What is Stratified Random

Introduction:

Stratified random is the process of set of members of the population which having  uniform subgroups  of sampling. In the stratum there is equally exclusive, all elements are considered in  one stratum in the process of population. In the stratum there is jointly exhaustive, population element is not presented. Stratified random can create a strong mean better  than the arithmetic mean for random sample. This process is simple sample statistics.


Strategies of Stratified Sample Statistics:


What is Stratified random?

Stratified sample statistics is the method to know what probability sampling in statistics .
The stratified sample statistics having proportional sample statistics.
In this separating the population into uniform subgroups and taking a sample random sample from each sample groups.
This process is simple sample statistics.
What are Choosing Stratified Sample Statistics?

The population having number of N elements.
The population is separated into H group which is known as strata.
All part of the population should be assigned to one of the stratum.
The number of annotations within every stratum Nh noted as total of all notations.
The researcher contains a probability sample from every stratum.

Examples:


Let us consider an examples,

Example1:

Let us see what is meant by Stratified random,

If the total population consists of 60% of gents and 40% ladies then the relative size of the above population  is 3 ladies and 2 gents .It will reflect the proportion.

Example2:

Let us see what is meant by Stratified random,

Let us consider worker’s of one company we are separate them into number of subgroups. There are three categories, which includes Managers, Team leaders and Staffs (Employees).Here Team leaders and Employees are relatively small percentage. If we did simple random fractions where total population n =200 in the sampling fraction of 20%. We can imagine 20 and 15 persons from the strata.

Growth Factor Math

Introduction to growth factor math:

Growth factor in math article deals with the definition of growth factor math and the model problems related to growth factor.

Definition of growth factor math:

Growth factor is defined, as the constant value that is multiplied by it self over a certain period.the growth factor is always a positive number. Growth factor cannot be represented in percentage.

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Formula to growth factor math:


When the growth rate is given

Increase in value = P* G*N

P is the principle or original value.

G is the growth rate.

N is the period.
Growth factor is calculating by dividing the increased value by original value

Growth factor = `(("increased value")/("original value" ))`


Model problems to growth factor math:


Problem: 1

What is growth factor of the original value $600 over a period of 7 years with the growth rate of 6%.

Solution:

The original value is $600

Period of time = 7 years

Growth rate is 6%

The increase value is `(600*7*(6/100))`

(6*7*6)

= 252

The increased value is $852

Now we have to calculate the growth factor:

Growth factor =` (("increased value")/("original value"))`

= `(852/600)`

= 1.42

The growth factor is 1.42

Problem: 2

What is growth factor of the original value $400 over a period of 9 years with the growth rate of 8%.

Solution:

The original value is $400

Period of time = 9 years

Growth rate is 8%

The increase value is `(400*9*(7/100))`

(4*9*7)

= 252

The increased value is $652

Now we have to calculate the growth factor:

Growth factor = `(("increased value")/("original value"))`

= `(652/400)`

= 1.63

The growth factor is 1.63


Problem: 3 what is growth factor of the numbers behind the numbers 30, 60, 120, 240,480

Solution:

To find the growth, we have to divide the previous value by present value

(60/30) = 2
(120/60) =2
(240/ 120)= 2
(480/240)=2


Here the growth factors between the numbers are 2

The growth factor of the number is 2

Math Grade 4 Fraction

Introduction for math grade 4 fraction:
A fraction is a part of a whole. Fractions consist of two numbers. The top number is called the numerator. The bottom number is called the denominator.

Numerator
denominator

In a fraction, if the numerator is smaller than the denominator, it is called as proper fraction. Proper fractions are in completely reduced form. If the numerator is bigger than the denominator, this type of fractions is called as improper fractions. If a fraction is constructed by a whole number and a proper fraction is called as mixed fraction.

