Write 2% as a decimal (not as a percentage).

The mean and variance of the uniform discrete random variable x that takes values from the set {1, 2, . . . n} is   and   .

For Discrete Uniform Distribution the probability mass function (pmf) is denoted by P(x)=1/n , where x=1,2,3,...,n.

in the given question

The mean of the Discrete Uniform Distribution is given by [tex]E(x)=\[\sum_{x=1}^{n}p(x)*x\][/tex]

By substituting the value of P(x)=1/n

[tex]E(x)=\[\sum_{x=1}^{n}\frac{1}{n} *x\][/tex]

[tex]=\frac{1}{n}\[\sum_{x=1}^{n}x\][/tex]

[tex]=\frac{1}{n} (1+2+3+4+...n)[/tex]

[tex]=\frac{1}{n} *\frac{n(n+1)}{2}[/tex]    ( as we know that sum of n terms is [tex]\frac{n(n+1)}{2}[/tex]  )

=[tex]\frac{n+1}{2}[/tex]

hence , [tex]\mu=\frac{n+1}{2}[/tex] ....(i)

The Variance of the Discrete Uniform Distribution is denoted by Var(x) and is given by [tex]Var(x)=E[(x-\mu)^{2}][/tex]

As we know that [tex]E(x)=\[\sum_{x=1}^{n}p(x)*x\][/tex]   similarly for E[(x-μ)²] we get

[tex]E[(x-\mu)^{2}]=E[x^{2} ]-\mu^{2}[/tex]

[tex]=E[x^{2}]-(\frac{n+1}{2} ) ^{2}[/tex]        ( we have found [tex]\mu=\frac{n+1}{2}[/tex] )  ....(ii)

For E[x²]

[tex]E(x^{2} )=\[\sum_{x=1}^{n}\frac{1}{n} *x^{2} \][/tex]

[tex]=\frac{1}{n}\[\sum_{x=1}^{n} x^{2} \][/tex]

[tex]=\frac{1}{n} (1^{2} +2^{2} +3^{2} +4^{2} +...+n^{2} )[/tex]

We know that [tex]1^{2} +2^{2} +3^{2} +4^{2} +...+n^{2} =\frac{n(n+1)(2n+1)}{6}[/tex]

Substituting the value in above equation we get we get

[tex]E[x^{2} ]=\frac{1}{n} *\frac{n(n+1)(2n+1)}{6}[/tex]

[tex]E[x^{2} ]=\frac{(n+1)(2n+1)}{6}[/tex]

Substituting the value of E[x²] back in equation (ii)

We get

[tex]Var[x]=\frac{(n+1)(2n+1)}{6} -( \frac{n+1}{2})^{2}[/tex]

[tex]=\frac{(n+1)(2n+1)}{6} -\frac{(n+1)^{2} }{4}[/tex]

[tex]=(n+1)(\frac{(2n+1)}{6} -\frac{(n+1) }{4})[/tex]

taking LCM as 12 and solving further we get

[tex]=(n+1)(\frac{4n+2-3n-3}{12} )[/tex]

[tex]=\frac{(n+1)(n-1)}{12}[/tex]

[tex]=\frac{n^{2}-1 }{12}[/tex]     (using identity of (a+b)(a-b)   )

Therefore , the mean and variance of the uniform discrete random variable x that takes values from the set {1, 2, . . . n} is [tex]\frac{n+1}{2}[/tex]  and [tex]\frac{n^{2}-1 }{12}[/tex]  .

Learn more about Mean and Variance here https://brainly.com/question/4882154

#SPJ4

Answer:

no 1 answer is asia

no 2 answer is europe

If ∠A ≅ ∠X and ∠C ≅ ∠Z , then ΔABC ∼ ΔXYZ by the AA Similarity Postulate.

Similar triangles are triangles that have congruent corresponding angles and proportional corresponding sides.

example:

If ΔABC ∼ ΔXYZ, then ∠A = ∠X, ∠B = ∠Y, and ∠C = ∠Z, and

AB/XY = BC/YZ = AC/XZ

AA (or AAA) or Angle-Angle Similarity Postulate states that if any two angles of a triangle are congruent to any two angles of another triangle, then the two triangles are similar to each other.

