Craig gets a bonus with his club for every frisbee golf hole on which he makes a score of 3. He played last week and scored a total of 3 on 5 holes. Craig will get an extra bonus if he has a total of 42 from scores of 3 after he finishes today. On how many holes does he need to score a 3 today?

Answer:

y-intercept is -4

Step-by-step explanation:

Since we are not told what to find, we can find the y intercept of the given graph.

The y-intercept is the point where the curve cuts the y-axis. According to the graph shown, we can see that the curve cuts the y axis at y = -4. Hence the y-intercept of the graph will be -4

Answer:kepler's 3rd law

Step-by-step explanation:

Answer:

The equation of line is as follows:

Slope-intercept form: \(y = 7x-5\)

Standard Form: \(-7x+y = -5\)

Step-by-step explanation:

Given that

Slope of line: 7

Point : (1,2)

Slope-intercept form of equation of line is given by:

\(y = mx+b\)

Here m is the slope and b is y-intercept.

Putting the value of slope

\(y = 7x+b\)

To find the value of b, we have to put the point in the equation

\(2 = 7(1) +b\\2 = 7+b\\2-7 = b\\b = -5\)

So the equation will be:

\(y=7x-5\)

The standard form of equation of line is:

\(Ax+By = C\)

To convert the equation in standard form, subtracting 7x from both sides

\(y-7x = 7x-5-7x\\-7x+y = -5\)

Hence, the equation of line is as follows:

Slope-intercept form: \(y = 7x-5\)

Standard Form: \(-7x+y = -5\)

The equation of a line in slope-intercept and standard form through (1, 2), slope = 7 is  7x - y = 5.

To find the equation of a line in slope-intercept and standard form.

First, we can write the equation in point-slope form. The point-slope formula states:

(y − y₁) = m (x − x₁)

Where m is the slope and

(x1, y1) is a point the line passes through.

Substituting the values from the problem gives:

(y − 2) = 7(x − 1)

Now, we need to convert to standard form.

The standard form of a linear equation is:

Ax + By = C

where, if at all possible,

A, B, and C are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

We convert as follows:

y − 2 = (7 × x) − (7 × 1)

y − 2 = 7x − 7

−7x + y − 2  = − 7

Adding 2 in both side.

−7x + y − 2 + 2 = − 7 +2

-7x + y = -5

7x - y = 5

Therefore,  the equation of a line in slope-intercept and standard form is 7x - y = 5.

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Answer:

Ummm

Step-by-step explanation:

So what do you need help with?

Answer:

\(\huge\boxed{y=\frac{1}{4}x + \frac{13}{4}}\)

Step-by-step explanation:

In order to find the equation to this line, we need to note that we see two points on this graph. Using these two points, we can use them to find the slope of the graph and use one to find the y-intercept.

We know that the slope of a line is defined by \(\frac{\Delta y}{\Delta x}\) (change in y / change in x). Therefore, we can use our two points that we know - (-5, 2) and (3, 4) to find the slope.

The change in y is \(4 - 2 = 2\), and the change in x is \(3 - (-5) = 3+5= 8\). Therefore, our slope is \(\frac{2}{8} = \frac{1}{4}\).

Now that we know our slope, our equation in slope-intercept form looks something like this.

\(y = \frac{1}{4}x + b\)

However, we still have b to solve for. We can solve for this by substituting a point we already know into the equation. Let's substitute (3, 4) inside.

So now we know that the y-intercept is \(\frac{13}{4}\). Plugging that into our equation finishes it off, leaving our final equation to be \(y = \frac{1}{4}x + \frac{13}{4}\).

Hope this helped!

Answer:

y= 1/4 + 13/4

Step-by-step explanation:

mark brainless please..

;-;

(did this question before)

lol

The values of x for the given equations are:

1. The value of x = 0

2. The values of x are ±1

3. The values of x are 0 and -7/16

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

To find the values of x in each of the equations, we need to simplify them using algebraic operations:

1. 8x² = 6x² + 5x²

Combining like terms on the right-hand side:

8x² = 11x²

Subtracting 6x² from both sides:

2x² = 0

Dividing both sides by 2:

x² = 0

Taking the square root of both sides:

x = 0

Therefore, the only solution to this equation is x = 0.

2.Similarly, we can calculate values of x for this equation:

-7x² + 6 = x² - 7x²

x² = 1

Taking the square root of both sides:

x = ±1

Therefore, the solutions to this equation are x = 1 and x = -1.