For example, `4/5` is a proper fraction (4 < 5)

`6/2 ` is an improper fraction (6 > 2)

2 `1/3 ` is a mixed fraction (2 is a whole number, `1/3 ` is a proper fraction)


Math 4 grade fraction – Methods and example problems:


Math 4 grade fraction - Adding fraction and adding unlike denominator:

Math 4 grade fraction- Addition fraction - Steps and problem:

To add algebraic fraction, follow these steps:

Write the given fraction and common denominator.
Added the numerators value.
Solution for the problem
Example:

` 2 / 5` + `8 / 5`

Solution:

`2 / 5` + `8 / 5`

= `(2 + 8) / 5`

= `10 / 5`

= 2

Math 4 grade fraction - Adding fraction involving unlike denominator – Steps and problem:

1. Express the fraction as equivalent fraction by finding the lowest common denominator (LCD) (the least numbers into which the denominator of two or more fractions will go evenly).

2. Add the numerator and place the sum over the lowest common denominator.

Example:

`5 / 6` + `4 / 3` =?

Solution:

These two fractions do not have the same denominators (lower numbers), so we must first find a common denominator of the two fractions, before adding them together.

For the denominators here, the 6 and 3, a common denominator for both is 6. LCD = 6

`5 / 6` = `5 / 6`

` 4 / 3 ` = `8 / 6`

`5 / 6` + `8 / 6 ` = `(5 + 8) / 6`

Answer = `13 / 6`

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Math 4 grade fraction - Subtracting fraction and subtracting unlike denominator:


Math 4 grade fraction - Subtraction fraction - Steps and problem:

To subtraction algebraic fraction, follow these steps:

Write the given fraction and common denominator.
Subtracted the numerators value.
Solution for the problem
Example:

`8 / 3 ` – `4 / 3`

Solution:

` 8 / 3` – `4 / 3`

= `(8-4)/3`

= `4 / 3`

Math 4 grade fraction - Subtracting fraction unlike denominator - Steps and problem:

1. Express the fraction as equivalent fraction by finding the lowest common denominator (LCD).

2. Subtract the numerator and place your answer over the lowest common denominator.

Example:

`15 / 4` – `6 / 2 ` =?

Solution:

These two fractions do not have the same denominators (lower numbers), so we must first find a common denominator of the two fractions, before subtracting them together.

For the denominators here, the 4 and 2, a common denominator for both is 4. LCD = 4

` 15 / 4 ` = `15 / 4`

`6 / 2` = `12 / 4`

` (15 / 4) ` – `(12 / 4) ` =  ` (15-12) / 4`

Answer = `3 / 4`

Matrice De Math

Introduction to matrice de math:
In mathematics, Matrix (plural: Matrices) is defined as the rectangular arrangements of elements in a rows and columns arranged with in the square brackets. The entries may be any type of elements such as numbers, polynomials and expressions. In math matrices can be expressed in terms of capital alphabetical letters.  Examples of matrices de math are:

A = `[[1,2,3, 1st row R1],[4,5,6, 2nd row R2],[7,8,9, 3rd row R3],[1st col,2nd col,3rd col,.],[C1,C2,C3,.]]`

Note:

Horizontal arrangements are called rows of the matrix.
Vertical arrangements are called column of the matrix.

Order of the matrix:


By using the number of rows and columns the order of the matrix is calculated. For example in the above mentioned matrix number of row is three and number of column is three. Hence the order of the above said matrix is 3 x 3.


Operations of matrix:

The operations of matrices are

Addition
Subtraction
Matrix multiplication
Transpose

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Examples of matrices:


Example 1:

If A =`[[1,2,1],[2,1,2],[2,2,1]]`and B =`[[3,2,1],[2,1,4],[3,5,1]]` .Then find A + B, A - B, A x B and AT.

Solution:

A + B = `[[1,2,1],[2,1,2],[2,2,1]]`+`[[3,2,1],[2,1,4],[3,5,1]]`

= `[[4,4,2],[4,2,6],[5,7,2]]`

Note:

Same order of the matrix can be added. The resultant matrix should also be the same order of matrix. Similarly, for subtraction.

