use the binomial theorem to write down and simplify all the terms of the expansion (1 - 1/4 x) raised to 5 ​

The correct option is C, the area of the triangle is 9 square units.

For a triangle of base B and height H the area is:

A = B*H/2

Here we can see that:

B = x

H = 2x

And we know that x = 6 - 3 = 3

Then we can use the value of x to find the values of H and B.

B = 3

H = 2*3 = 6

Now we can replace these two values in the formula for the area, then we will get the area of the triangle:

A = 3*6/2 = 3*3 = 9 square units.

When x = 3, the area is 9 square units.

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The total number of words which starts and end with the letter N formed from the letters of the word NIPUN is 4

To form words that start and end with the letter N, we need to first fix the letter N at the beginning and end of the word. This leaves us with the letters I, P, and U to arrange in the middle.

There are 3! (3 factorial) ways to arrange these 3 letters, which is equal to 3 × 2 × 1 = 6.

However, we need to divide by the number of times each letter appears in the word, which is 1 for each of the letters I, P, and U.

So the total number of words that can be formed is 6/1/1/1 = 6.

But we only want the words that start and end with the letter N, so we need to divide by the number of times the letter N appears in the word, which is 2.

So the final answer is 6/2 = 3.

Therefore, the total number of words which starts and end with the letter N formed from the letters of the word NIPUN is 3.

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The mass of suitcase D is 2x -2 kg.

What is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the names given to these symbols because they lack fixed values.

As per the given data:

mass of A = x kg

B has a mass 6 kg less than A.

C has a mass twice of B

total mass = 6x - 20 kg

Let's consider mass of D as M.

mass of B = x - 6

mass of C = 2(x - 6)

For the total mass:

x + x - 6 + 2(x - 6) + M = 6x - 20

2x - 6 + 2x - 12 + M = 6x - 20

4x - 18 + M = 6x - 20

M = 2x - 2 kg

Hence, mass of suitcase D is 2x -2 kg.

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A summary is a brief overview of the main points or important details of a text or event. In the case of the statements provided, option A, "My sister's wedding was a success," is the best example of a summary.

A summary provides a general overview of the event without going into specific details about how things looked, felt, smelled, or tasted, as does option A.

Options B and C, "I ate yummy salmon at my sister's wedding" and "My dress at my sister's wedding was blue," are not summaries because they focus on specific details rather than providing an overview of the event.

In conclusion, alternative A. My sister's wedding was a success is correct.

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From the equation of the least squares regression line, we can say that the height of the flower compared to the soil line, in the beginning, is 3.16 units and it grows by 0.56 units each day.

A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. Two expressions joined by an equal sign form a mathematical statement known as an equation. The expression on the left and the expression on the right is shown to be equal in relation to one another.

LHS = RHS (left-hand side = right-hand side) appears in all mathematical equations. You can solve equations to determine an unknown variable's value, which corresponds to an unknown quantity. It is not an equation if there is no "equal to" symbol in the statement. It will be taken into account as an expression.

Given,

The predicted height = 0.56

Days in soil = 3.16

The y-axis of the plot is the height of the line compared to the soil line.

The x-axis gives the number of days.

from the equation of the least squares regression line, we get the above predicted height and the days in the soil.

y  = mx+b is the equation of a line.

Then, we can say that,

m = slope = 0.56

b = y-intercept = 3.16

Therefore from the equation of the least squares regression line, we can say that the height of the flower compared to the soil line, in the beginning, is 3.16 units and it grows by 0.56 units each day.

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The proportion that could be used to solve for x is 32/x = 12/15. The correct option is 3.

There are two primary methods for resolving proportional problems: cross-products and cross-multiplications. Using proportions and ratios.

By cross-multiplying, you multiply the denominator of the second ratio by the numerator of the first ratio.

Then you set that equal to the first ratio's denominator multiplied by the second ratio's numerator. By cross-multiplying the above proportion as an example, we may find the value of x.

24/9 = 32/12 = x/15

32/12 = x /15

32/x = 12/15

Thus, the correct option is 3) 32/x = 12/15.

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The question is incomplete. The missing options are written below:

The accompanying diagram shows two similar triangles. Which proportion could be used to solve for x?

