function.

The function g(x) = 4 · (0.8)ˣ translated from its parent function will be translated by a vertical stretch of 4. Then the correct option is A.

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The correct answer is Option 1.

The group of symmetries of a regular tetrahedron is known as the tetrahedral group, and is denoted by $T_d$. This group consists of all the symmetries of a regular tetrahedron, including orientation-reversing symmetries.

The regular tetrahedron is a three-dimensional object with four faces that are all equilateral triangles. It is one of the five Platonic solids, which are convex polyhedral with congruent faces and regular polygonal faces. The tetrahedral group $T_d$ contains a total of 24 symmetries, which can be divided into two classes: rotational symmetries and reflection symmetries. The rotational symmetries consist of 8 proper rotations, which are rotations that preserve the orientation of the tetrahedron, and 6 improper rotations, which are rotations that reverse the orientation of the tetrahedron. The reflection symmetries consist of 6 plane reflections that reflect the tetrahedron across one of its faces.

To understand the symmetries of the tetrahedron, it is helpful to think about the symmetries of an individual face. An equilateral triangle has 6 symmetries: 3 rotational symmetries (120 degree rotations about the center of the triangle), and 3 reflection symmetries (across the lines of symmetry of the triangle). The regular tetrahedron has four faces, so these symmetries can be applied to each face independently, resulting in a total of $6^4=1296$ symmetries. However, many of these symmetries are not distinct, and can be generated by combinations of the tetrahedral group's 24 symmetries. Thus, the tetrahedral group $T_d$ is the group of all the distinct symmetries of a regular tetrahedron.

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The equation of the line (blue line) becomes: 4x + y = 3

The set of points that make up a line in a coordinate system are represented algebraically in the equation of the line. The equation of a line is just an algebraic equation which represents the several points that all together form a line there in coordinate axis as a set of variables x, and y.

A straight line has the equation y=mx+c, where c is the height at which the line crosses the y-axis, commonly known as the y-intercept, and m is the gradient.

As, it cut the point in the x-axis at the point 4 and cut the y-axis at the point 1 and the intercept becomes 3.

Thus, the equation of the blue line becomes: 4x + y = 3

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Answer:

Camillo will spend $48.75 dollars

Step-by-step explanation:

Since the better buy cost $1.95 we multiply.

1.95 * 25 = 48.75

So, the answer is 48.75

Hope this helps! :)

The surface area of the triangular prism is 313.47 cm².

Given is a triangular prism, we need to find the surface area,

A triangular prism is a 3D shape with two identical faces in the shape of a triangle connected by three rectangular faces. The rectangular faces are referred to as the lateral faces, while the triangular faces are called bases. The bases are also called the top and the bottom (faces) of the prism.

Triangular Prism Meaning: A triangular prism is a 3D polyhedron with three rectangular faces and two triangular faces. The 2 triangular faces are congruent to each other, and the 3 lateral faces which are in the shape of rectangles are also congruent to each other. Thus, a triangular prism has 5 faces, 9 edges, and 6 vertices. Observe the following image of a triangular prism in which l represents the length of the prism, h represents the height of the base triangle, and b represents the bottom edge of the base triangle.

so, the surface area of a triangular prism =

perimeter × length + 2 × base area

So,

SA = (4.5+7.2+9) × 8.1 + 2 × 8.1 × 9

= 167.67 + 145.8

= 313.47

Hence the surface area of the triangular prism is 313.47 cm².

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Answer:

49π m² or 153.94 m²

Step-by-step explanation:

Area of a circle: A = πr²

We are given r as 7, so simply plug it in

A = π(7)^2

A = 49π m²

Answer: \(f^{-1} (x) = \sqrt{x} +1\)

Step-by-step explanation:

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

We know straight away the inverse will be a square root function. We also know that this inverse will have a restriction on the domain, (because you can only take the square root of a positive number).

So, to find the inverse, first we'll switch the x and y and solve for y:

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

\(x = (y-1)^2\), (factor!)

±\(\sqrt{x} = y - 1\)

So, the inverse "function" is:

\(f^-1(x)\) = ±\(\sqrt{x} +1\)

But theres an issue here!

If we tried graphing this, this "function" would not pass the vertical line test, so its not really a function at all!

We need to restrict the domain to only include the values that are above the x axis.

So our final inverse function is:

\(f^{-1} (x) = \sqrt{x} +1\)

The zeros of the function defined by

h(x) = x³ – 4x² – 5x are x = 0, x = 5 and x = -1

The zeros of a function, also referred to as roots or x-intercepts, occur at x-values where the value of the function is 0. It is simply the values of x when f(x) is equal to 0.