So, given that ∠A ≅ ∠X and ∠C ≅ ∠Z, then ΔABC ∼ ΔXYZ by the AA Similarity Postulate.

To learn more about AA Similarity Postulate: https://brainly.com/question/21247688

#SPJ4

Answer:True

Step-by- by step

Irrational numbers are square roots of numbers , when two irrational numbers are multiply together, it is called rationalization and this gives a rational value, So the answer is true.

Answer: x = 3/4

Step-by-step explanation:

The first step to solve this equation would be to simplify both sides of the equation by multiplying

1/4*12 - 1/4*8x = 2/3*6x

3 - 2x = 2x

3= 2x+2x

3=4x

x=3/4

Answer:

Step-by-step explanation:

AS THERE ARE 2 fractions 1/4 and 2/3, one way would be to first get rid of these by multiplying through by the LCM  12, giving:

12*1/4(12 – 8x) = 12*2/3(6x)

3(12 - 8x) = 8(6x)

36 - 24x = 48x

36 = 72x

x = 1/2.

The correct equation is:

|x - 32| = 0.78

In this case, x represents both the maximum and minimum accepted volumes.

We know that the mean volume is 32 fluid ounces, and the acceptable error is 0.78 fluid ounces.

Then the maximum acceptable volume is 32 + 0.78 fluid ounces, and the minimum acceptable volume is 32 - 0.78 fluid ounces.

This means that the absolute value of the difference between x, the volume, and 32, must be equal to 0.78

This is written as:

|x - 32| = 0.78

In this case, x represents both the maximum and minimum accepted volumes.

If you want to learn more about absolute value:

https://brainly.com/question/1782403

#SPJ1

A glide reflection is commutative. Reversing the direction of the composition will not affect the outcome.

A composite transformation is a glide reflection, right?

Which of the ensuing characteristics is unaffected by a glide reflection?

Learn more about glide reflections

brainly.com/question/2254222

#SPJ4

We can conclude that the value of x is (∠MNP + 66)/8 and angle m∠RNM = ∠RNQ - ∠MNP + 78.

So,

Now, substitute 'x = (∠MNP + 66)/8' in 8x + 12:

Hence, m∠RNM = ∠RNQ - ∠MNP + 78

Therefore, in the given question value of x is (∠MNP + 66)/8 and angle m∠RNM = ∠RNQ - ∠MNP + 78.

Know more about angles here:

https://brainly.com/question/25716982

#SPJ9

The required width of the rectangle is 10 meters.

Given that,
A rectangular field has a perimeter of 150m The field is 15 meters longer than it is wide. The width of the field is x meters.

The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.

Here,
The area of the rectangle = length * width
150 = 15 * x
x = 150 / 15
x = 10

Thus, the required width of the rectangle is 10 meters.

Learn more about rectangles here:

brainly.com/question/15019502

#SPJ1

The coordinates of the vertices of new triangle are [tex]A^{I}[/tex](-1,3),[tex]B^{I}[/tex](-1,0),[tex]C^{I}[/tex](0,0).

Given that the coordinates of the triangle be (-5,5), (-5,-1) and (3,-1)

We are required to find the coordinates of the new triangle.

Scale Factor is basically used to scale shapes in different dimensions.

Coordinates are the points that lie on the plane surface.

As we can see in the picture, the coordination of the vertices of the triangle be A(-5,5), B(-5,-1) and C (-3,-1).

=1/2 [tex]\left[\begin{array}{ccc}-5+3&-5+3&-3+3\\5+1&-1+1&-1+1\\\end{array}\right][/tex]

=1/2 [tex]\left[\begin{array}{ccc}-2&-2&0\\6&0&0\\\end{array}\right][/tex]

=[tex]\left[\begin{array}{ccc}-1&-1&0\\3&0&0\\\end{array}\right][/tex]

Hence the coordinates of the vertices of new triangle are [tex]A^{I}[/tex](-1,3),[tex]B^{I}[/tex](-1,0),[tex]C^{I}[/tex](0,0).

Learn more about scale factor at https://brainly.com/question/25722260

#SPJ1

The domain is {0, -1, -2, -3} and the range is {0, -1, 2, 3}

The given relation is {(-3,2), (-1,3), (0,0), (-2,-1)}. Here, the relation is given as a set of ordered pairs. Domain in mathematics is defined as the all the inputs that are possible to be part of functions. Range refers to the values assumed by function and these are the output values.