1) x/ 24 = 9/ 15

2) 24/9 = 15/x

3) 32/x = 12/15

4) 32/12 = 15/x

The equation of total time taken by the commuter in travelling is 14x + 11, thus the correct option (b).

An algebraic equation can be defined as a mathematical statement in which two expressions are equivalent. Algebraic equations usually consist of variables, coefficients and constants .

Algebraic equations are also called polynomials because they contain polynomials on both sides of the equality sign. Algebraic equations consist of variables, coefficients, constants, and algebraic operations such as addition, subtraction, multiplication, division, and exponentiation.

According to the question:

(4x + 13) + (10x - 2) = 4x + 10x + 13 - 2

                               = 14x + 11

Thus, the equation for the total time taken is 14x + 11.

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2x should be added to 3x to get 5x.

To find out what should be added to 3x to get 5x, we can use simple algebra. We can set up an equation as follows:

3x + ? = 5x

Next, we can isolate the unknown variable on one side of the equation by subtracting 3x from both sides:

? = 5x - 3x

Simplifying the right side of the equation gives us:

? = 2x

Therefore, the answer is 2x. This means that 2x should be added to 3x to get 5x.

In conclusion, 2x should be added to 3x to get 5x.

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The solutions to the equation are w = (5 + i√(5))/(10) and w = (5 - i√(5))/(10). These are the fully simplified answers.

To solve the equation 10w(w-1)+3=0 using the Quadratic Formula, we first need to rearrange the equation to the standard form of a quadratic equation, which is ax²+bx+c=0.

In this case, we can distribute the 10w to get 10w²-10w+3=0. This gives us the values of a=10, b=-10, and c=3.

Now, we can plug these values into the Quadratic Formula, which is:

w = (-b ± √(b²-4ac))/(2a)

w = (-(-10) ± √((-10)²-4(10)(3)))/(2(10))

w = (10 ± √(100-120))/(20)

w = (10 ± √(-20))/(20)

w = (10 ± √(-1)(20))/(20)

w = (10 ± √(-1)√(20))/(20)

w = (10 ± i√(20))/(20)

w = (10 ± i√(4)√(5))/(20)

w = (10 ± 2i√(5))/(20)

w = (5 ± i√(5))/(10)

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You will have 4500L of water in the tank after it rains 90mL.

If it rains 90mL and you have a tank with a roof area of 50m^2, you can calculate the amount of water collected in the tank using the following formula:

Amount of water collected = (Rainfall in mm) x (Roof area in m^2)

In this case, the amount of water collected would be:

Amount of water collected = (90mm) x (50m^2)

Since 1mm of rain is equivalent to 1L of water per square meter, we can convert the rainfall from mm to L:

Amount of water collected = (90L/m^2) x (50m^2)

Simplifying the equation gives us:

Amount of water collected = 4500L

Therefore, you will have 4500L of water in the tank after it rains 90mL.

I hope this helps! Let me know if you have any further questions.

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Answer:

Step-by-step explanation:

1500 + 5000x 0.055 - $1775

1500 + 10000 x 0.055 = $2050

with option 1 he would make 1775 to 2050

                   2400 + 5000 x0.04 =2600

                   2400 + 10000 x 0.04 = 2800

With option 2 hw would make $2600 to $2800

                                     simple calculation  :)

The response to the given question would be that JK || ML is a pair of parallel sides, and JM and KL are equal in length, making JKLM a trapezoid, more particularly an isosceles trapezoid.

In terms of geometry, a quadrilateral is a four-sided polygon with four edges and four corners. Its origins are in the Latin terms quadri and latus (meaning "side"). A rectangle is a two-dimensional shape with four sides, four vertices, and four corners. Two main types of concave and convex exist. Convex quadrilaterals also have a number of subclasses, such as trapezoids, parallelograms, rectangles, rhombuses, and squares. A rectangle is a two dimensional shape with four straight sides. Quadrilaterals come in many various shapes, such as parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

The quadrilateral JKLM's shape may be ascertained using the information provided as follows:

JK = ML signifies that the lengths of the opposing sides are equal.

JM = KL denotes that the length of neighbouring sides is the same.