3. 7x² + 9x² = -6x² - 7x

x(16x + 7) = 0

Using the zero product property:

x = 0 or 16x + 7 = 0

Solving for x in the second equation:

16x = -7

Dividing both sides by 16:

x = -7/16

Therefore, the solutions to this equation are x = 0 and x = -7/16.

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The area of the polygon is solved to be  1044 squared cm

The area of the composite polygon is solved by dividing the object into two sections. Then adding up the areas

Section 1 has dimensions:

length * width = 46 * 14 = 644

section 2 has dimensions:

length = 46 - 21 = 25

width = 30 - 14 = 16

Area = 25 * 16 = 400

Area of the composite figure

section 1  + section 2

= 644 + 400

= 1044 squared cm

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Answer:

16.028 yards

Step-by-step explanation:

1 inch=0.0833333 foot

24 inches=0.0833333×24

=1.9999992 foot

The mirror is square shaped and each side is 24 inches

If each 24 inches=1.9999992 foot

Then,

4 sides of 24 inches=1.9999992×24

=47.9999808 foot

Maria has 1 foot of trim left

Total Length of trim when she started=47.9999808+0.0833333

=48.0833141 foot

=16.02777136667 yards

Approximately,

16.028 yards

Answer:

It should be D.

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

S1 let a and b be the digits of the number

so a 2 digit number cab written as - 10×a + b

eg - 68 as 6×10 + 8

S2 ) according to ques

a + b = 6    - eqn 1

(10×a + b) - (10×b + a) = 18

9×a - 9×b = 18

a - b = 2   - eqn 2

S3)from eqn 1 and eqn 2

we get a = 4 and b = 2

hence number is 42

Answer:

k = 1/3

Step-by-step explanation:

a = kx²

12 = k * 6²

k = 12/36

k = 1/3

Answer: k = 1/3

Given f(x)=2−∣x−5∣

Domain of f(x) is defined for all real values of x.

Since, ∣x−5∣≥0⟹−∣x−5∣≤0

⟹2−∣x−5∣≤2⟹f(x)≤2

Hence, range of f(x) is (−∞,2].

The domain of the function  y= 2√x-6 is [6, ∞).

A relation is a function if it has only One y-value for each x-value.

In the given function, we have a square root of x-6 which means that the value inside the square root must be non-negative, otherwise the function will not be real.

Therefore, we have x - 6 ≥ 0

Adding 6 to both sides, we get:

x ≥ 6

So, the domain of the function y = 2√(x-6) is all real numbers greater than or equal to 6.

In interval notation, we can write the domain as:

Domain: [6, ∞)

Hence, the domain of the function  y= 2√x-6 is [6, ∞).

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Step-by-step explanation:

give me brainly lsssssss

Answer:

It would be 30 mph

Step-by-step explanation:

45/6=7.5

7.5*4=30

Answer:

30 minutes

Step-by-step explanation:

Each mile takes him 7 minutes 30 seconds. So you will do 7.5 x 4 to get 30 minutes

Answer:

12.7 units

Step-by-step explanation:

Formula to get the distance between the two points \((x_1,y_1)\) and \((x_2,y_2)\) is,

d = \(\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\)

From the picture attached,

Sherry is at the origin(0, 0) and going to the top (12, 4)

Distance between these points will be,

d = \(\sqrt{(12-0)^2+(4-0)^2}\)

d = \(\sqrt{160}\)

d = \(4\sqrt{10}\)

  ≈ 12.7 units

Therefore, Sherry has to travel 12.7 units on the ramp.

Triangle KVM is similar to triangle BVG because angle M = angle G = 90° and angle V is common to both triangles.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio.

For two triangles to be similar, the corresponding angles must be congruent i.e equal.. Also the ratio of the corresponding sides of similar triangles are equal.

angle M and G are both 90° , this means they are equal.

angle KVM = BVG

therefore angle K = angle B

Since all the corresponding angles are equal, we can say triangle KVM is similar to triangle BVG

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\(V = \pi(3)^2(21)\) is the equation that shows the volume of the given cylinder.

The following formula may be used to determine a cylinder's volume:

\(V=\pi r^2h\)

Where r is the radius of the cylinder's base, h is its height and is a mathematical constant that denotes the ratio of a circle's circumference to its diameter.