A – B = `[[1,2,1],[2,1,2],[2,2,1]]` - `[[3,2,1],[2,1,4],[3,5,1]]`

=  `[[-2,0,0],[0,0,-2],[-1,-3,0]]`

Matrix multiplication:

A x B = `[[1,2,1],[2,1,2],[2,2,1]]` x `[[3,2,1],[2,1,4],[3,5,1]]`

=  `[[3+4+3,2+2+5,1+8+1],[6+2+6,4+1+10,2+4+2],[6+4+3,4+2+5,2+8+1]]`

=  `[[10,9,10],[14,15,8],[13,11,11]]`

Note:

Different order of matrices can be multiplied. If matrix A of order p x q is multiplied with the matrix B of order q x r, then the resultant matrix is p x r.

Matrix Transpose:

A   = `[[1,2,1],[2,1,2],[2,2,1]]`

AT = `[[1,2,2],[2,1,2],[1,2,1]]`

Note:

Interchanging rows into columns and columns into rows is known as transpose of the matrices de math.

These are the concepts on matrices de math.

World Math Word Problems

Introduction to world math word problems:

In mathematics education, the term word problem is often used to refer to any mathematical exercise where significant background information on the problem is presented as text rather than in mathematical notation. As word problems often involve a narrative of some sort, they are occasionally also referred to as story problems and may vary in the amount of language used.(Source - Wikipedia )

In this article of world math word problems, we are going to discuss some word problems on world math.

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Examples for World math word problems:


Example 1:

At a car park there are 70 vehicles, 40 of which are trucks, 25 are buss and the remainder are vans. Find the probability of

a) Bus leaving first.

b) Van leaving first.

Solution:

a) Let S be the sample space and A be the event of a bus leaving first.

n(S) = 70

n(A) = 25

Probability of a bus leaving first:

P(A) = 25/70 = 5/14

b) Let B be the event of a van leaving first.

n(B) = 70 – 40 – 25 = 5

Probability of a van leaving first:

P(B) = 5/70 = 1/14

Example 2:

Three times the larger of two numbers is three more than the three times the smaller, and the sum of three times the larger and four times the smaller is 73. Find out the numbers.

Solution:

Let x be the larger number and y be the smaller number.

Three times the larger = 3x

Three more than the three times the smaller = 3y + 3

Relationship:  3x = 3y + 3

Three times the larger = 3x

Three times the smaller = 4y

Relationship: 3x + 4y = 73

Now, we have two equations

3x = 3y + 3

3x + 4y = 72

From the first eqn,substitute the value of 3x in the second eqn

The equation will be,

3y+3+4y = 73

7y + 3 = 73

7y = 70

y = 10

Plug in y = 10 in the equation

3x = 3y + 3

3x = 3(10) + 3

3x = 30 + 3

x = 11

Larger number x  = 11

Smaller number y = 10.

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Additional World math word problem:


Example 1:

A side of a large tent is in the shape of an isosceles triangle whose area given is 22.5 m2 and whose base is four feet shorter than its height. Find the height of the tent.

Solution:

Height of the side   =  x

Base of the side      =  x – 4

Area of the triangle  = `<< 1/2>>` b * h

22.5  = `<< 1/2>>` ( x - 4 ) * x

22.5  = `<< 1/2>>`   x^2 - 4 x

45  =  x^2 - 4 x

x^2 - 4 x - 45 = 0

x^2 - 9x + 5x - 45 = 0

x ( x -9 ) + 5( x - 9 ) = 0

( x - 9 ) ( x + 5 )  = 0

( x - 9 ) = 0  and ( x + 5 ) = 0

x  = 9  and  x = - 5

Height of the tent x = 9 feet.

Square Root in Math

Introduction to square root in math:

In math, we use a radical symbol which is known as square root. Square root is also said to be as radical and the radical symbol is (sqrt). Rubicund is referred to a number which is present inside the root (i.e. sqrt (x), here x is referred as rubicund). Square root math is deals with the different properties of expressing square root by using various calculations. Let us see what properties of square root in math briefly.