Nevertheless, we lack sufficient knowledge to establish whether or not opposing angles are equal.

As a result, using the information provided, the quadrilateral JKLM would be classified in the following way:

JK || ML is a pair of parallel sides, and JM and KL are equal in length, making JKLM a trapezoid, more particularly an isosceles trapezoid.

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We get the cartesian equation of the plane:

-48x - 28y + 20z = -240

To find the cartesian equation of a plane using the given vectors u and v, we need to find a normal vector to the plane. A normal vector is a vector that is perpendicular to the plane. We can find a normal vector by taking the cross product of u and v. The cross product of two vectors u and v is given by:

n = u x v = <(u2*v3 - u3*v2), (u3*v1 - u1*v3), (u1*v2 - u2*v1)>

Plugging in the values for u and v, we get:

n = <-6,8,4> x <2,-6,-9> = <(8*-9 - 4*-6), (4*2 - -6*-6), (-6*-6 - 8*2)>

n = <-72+24, 8-36, 36-16> = <-48, -28, 20>

Now that we have a normal vector to the plane, we can use it to find the cartesian equation of the plane. The cartesian equation of a plane is given by:

n1(x-x0) + n2(y-y0) + n3(z-z0) = 0

where n =  is the normal vector and (x0, y0, z0) is a point on the plane. We can use the vector u as a point on the plane, so (x0, y0, z0) = (-6, 8, 4). Plugging in the values for n and (x0, y0, z0), we get:

-48(x+6) - 28(y-8) + 20(z-4) = 0

Simplifying, we get the cartesian equation of the plane:

-48x - 28y + 20z = -240

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A) To change the rectangular coordinates (-5√3, 5) to polar coordinates, we need to find the radius r and the angle θ.

The radius r can be found using the Pythagorean theorem:
r = √(x^2 + y^2)
r = √((-5√3)^2 + (5)^2)
r = √(75 + 25)
r = √100
r = 10

The angle θ can be found using the inverse tangent function:
θ = tan^(-1)(y/x)
θ = tan^(-1)(5/(-5√3))
θ = tan^(-1)(-√3/3)
θ = -π/6

So, the polar coordinates are (10, -π/6).

B) Given a = (-5, 2) and b = <4, -7>, we need to find 3a - 4b.

3a = 3(-5, 2) = (-15, 6)
4b = 4(4, -7) = (16, -28)

3a - 4b = (-15, 6) - (16, -28) = (-15 - 16, 6 - (-28)) = (-31, 34)

So, the answer is (-31, 34).

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We can see that there are 3 data points in the 1-5 class, 3 data points in the 6-10 class, 2 data points in the 11-15 class, and 0 data points in the 16-20 class.

To build a frequency distribution table for the given data, we will first sort the data into the appropriate class limits and then tally the frequency of each class. We will use the following columns in our table: class limits, tally, and frequency.


 
 Class Limit   Tally              Frequency
   1-5                      |||                        3
  6-10                     |||                        3
  11-15                      ||                        2
 16-20                                               0
   

 

The distribution of the data is shown in the table above. The class limits are the ranges of values that the data falls into. The tally column is used to count the number of data points in each class, and the frequency column is the total number of data points in each class. By using this table, we can see that there are 3 data points in the 1-5 class, 3 data points in the 6-10 class, 2 data points in the 11-15 class, and 0 data points in the 16-20 class.

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Class B has higher percentage of girls than class A that is 26.6 % more.

A percentage is a number or ratio that can be expressed as a fraction of 100. If you need to calculate the percentage of a number, divide the number by the whole number and multiply by 100. Percentages therefore mean 1 in 100.

Given,

Total number of students in class A = 60

Number of girls student in class A = 28

percentage of girls in class A

= (28/60)×100

= 0.467 × 100

= 46.7%

Total number of students in class B = 60

Number of girls student in class B = 44

percentage of girls in class A

= (44/60)×100

= 0.733 × 100

= 73.3 %

Difference in percentage of girls in class A and class B.

= 73.3% - 46.7%

= 26.6%

Hence, class B has 26.6 percent more girls than class A.