We must first determine the radius of the cylinder's base in order to utilize this formula to calculate the fulgurite's volume. The radius is equal to half of the base's diameter, or 3 inches since we know it to be 6 inches.

When we enter the values we are aware of into the formula, we obtain:

\(V = \pi(3)^2(21)\)

Therefore, the expression that represents the volume is \(V = \pi(3)^2(21)\)

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We have three vertices with degrees 0, 1, and 2. When n = 4, we have four vertices with degrees 0, 1, 2, and 3.

Constructing the isomorphism types of r-regular graphs:

An r-regular graph is a graph in which every vertex has r adjacent vertices, and the degree of every vertex is r. We can easily construct a graph by connecting the vertices together with edges. The problem is to determine the number of non-isomorphic r-regular graphs for total nodes n = 1, 2, 3, 4.

Using the Havel–Hakimi algorithm, we can create isomorphism types of r-regular graphs. The Havel–Hakimi algorithm is an algorithm for determining whether a given sequence of integers is graphical, which means whether there exists a finite simple graph with that degree sequence. This algorithm works by constructing a sequence of degree-preserving graph operations. Then, we can use the algorithm to produce the isomorphism types of r-regular graphs for total nodes n = 1, 2, 3, 4. For example, when n = 1, we have one vertex with degree 0. When n = 2, we have two vertices with degrees 0 and 1. When n = 3, we have three vertices with degrees 0, 1, and 2. When n = 4, we have four vertices with degrees 0, 1, 2, and 3.

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Answer:  your equation is poorly written/wrong hence I used the equation below

answer :  $289156.63

Step-by-step explanation:

applying the formula to calculate monthly repayment of Mortgage

M = P [ r(1+r)^n / ( ( 1+r )^n ) -1 ) ]  -----  ( 1 )

M = Total monthly payment = 800 * 12 * 30 = $ 288,000

P = ?

r = 5.2% / 12 = 0.4%

n = 30 * 12 = 360 months

Back to equation 1

P = M / [ r(1+r)^n / ( ( 1+r )^n ) -1 ) ]

   = 288000 / [ 0.004 ( 1.004)^360 / (( 1.004)^360 ) - 1 ) ]

   = 288,000 / -0.996  =  - $289156.63 ( It has a negative value because It is a loan borrowed )

Answer:

• first get the value of u

\(7u - 4 = 3 \\ 7u = 3 + 4 \\ 7u = 7 \\{ \underline{ \: \: u = 1 \: \: }}\)

• find the value of 9u + 4:

\(9u + 4 = 9(1) + 4 \\ = 9 + 4 \\ { \underline{ \underline{ \: \: 13 \: \: }}}\)

Answer:

\(7u - 4 = 3 \\ 7u = 4 + 3 \\ 7u = 7 \\ u = \frac{7}{7} \\ \boxed{u = 1} \\\\f(u) = 9u + 4 \\ f(1) = 9(1) + 4 \\f(1) = 9 + 4 \\ \boxed{f(1) = 13 }\)

Using trigonometric identities and algebraic manipulations, we derive an expression for sin x and cos x in terms of cos y. The value of (sin x + cos x)(sin y + cos y) is 2.49.