The domain of the function is the set of x- coordinates.

∴ The domain is {0, -1, -2, -3}

The Range of the function is the set of y- coordinates.

∴The Range is {0, -1, 2, 3}

Hence, the domain is {0, -1, -2, -3} and the range is {0, -1, 2, 3}.

Know more about Domain and Range of a relation:

brainly.com/question/26098895

#SPJ4

Answer:

The coefficients of the expansion are given by the 6th row of Pascal's triangle, where the top row is row zero, the next is row one, etc. The coefficients of the 6th row are used because we are expanding to the 6th power. The coefficients are 1 , 6 , 15 , 20 , 15 , 6 , 1 .

mark me as Branlist answer.Hope it helps.

Ф2 = E2 L² is  the electric flux through the cube face in the plane z = 0.

What exactly are electric flux and unit?

given ,

          edge length = L

 Area of each surface = L²

Ф = E . A

    = E . A Cos θ

Φ1 = E1  A Cosθ

Φ1 = E1 L²

Similarly we get

Ф2 = E2 L²

Learn more about electric flux

brainly.com/question/14544020

#SPJ4

Answer:

B. Thousandths

Step-by-step explanation:

Let's compare the numbers:

2.7693

2.7602

^ This is where the numbers first differ.

This number is three spaces to the right of the decimal, so it is in the thousandths place.

Referring  to the circle ED  is the chord that is not a diameter.

The circle is one of the shapes with consists of all points with identical distances from its center. A particular circle is named by its center.Here diameter of the circle is the distance across the circle through the center, whereas a chord is a line segment that joins two points on a curve on the circle since the diameter is satisfieding the points of a chord but a chord is not a diameter, as diameter are the line that just passes through the center of the circle, whereas the chord doesn't cross from the center of the circle, thus it can be quoted that, every diameter is a chord, but not every chord is a diameter.

To know  more about circle refer to the link https://brainly.com/question/12930236?referrer=searchResults.

#SPJ4

The equation of the line 3x + 2y = 6 is perpendicular with the equation of the line (A) 4x - 6y = 3.

Two lines are perpendicular with each other if they form right angle at the point of their intersection. The slopes of perpendicular lines are negative reciprocal of one another.

The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points.

In an equation in standard form, ax + by = c, the slope, m,  of the line is equal to a/b. On the other hand, in an equation in slope-intercept form, y = mx + b, m is the slope.

Determine the slope of the given line and each given choices:

3x + 2y = 6

m = a/b = 3/2

(A) 4x - 6y = 3

m = a/b = 4/-6 = -2/3

(B) y = -(3/2)x + 4

m = -3/2

(C) 2x + 3y = 12

m = a/b = 2/3

(D) y = (3/2)x + 1

m = 3/2

Since the slope of the given line is 3/2, taking its negative reciprocal, the slope of the perpendicular line should be -2/3. The line with the slope of -2/3 is (A) 4x - 6y = 3.

Hence, (A) 4x - 6y = 3 is perpendicular with 3x + 2y = 6.

Learn more about perpendicular lines here: https://brainly.com/question/7098341

#SPJ4

The equation in point-slope form of the line having the slope m=1/4 and contains the point (3,-1) is [tex]y+1=\frac{1}{4}(x-3)[/tex]

Given,

The slope m= [tex]\frac{1}{4}[/tex]

The point = (3,-1)

We know the point-slope form,

[tex]y-y_{1}=m(x-x_{1})[/tex]

Substitute the values in the equation

[tex]y-(-1)=\frac{1}{4} (x-3)\\y+1=\frac{1}{4}(x-3)[/tex]

Hence, the equation in point-slope form of the line having the slope m=1/4 and contains the point (3,-1) is [tex]y+1=\frac{1}{4}(x-3)[/tex]

Learn more about point-slope form here

brainly.com/question/24436844

#SPJ4

Using linear functions, the costs are given as follows:

For 4 hours, the difference is costs between the company that charges the most and the one that charges the least is of $15.

A linear function is modeled by:

y = mx + b

In which:

For Company A, we have two points on the column: (2, 33), (3, 49). Hence for one additional hour, the cost increased by $16, hence the slope is of 16 and:

A(x) = 16x + b.