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x1 = 5 and x2 = 0

The following LP problem in a spreadsheet MAX: 4x1 + 4x2 Subject to: 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0.A spreadsheet is a type of software that allows users to store and analyze data in a grid-like format of rows and columns. Spreadsheets are commonly used for data entry, financial modeling, and other calculations.In the given problem, we are supposed to find the maximum value of the function 4x1 + 4x2 subject to the constraints 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0.The first two constraints are represented by inequalities. That means, the values of x1 and x2 can be any non-negative values that satisfy the constraints. Mathematically, the constraints can be represented as:2x1 + 4x2 <= 20⇒ x2 <= 5 - 0.5x1--------(1)3x1 + 5x2 <= 15⇒ x2 <= 3 - 0.6x1--------(2)Note that, we have represented the constraints in such a way that x2 is the subject of the inequality. This is done to make it easier to graph and find the feasible region.To find the feasible region, we need to graph both inequalities (1) and (2) on a coordinate plane. The feasible region is the shaded area that is common to both regions. It is given below:The feasible region is the triangular-shaped region. Since x1 and x2 are both non-negative, we need to consider only the values of x1 and x2 that are within the feasible region.Now, to maximize the function 4x1 + 4x2, we need to find the optimal solution. We do this by finding the intersection points of the lines that represent the equation 4x1 + 4x2 = k, where k is a constant.The equation 4x1 + 4x2 = k can be rearranged as x2 = (-x1 + k/4)This equation represents a line with a slope of -1 and a y-intercept of k/4. We can graph this line for different values of k to find the optimal solution. The line for k = 0 is shown below:We can see that the line passes through the feasible region at point (0, 0) and (5, 0). This means that the maximum value of the function is 4x1 + 4x2 = 4(5) + 4(0) = 20 at point (5, 0).Thus, the maximum value of the function 4x1 + 4x2 subject to the constraints 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0 is 20 at x1 = 5 and x2 = 0.

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The height of the flagpole is approximately 23,047.11 feet.

To resolve this issue, we can make use of the similar triangles property. The teacher, the flagpole, and each of their corresponding triangles are similar because they have the same angles.

Let h be the height of the flagpole. Then, we can set up the following proportion:

h / 3112 = 612 / 9

When we simplify this ratio, we obtain:

h = (3112 x 612) / 9

h = 207424 / 9

h ≈ 23,047.11 feet

Hence, the flagpole is roughly 23,047.11 feet tall.

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The total surface area of the tires making contact with the ground at any one time for the truck with 18 wheels, tire radius of 21 in, tire width of 12 in, and 20% contact area is approximately 5700.24 square inches.

The surface area of one tire making contact with the ground can be calculated as follows:

The diameter of the tire is 2 * radius = 2 * 21 in = 42 in

The length of the portion of the tire making contact with the ground is 20% of the circumference of the tire = 0.2 * π * 42 in ≈ 26.39 in

The width of the tire making contact with the ground is given as 12 in

Therefore, the surface area of one tire making contact with the ground is approximately 26.39 in * 12 in = 316.68 square inches

Since the truck has 18 wheels, the total surface area of all the tires making contact with the ground at any one time is 18 * 316.68 square inches = 5700.24 square inches.

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The Circumference of the given circle with a radius of 6 meters and л’s value of 3.14 is 37.68 meters.

In 2-D Geometry, the circumference of the circle is the perimeter running around the circle.

The Circumference of a circle is given by the following formula:

C=2 лr…..(i),

Where,

C = Circumference of the circle,

Л = 3.14 (given value)

r= Radius of the circle = 6 meters (given).

Substituting the values of each variable in equation (i), we get;

C = 2 лr = 2x3.14x6 meters,

Or, C = 37.68 meters

Therefore, the circumference of the given circle is 37.68 meters

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Answer:

The total commission earned by the company is 10% of the selling price, which is:

0.10 x $180,000 = $18,000

Marge receives 1/4 of the company's commission, which is:

(1/4) x $18,000 = $4,500

Therefore, Marge receives $4,500 in commission.

The volume of the prism would be h(60 - hp/2) cubic feet.

Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫∫ F(x, y, z) dx dy dz

Given is that the surface area of the right prism is 120 feet.