For x = 0, we substitute 0 for x in the function h(x);

h(0) = (0)³ - 4(0)² - 5(0)

h(0) = 0

For x = 1, we substitute 1 for x in the function h(x);

h(1) = (1)³ - 4(1)² - 5(1)

h(1) = 1 - 4 - 5

h(1) = -8

For x = -5, we substitute -5 for x in the function h(x);

h(-5) = (-5)³ - 4(-5)² - 5(-5)

h(-5) = -125 - 100 +25

h(-5) = -200

For x = 5, we substitute 5 for x in the function h(x);

h(5) = (5)³ - 4(5)² - 5(5)

h(5) = 125 - 100 - 25

h(5) = 0

For x = -1, we substitute -1 for x in the function h(x);

h(-1) = (-1)³ - 4(-1)² - 5(-1)

h(-1) = -1 - 4 + 5

h(-1) = 0

Therefore, the values of x that makes the function h(x) = x³ – 4x² – 5x equal to zero are; 0, 5, and -1, they are the zeros of the function h(x).

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The probability that a randomly selected Atlantic cod has a length of 53.68 cm or less is given by the equation P ( x > 38.68 ) = 0.99865

The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.

The Z-score is calculated using the formula:

z = (x - μ)/σ

where z: standard score

x: observed value

μ: mean of the sample

σ: standard deviation of the sample

Given data ,

Let the probability that a randomly selected Atlantic cod has a length of 53.68 cm or less be represented as P

Now , the equation will be

The observed value of x = 38.68 cm

The mean of the sample μ = 49.9 cm

The standard deviation of the sample σ = 3.74 cm

Now , z-score is calculated using the formula:

z = (x - μ)/σ

Substituting the values in the equation , we get

z = ( 38.68 - 49.9 ) / 3.74

z = -3

Now ,the p value from the z table is

P ( x > 38.68 ) = 1 - P ( x < 38.68 )

P ( x < 38.68 ) = 0.0013499

P ( x > 38.68 ) = 0.99865

And , the probability is P ( x > 38.68 ) = 0.99865 = 99.865 %

Hence , the probability is 84.392 %

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The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

175792

Step-by-step explanation:

8 x 2 = 16

16 x 10987 = 175792

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

The standard deviation of the response time is 1.53 minutes.

To get standard deviation, we will determine z-scores corresponding to the given percentiles and use them to calculate the standard deviation.

Z-score = z = (x - μ) / σ

For the lower bound of 10 minutes:

z = (10 - 13) / σ

For the upper bound of 16 minutes:

z = (16 - 13) / σ

As normal distribution is symmetric, the z-score corresponding to the lower tail of 2.5% is -1.96, and the z-score corresponding to the upper tail of 2.5% is 1.96.

Using z-scores, we set up  equations:

(10 - 13) / σ = -1.96

(16 - 13) / σ = 1.96

Solving the first equation:

-3 / σ = -1.96

σ = -3 / -1.96

Solving the second equation:

3 / σ = 1.96

σ = 3 / 1.96

Dividing both sides by 1.96:

-3 / 1.96 = σ

1.53 = σ

Full question:

The respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes. What is S.D. of the response time.

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Answer:

no

Step-by-step explanation:

The graph of the function would be a parabola with zeros at (0,0), (-1,4), (-3,0), (2,0), (0,-2), (3,0), (-1,0), (0,-3).

A function is a mathematical relationship between two or more variables where one variable (the output) is determined by the values of the other variables (the inputs). Functions are often written as an equation, such as y = f(x), where x is the input and y is the output. The equation defines the relationship between x and y and how the output (y) changes as the input (x) changes. Functions can be used to model real-life situations, such as predicting population growth or modeling the motion of objects.

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Answer:

180

Step-by-step explanation:

Answer:

1.6

Step-by-step explanation:

i used calculator

Answer:  1.6

Step-by-step explanation:

The distance between the two ship based on the angle of depression is 42 meters.

The distance of each ship can be calculated thus:

TanX = opposite / Adjacent

The first ship:

Tan53 = distance/ 82

distance= 108.82 meters

The second ship:

Tan39 = distance/ 82

distance= 66.40 meters

The Difference between the ships are :

Therefore, the distance between the two ships is 42 meters.

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Using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.

So, tiles needed to cover the wall:

Calculate the area of a tile as follows:

Now, calculate the area of the wall as follows:

Then, tiles needed to cover the wall:

Which means: 80½

Therefore, using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.

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Answer:

$5.62 it could also possibly be $5.63 if you have to round up.

Step-by-step explanation:

Answer: $5.63

Step-by-step explanation: multiply 4.5 by the price per pound.

Answer:

17

Step-by-step explanation:

STUDY HARD GUYS I NEED HW HELP

Answer:

C. 0i

Step-by-step explanation:

Edge 2020

(1 + i) + 0i = 1 + i

Answer:

C

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

mean is calculated as

mean = \(\frac{sum}{count}\)

Here mean = 316 and sum = 3792 , count n is required to be found, so

\(\frac{3792}{n}\) = 316 ( multiply both sides by n )

3792 = 316n ( divide both sides by 316 )

12 = n

There are 12 observations in the data

Answer:

i think it is 1/4