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Different properties of square root in math:


Different properties of square root in math are described below,

General expression with exponent and radical:

`^nsqrt (a) ^m`   =`(^nsqrt (a)) ^m`   = (`a1/n) ^m ` = `am/n`

Multiplication property for radical expression: `^nsqrt (ab)` = `(^nsqrt (a))` ` (^nsqrt (b))`

Division property for radical expression: `(^nsqrt (a/b))` = `(^nsqrt (a))` / `(^nsqrt (b))`

Example for square root in math:


Example for square root in math: Add: `(8 * sqrt (2))` `-` `(6 * sqrt (2)) ` `+ ` `(9 * sqrt (2))`

Solution: Unite like terms by adding together the numerical coefficients.

`(8 - 6 + 9) * sqrt (2)`

` (17 - 6) * sqrt (2)`

After adding together, we get the answer like,

` 11 * sqrt (2)`

Answer: `(8 * sqrt (2))-(6 * sqrt (2)) + (9 * sqrt (2)) = 11 * sqrt (2)`

Example for square root in math:   Simplify, `sqrt (64)` `+ ` `sqrt (8)`

Solution: Take the given question and split the terms like,

`Sqrt (4 * 16)` `+ ` `sqrt (2 * 2 * 2)`

Rewrite the square root by using product of square root theorem.

`sqrt (4) * sqrt (16)` `+ ` `sqrt (2) * sqrt (2) * sqrt (2)`

`sqrt (2)* sqrt (2)* sqrt (4)* sqrt (4) ` `+` `sqrt (2) * sqrt (2) * sqrt (2)`

To simplify even further we use the definition of square root,

`(2 * 4) + 2(sqrt (2))`

Simplify by adding like terms to get the answer.

`(8 + 2(sqrt (2)))`

Simplify: `sqrt (64) + sqrt (8) = (8 + 2(sqrt (2)))`

Practice problem for square root in math:

Example for square root in math:` (^3sqrt (729))`

Answer: cubic root of (729) = `9^3`

Example for square root in math: `(^4sqrt (1296))`

Answer: fourth root of (1296) = `6^4`

Example for square root in math: `(sqrt (1225))`

Answer: (sqrt (1225))= 35

Point Math Term

Introduction to point math term:

The zero-dimensional object is called as point and it is defined the objects in space in math term. It is also referred as simple geometric concepts. The term point is represented in n-dimensional space and it is specified by dot. It give the exact position of object on surface. The diameter of point is 0.2 mm.

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Explanation for point in math


Math Euclidean geometry:

Euclidean geometry has a framework for point representation and in Euclidean space ordered pairs are called as point. The ordered pairs are represented as (x, y).  Here x is represent the horizontal axis number and y represent the vertical axis number.

In three-dimensional space, the ordered pairs are represented as (x, y, z) and z is represent the depth. The straight lines are created by connect the points in math. The key for point construction is postulates by Euclid.

Other branches of math:

The point-set topology is explain the topological space by point. The noncommutative geometry and pointless topology is fundamental of notion term.

The points arranged in some order and create a higher dimensional geometry like line, plane and space. These are considered as basic structures in geometry.

Coordinates of a point:

In two-dimensional plane, the position of point is defined by ordered pairs in math. The term coordianates is express the location of objects in two dimensional plane.These coordinate points are plotted in xy axis.

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More about point term


Decimal point term:

The decimal point is one type of number representation. This is define the place value of numbers like tens, hundreds and so on. For example the multiplication of 0.2 x 2 = 0.4 here 0.2 and 0.4 are decimal value.This is used in decimal expansion.

Fixed point:

The function’s fixed point is mapped to itself.If the real number is proceed with function and get the same number as output means that real number is called as fixed point. Here the number is considered as point.