The formula for finding the surface area for the right prism is -

A = 2b + hP

2b + hp = 120

We can write the base area as -

2b = 120 - hp

b = 60 - hp/2

The volume of the prism would be -

V = base area x height

V = (60 - hp/2) x (h)

V = h(60 - hp/2)

Therefore, the volume of the prism would be h(60 - hp/2) cubic feet.

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The Ratio fractions decimal percent is as follows:

17% as a decimal = 0.17

17% as a fraction = 17/100

17% as a ratio = 17:100

3/4 as a decimal = 0.75

3/4 as a fraction = 3/4

3/4 as a ratio = 3:4

To convert 17% to a decimal, we move the decimal point two places to the left, which gives us 0.17.

To convert 3/4 to a decimal, we divide 3 by 4, which gives us 0.75.

To convert 0.17 to a fraction, we write it as 17/100 and simplify by dividing both the numerator and denominator by the greatest common factor, which is 17 in this case. Therefore, 0.17 as a simplified fraction is 17/100.

To convert 0.75 to a fraction, we write it as 75/100 and simplify by dividing both the numerator and denominator by the greatest common factor, which is 25 in this case. Therefore, 0.75 as a simplified fraction is 3/4.

To convert 17% to a ratio, we write it as 17:100.

Therefore:

17% as a decimal = 0.17

17% as a fraction = 17/100

17% as a ratio = 17:100

3/4 as a decimal = 0.75

3/4 as a fraction = 3/4

3/4 as a ratio = 3:4

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The functions that are odd or even can be determined by replacing x with -x and seeing if the function remains the same or changes sign.

(a) f(x) = -tan(x) is an odd function because f(-x) = -tan(-x) = tan(x) = -f(x)

(b) f(x) = tan(x+T/2) is an odd function because f(-x) = tan(-x+T/2) = -tan(x+T/2) = -f(x)

(c) f(x) = tan(x)+cot(x) is neither an odd nor an even function because f(-x) = tan(-x)+cot(-x) = -tan(x)-cot(x) ≠ f(x) or -f(x)

(d) f(x) = 5cot(x) is an even function because f(-x) = 5cot(-x) = 5cot(x) = f(x)

(e) f(x) = (tan(x))2 is an even function because f(-x) = (tan(-x))2 = (tan(x))2 = f(x)

(f) f(x) = tan(4x) is an odd function because f(-x) = tan(4(-x)) = -tan(4x) = -f(x)

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The decimal fοrm οf the mixed fractiοn 33 2/3, apprοximated tο the nearest tenth, is 33.67.

A mixed fractiοn is οne that is represented by bοth its quοtient and remainder. Sο, a mixed fractiοn is a cοmbinatiοn οf a whοle number and a prοper fractiοn. A fractiοn represents a piece οf a larger tοtal. Tο learn hοw tο determine the precise values οf mixed numbers, it is crucial tο cοnvert a mixed number tο a decimal. A mixed number can be cοnverted tο decimal fοrm using οne οf twο techniques:

the mixed number is changed intο an imprοper fractiοn.

by first changing the given mixed number's fractiοnal pοrtiοn tο decimal, then adding the whοle number pοrtiοn tο it.

Nοw the given fractiοn is 33 2/3.

This is a mixed fractiοn because it has a whοle number οf 33 and a fractiοn οf 2/3.

This mixed fractiοn can be cοnverted tο a decimal number by finding the value οf the fractiοn part οf the number and adding it tο the whοle number.

Sοlving fractiοnal parts,

2/3 = 0.66666 = 0.67 (Rοunding tο the nearest tenth)

Nοw add tο the whοle number.

33 + 0.67 = 33.67

Therefοre the decimal fοrm οf the mixed fractiοn 33 2/3 is 33.67.

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Using algebra we can conclude that Mrs. Ong brought a total of 12 fruits.

Algebra is a discipline of mathematics that studies symbols and the mathematical operations that can be applied to them.

These symbols are referred to as variables because they don't have predetermined values.

These symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations in order to ascertain the values.

Now, let the total fruits be x.