1. Start with the given equations sin(x+y) = 0.9 and sin(x-y) = 0.6.
2. Rewrite the equations using trigonometric identities. For sin(x+y) = 0.9, we have sin x cos y + cos x sin y = 0.9. For sin(x-y) = 0.6, we have sin x cos y - cos x sin y = 0.6.
3. Add the two equations together to eliminate the sin x cos y term: 2 sin x cos y = 1.5.
4. Divide both sides by 2 to solve for sin x cos y: sin x cos y = 0.75.
5. Square both sides of the equation to get (sin x cos y)^2 = 0.75^2. This gives us sin^2 x cos^2 y = 0.5625.
6. Use the trigonometric identity sin^2 x + cos^2 x = 1 to rewrite sin^2 x as 1 - cos^2 x: (1 - cos^2 x) cos^2 y = 0.5625.
7. Expand and rearrange the equation: cos^2 x cos^2 y - cos^4 x = 0.5625.
8. Use the identity cos^2 x = 1 - sin^2 x to substitute for cos^2 x: (1 - sin^2 x) cos^2 y - (1 - sin^2 x)^2 = 0.5625.
9. Expand and simplify: cos^2 y - sin^2 x cos^2 y - (1 - 2sin^2 x + sin^4 x) = 0.5625.
10. Combine like terms: cos^2 y - sin^2 x cos^2 y - 1 + 2sin^2 x - sin^4 x = 0.5625.
11. Rearrange the equation to isolate sin^2 x terms: sin^4 x - sin^2 x (cos^2 y + 2) + cos^2 y - 1 + 0.5625 = 0.
12. Combine like terms: sin^4 x - sin^2 x (cos^2 y + 2) + cos^2 y - 0.4375 = 0.
13. Solve the quadratic equation for sin^2 x: sin^2 x = [(cos^2 y + 2) ± √((cos^2 y + 2)^2 - 4(cos^2 y - 0.4375))] / 2.
14. Simplify the expression: sin^2 x = [(cos^2 y + 2) ± √(cos^4 y + 4cos^2 y + 4 - 4cos^2 y + 1.75)] / 2.
15. Further simplify: sin^2 x = [(cos^2 y + 2) ± √(cos^4 y + 5.75)] / 2.
16. Since 0 ≤ y ≤ x ≤ π/2, the value of cos y is positive. Therefore, cos^2 y + 2 is positive.
17. Thus, the equation simplifies to sin^2 x = (cos^2 y + 2 + √(cos^4 y + 5.75)) / 2.
18. Take the square root of both sides: sin x = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2].
19. Since 0 ≤ y ≤ x ≤ π/2, the value of sin x is positive.
20. Therefore, sin x + cos x = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2] + √(1 - sin^2 x).
21. Substituting the values of sin x and cos x, we have sin x + cos x = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2] + √(1 - [(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2]).
22. Simplify the expression: sin x + cos x = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2] + √[(2 - cos^2 y - √(cos^4 y + 5.75)) / 2].
23. Multiply the two terms: (sin x + cos x)(sin y + cos y) = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2] * √[(2 - cos^2 y - √(cos^4 y + 5.75)) / 2].
24. Simplify: (sin x + cos x)(sin y + cos y) = √[(cos^2 y + 2 + √(cos^4 y + 5.75))(2 - cos^2 y - √(cos^4 y + 5.75))] / 2.
25. Multiply the terms inside the square root: (sin x + cos x)(sin y + cos y) = √[4 - 2cos^2 y - 2√(cos^4 y + 5.75) + 4√(cos^2 y + 2) - 2cos^2 y + cos^4 y + 5.75] / 2.
26. Combine like terms: (sin x + cos x)(sin y + cos y) = √[5 + 2√(cos^2 y + 2) + 2cos^2 y - 2cos^2 y - 2√(cos^4 y + 5.75)] / 2.
27. Cancel out the common terms: (sin x + cos x)(sin y + cos y) = √[5 + 2√(cos^2 y + 2) - 2√(cos^4 y + 5.75)] / 2.
28. Simplify the expression: (sin x + cos x)(sin y + cos y) = √[5 - 2√(cos^4 y + 5.75) + 2√(cos^2 y + 2)] / 2.
29. The value of (sin x + cos x)(sin y + cos y) is 2.49.

Therefore, the value of (sin x + cos x)(sin y + cos y) is 2.49.

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In this problem, we use the product-to-sum trigonometric identities and the given information that sin(x+y) = 0.9 and sin(x-y) = 0.6 to find that the value of (sin x + cos x)(sin y + cos y) equals 1.5.

In this problem, you're asked to find the value of (sin x + cos x)(sin y + cos y). Before we solve it directly, let's take advantage of the given information: sin(x+y) = 0.9 and sin(x-y) = 0.6.

To solve this, we can use the product-to-sum trigonometric identities: sin(A)+cos(A)sin(B)+cos(B) = sin(A+B)+sin(A-B). According to the problem, sin(x+y) = 0.9 and sin(x-y)=0.6. Therefore, we have 0.9 + 0.6 which results in 1.5. Thus, the value of (sin x + cos x)(sin y + cos y) equals 1.5.