When x = 2, A(x) = 33, hence we use it to find b as follows:

33 = 16(2) + b

b = 1.

Hence:

A(x) = 16x + 1.

Companies B and C have intercepts of 0, while the slopes are hourly costs, hence:

For 4 hours, the costs are given as follows:

The difference is:

72 - 57 = 15.

For 4 hours, the difference is costs between the company that charges the most and the one that charges the least is of $15.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer:

1, 3 and 5

Step-by-step explanation:

You can formulate the postulate as:

x² + (x + 2)² + 15 = (x + 4)²

Which simplifies to x² - 4x + 3 = 0, with solutions x=1 and x=3

so 1, 3 and 5 must be the other tuple.

The coordinates are (100, 173.2) after 5 seconds.

What are examples of coordination?

Let x represent the angle of rotation in 5 seconds.

[tex]\frac{Irotation }{time} = \frac{current position}{time}[/tex]

360° / 30 = x°/ 5

30x = 1800

x = 60°

To find the coordinates, use sine and cosine ratios.

Sin60 = opposite/ hypotenuse

sin60 = y / 200

 y = 200sin60

y ≈ 173.2

cos60 = adjancent/ hypotenuse

cos60 = x / 200

x = 200cos60

x = 100

The coordinates are (100, 173.2).

Learn more about coordinates

brainly.com/question/27749090

#SPJ4

Yes, a unit rate is a rate at which the the comparison is one unit.

A unit rate is a ratio between two separate units with one as the denominator.

Examples include miles/hour, kilometers/hour, meters/sec, salaries/month, etc. The most fundamental and historically significant field of mathematics is arithmetic, which is also the one we use the most frequently in daily life. This subject is all about mathematical procedures and problems centered on numbers.

           We actually solve mathematical puzzles during our daily activities, whether we mean to or not. For instance, whether buying fruits or vegetables, engaging in other transactions, or determining how quickly something will happen, etc.

When comparing two different kinds of numbers with distinct units, a rate is a ratio that is employed. The unit rate, on the other hand, shows how many units of one quantity are equal to one unit of another. When the denominator of a rate is 1, we refer to it as a unit rate.

To learn more about unit rate; visit: https://brainly.com/question/11258929

#SPJ9

FA recursive formula allows us to find each term in the geometric sequence using the previous term. Each new term is the product of the common ratio for that sequence and the previous term of that unknown or to-be-found term. If the common ratio is 9, each term is nine times the previous term.

The general term for the geometric sequence is,

an= a1 * r ^ (n-1)

Where "an" refers to the nth term of the sequence, a1 is the first term known as the sequence, and r is the common ratio, n is its position or the number.

Now the given values are,

a₁ = -1 and r = -1

Sequence: -1, 1, -1, 1, -1, 1, -1, 1, -1 ...

We can easily identify the first three terms from the above sequence.

3rd value: -1

More problems related to a similar concept are solved in the link below.

brainly.com/question/17102965?referrer=searchResults

#SPJ4

The equation of the line in point-slope form, with slope equal to 5/6 and passing through the point located at (22 , 12), is (y - 12) = 5/6(x - 22).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Using the point slope form, plug in the values to set up the equation.

(y - y1) = m(x - x1)

where m = 5/6 and (x1 , y1) = (22 , 12)

(y - 12) = 5/6(x - 22)

In slope-intercept form, the equation of the line is:

(y - 12) = 5/6(x - 22)

y - 12 = 5/6 x - 110/6

y = 5/6 x - 19/3

In standard form, the equation of the line is:

y = 5/6 x - 19/3

5/6 x - y = 19/3

Multiplying both sides by 6,

5x - 6y = 38

To learn more about equation in point-slope form: https://brainly.com/question/24907633

#SPJ4

Answer:  x=55 over 6

Step-by-step explanation:

Answer:

2.08 × [tex]10^{7}[/tex]

Step-by-step explanation:

Multiply 4 × 5.4 to get 20.8. Then multiply [tex]10^{-2}[/tex] × [tex]10^{8}[/tex] = [tex]10^{6}[/tex]

However, that is not an answer. So, you can divide 20.8 by 10 and multiply [tex]10^{6}[/tex] × 10.

Then you get 2.08 × [tex]10^{7}[/tex]