Oranges = 1/2 x - 3

Pears = [x - 1/2 (1/2x -3 ) ]- 2= x - 1/4x + 3/2 - 2 = 3x /4 - 1/2

Apples = x - 1/2 (3x /4 - 1/2) - 1

           = x - 3/8 x + 1/4 - 1 = 5x /8 - 3/4

Mangoes = 5

x - 5x/ 8 + 3/4 = 5

3x /8 + 3/4 = 5    

3x + 6 = 40

3x = 34

x = 11.333

Therefore, using algebra we can conclude that Mrs. Ong brought a total of 12 fruits.

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Complete question:

Mrs. Ong bought some fruits. 3 fewer than 1/2 of the fruits were oranges. 2 fewer than 1/2 of the remaining fruits were pears. 1 fewer than half of the remaining fruits were apples and the remaining 5 fruits were mangoes.

How many fruits did Mrs Ong buy altogether?

Answer: 3

Step-by-step explanation:

To find the x value, we must plug 6 in for y

6 = 15 - 3x

-9 = -3x

3 = x

Hope this helps!

The conditional density function ????(????|???? = y) = 1/y. This is a valid density function because it is non-negative and integrates to 1.

So the answer is ????(????|???? = y) = 1/y.

The question asks us to find the conditional density function ????(????|???? = y) given the joint density function ????(x, y) = 6y(1 − y), 0 ≤ x ≤ y ≤ 1.

To find the conditional density function, we need to divide the joint density function by the marginal density function of y.

The marginal density function of y can be found by integrating the joint density function with respect to x:

????(y) = ∫????(x, y) dx = ∫6y(1 − y) dx = 6y(1 − y) ∫dx = 6y(1 − y) (x) |0≤x≤y = 6y(1 − y) (y - 0) = 6y^2(1 − y)

Now we can find the conditional density function by dividing the joint density function by the marginal density function:

????(????|???? = y) = ????(x, y)/????(y) = 6y(1 − y)/6y^2(1 − y) = 1/y

Therefore, the conditional density function ????(????|???? = y) = 1/y. This is a valid density function because it is non-negative and integrates to 1.

So the answer is ????(????|???? = y) = 1/y.

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So, the solution to the system of equations is:

x = -26/7
y = -25/7
z = -37/7

Solving a system of linear equations by the Matrix Inversion method involves finding the inverse of the coefficient matrix, multiplying it by the constant matrix, and solving for the variables.

First, we need to write the system of equations in matrix form:

[ 2 6 2 ] [ x ] [ 8 ]
[ 6 6 3 ] [ y ] = [ -3 ]
[ 2 3 1 ] [ z ] [ 3 ]

Next, we need to find the inverse of the coefficient matrix:

A = [ 2 6 2 ]
[ 6 6 3 ]
[ 2 3 1 ]

The determinant of A is:

det(A) = 2(6-9) - 6(2-6) + 2(18-6) = -6 + 24 + 24 = 42

The adjoint of A is:

adj(A) = [ (6-3) (-2+6) (-18+6) ]
[ (-6+3) (2-4) (12-6) ]
[ (6-18) (-2+12) (2-18) ]

= [ 3 4 -12 ]
[ -3 -2 6 ]
[ -12 10 -16 ]

The inverse of A is:

A' = (1/det(A))adj(A) = (1/42)[ 3 4 -12 ]
[ -3 -2 6 ]
[ -12 10 -16 ]

= [ 1/14 2/21 -4/7 ]
[ -1/14 -1/21 2/7 ]
[ -4/7 5/21 -8/21 ]

Now, we can multiply the inverse of A by the constant matrix to find the solution:

[ x ] [ 1/14 2/21 -4/7 ] [ 8 ]
[ y ] = [ -1/14 -1/21 2/7 ] [ -3 ]
[ z ] [ -4/7 5/21 -8/21 ] [ 3 ]

= [ (8/14) + (16/21) + (-32/7) ]
[ (-8/14) + (-3/21) + (-6/7) ]
[ (-32/7) + (15/21) + (-24/21) ]

= [ -26/7 ]
[ -25/7 ]
[ -37/7 ]

So, the solution to the system of equations is:

x = -26/7
y = -25/7
z = -37/7

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