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Answer:

1. The area is found by using the formula for a rectangle

The area is 150 cm²

2. The area is found by the definite integral for the area between two points under a curve

3. The methods are different

The methods are different because the area of figure A is found by the multiplication between the dimensions, while the area of figure B is found by the difference between the values of the integral of the function between the points

Step-by-step explanation:

1. The area of the shaded figure A is found by multiplying the dimensions of the figure, which is the length multiplied by the breadth of the figure

From the question, we have;

The area of the rectangular figure, A = Length × Breadth

The length of the figure = 15 cm

The breadth of the rectangular figure = 10 cm

Therefore, we have;

A = 15 cm × 10 cm = 150 cm²

The area of the rectangular figure, A = 150 cm²

2. The bell shape of the figure B is obtained from a function f(x) as obtained from MIT mathematics website as follows;

\(f(x) = e^{-t^2}\)

Therefore the area of the shaded region in the bell shaped figure between the points 0 and 1 on the x-axis is found by integration as follows;

\(A = \int\limits^1_0 {e^{-t^2}} \, dt = \dfrac{1}{2} \cdot \sqrt{\pi} \times erf(t)\)

Using a graphing calculator, we have;

\(A = \int\limits^1_0 {e^{-t^2}} \, dt \approx 0.746824\)

3. The method of finding the area of figure A is different from the method of finding the area of the figure B

The methods are different because the area of figure A is the area of the whole figure of a geometric shape with known formula for area while the area of of the shaded region has no predefined formula but is calculated using the calculus for the area under a curve.

0.0515  is probability of exactly six successes .

What is probability in math?

Binomial probability with

Number of trials (n) = 8

probability of success ( ρ ) = 0.95

              ρ = 0.95

     p + q = 1

        q = 1 - p

            = 1 - 0.95

        q = 0.05

 x ~  bin( n , ρ )

       ρ( X = x ) = ⁿCₓ Pˣ . qⁿ⁻ˣ

the probability of exactly six success .

    ρ ( X = 6 ) = ⁸C₆ ( 0.95)⁶ ( 0.05 )⁸ ⁻⁶

                     = 28 ( 0.7351 ) ( 0.05)²

                       = 28 ( 0.7351 ) ( 0.0025 )

                        = 0.051457

        ρ( X = 6 ) = 0.0515

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Answer:

The coordinates of the vertices of \(\bigtriangleup A'B'C'\) are \(A'=(-2,8)\), \(B'=(-17,-4)\) and \(C'=(-9,0)\).

Step-by-step explanation:

Let be \(A =(7,3)\), \(B = (-8,6)\) and \(C = (0,-5)\) the vertices of the original triangle, as well as \(\vec t = \left<-9, 5\right>\), the coordinates of the vertices of the new triangle are, respectively:

\(A' = A + \vec t\)

\(A' = (7,3)+(-9,5)\)

\(A' = (7-9,3+5)\)

\(A'=(-2,8)\)

\(B' = B + \vec t\)

\(B' = (-8,6)+(-9,5)\)

\(B' = (-8-9,-9+5)\)

\(B'=(-17,-4)\)

\(C' = C + \vec t\)

\(C' = (0,-5)+(-9,5)\)

\(C' = (0-9,-5+5)\)

\(C'=(-9,0)\)

The coordinates of the vertices of \(\bigtriangleup A'B'C'\) are \(A'=(-2,8)\), \(B'=(-17,-4)\) and \(C'=(-9,0)\).

Answer:

Step-by-step explanation:

9 increased by a number x

Expression:  9 + x

a number x more than −12

x + ( -12 )

Expression:6- x

Answer:

1) 14135 = B) múltiplo de 5 C) múltiplo de 11

Step-by-step explanation:

Para saber si un numero es un multiplo de otro simplemente tenes que dividir el otro numero por el primero y si el resultado es un numero entero (sin resto y que no es un decimal) entonces es un multiplo de ese numero. En esta pregunta el primer numero (14135) es multiplo de 5 y de 11 por que al dividir no quedan restos, pero no es multiplo de 3 por que si quedan restos.

14135 / 3 = 4,711.666

14135 / 5 = 2,827

14135 / 11 = 1,285

El segundo numero (11234125723) no es multiplo de ninguna de las opciones por que todos dejan restos.

11,234,125,723 / 3 = 3,744,708,574.33333

11,234,125,723 / 5 = 2,246,825,144.6

11,234,125,723 / 11 = 1,021,284,156.636363

The correlation coefficient between X and Y for the given moments is equal to (b + c) / √(b²(1 + 2c) + 2bc²).

Y = a + bX+cX²

To find the correlation coefficient between two random variables X and Y,

Calculate their covariance and standard deviations.

Find the covariance between X and Y.

The covariance between X and Y is ,

cov(X, Y) = E[(X - E[X])(Y - E[Y])]

To calculate this, find the expected values E[X] and E[Y].

Since we are given the first four moments of X,

Use them to find the mean (E[X]) and the variance (Var[X]) of X,

E[X]

= μ

= 1

Var[X]

= E[X²] - (E[X])²

= 2 - 1²

= 2 - 1

= 1

Now let us find E[Y],

E[Y] = E[a + bX + cX²]

= a + bE[X] + cE[X²]

To calculate E[X²], use the second moment of X,

E[X²] = 2

Substituting these values, we have,

E[Y] = a + b(1) + c(2)

Now calculate the covariance,

cov(X, Y)

= E[(X - E[X])(Y - E[Y])]

= E[X·Y - X·E[Y] - E[X]·Y + E[X]·E[Y]]

= E[X·Y] - E[X]·E[Y] - E[X]·E[Y] + E[X]·E[Y]

= E[X·Y] - E[X]·E[Y]

The second moment of XY,

E[XY]

= E[(a + bX + cX²)X]

= E[aX + bX² + cX³]

= aE[X] + bE[X²] + cE[X³]

To calculate E[X³], use the third moment of X,

E[X³] = 3

Substituting these values, we have,

E[XY]

= aE[X] + bE[X²] + cE[X³]

= a(1) + b(2) + c(3)

= a + 2b + 3c

Finally, substitute the expressions for E[XY] and E[X]·E[Y] back into the covariance formula to obtain,

cov(X, Y)

= E[XY] - E[X]·E[Y]

= (a + 2b + 3c) - (1)(a + b(1) + c(2))

= a + 2b + 3c - a - b - 2c

= b + c

Next, calculate the standard deviations of X and Y.

The standard deviation of X is the square root of the variance,

σ(X)

= √Var[X]

= √1

= 1

The standard deviation of Y can be calculated as follows,

Var[Y]

= Var[a + bX + cX²]

= Var[bX + cX²]

= b²Var[X] + c²Var[X²] + 2bcCov[X, X²]

Var[X] and Var[X²] from the given moments,

Var[X] = 1

Var[X²]

= E[X⁴] - (E[X²])²

= 4 - 2²

= 4 - 4

= 0

Substituting these values, we have,

Var[Y]

= b²Var[X] + c²Var[X²] + 2bcCov[X, X²]

= b²(1) + c²(0) + 2bcCov[X, X²]

= b² + 2bcCov[X, X²]

Since Cov[X, X²] = b + c, substitute this back into the equation,

Var[Y]

= b² + 2bc(b + c)

= b² + 2b²c + 2bc²

= b²(1 + 2c) + 2bc²

The standard deviation of Y is the square root of the variance,

σ(Y)

= √Var[Y]

= √(b²(1 + 2c) + 2bc²)

Finally, calculate the correlation coefficient,

p(X, Y)

= cov(X, Y) / (σ(X) · σ(Y))

= (b + c) / (1 · √(b²(1 + 2c) + 2bc²))

= (b + c) / √(b²(1 + 2c) + 2bc²)

Therefore, the correlation coefficient between X and Y is given by (b + c) / √(b²(1 + 2c) + 2bc²).

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Therefore , the solution of the given problem of  surface area comes out to be  unused space is equal to 2π - (5π/6 + √3/2) m² .

Its surface area serves as a proxy for how much overall space it occupies. The whole environment of a three-dimensional shape is taken into account when calculating its surface area. The overall size of something is its surface area. The volume of water in a cuboid can be determined by summing the face on each of the six rectangular sides. To determine the box's measurements, apply the following formula: For 2lh, 2lw, & 2hw, the surface is exactly the same (SA). The region is represented by the surface area of the muti form.

Here,

Given:

AB = D = 4 m (R = 2 m)

The size of the AB semicircle is:

=> Area = πr²/2

=>A = 2π

The dimensions of the little semicircle are a=5/6 + 2/3/2 m2 and a=5/6 + 3/2 m2.

The remainder area is therefore equal to A- a.

= 2π - (5π/6 + √3/2) m²

The unused space is equal to 2π - (5π/6 + √3/2) m²

Therefore , the solution of the given problem of area comes out to be  unused space is equal to 2π - (5π/6 + √3/2) m² .

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