ordered pair

Let us learn about ordered pair

An ordered pair has a pair of elements which occur in a definite order.An ordered pair has a pair of elements which occur in a definite order.

Take two numbers 3 and 5. If they form a pair (3,5) and the order of the numbers cannot be changed, these numbers are said to form an ordered pair.

(3, 5)# (5, 3)

If two ordered pairs (a, b) and (x, y) are equal,=> (a, b) = (x, y) then a = x,

b = y.

Example

If (3, y) = (x, 4) find x and y.

Since the ordered pairs are equal, then the first element of first pair = the first element of the second pair => x = 3, similarly y = 4.

Ans: x = 3, y = 4

In our next blog we shall learn about hands on equations

I hope the above explanation was useful.Keep reading and leave your comments.

square root of 225

This describes a "long hand" or manual method of calculating or extracting square roots. Calculation of a square root by hand is a little like long-hand division.

A square root of a number is the number that is multiplied by itself and gives the first number. For example, 2 is the square root of 4, because 2×2=4. Only numbers bigger than or equal to zero have real square roots, and a number bigger than zero has two square roots

square root of 225 = 3.873

Square root is the form of radical in which it is the method used in the mathematics. It has been given that the symbol for the radical form is (root) √. The value which is placed in the radical form is called as the radicand, in which it is the numeric value for the radical symbol of form (root) √. There are number of methods available in the root methods to solve they are,

Solve the square root of 225.

Solution:

Method 1: Long division method

15

1 | 225

| 1

25 | 125

| 125

0

The exact value for the square root of √225 is 15

Method 2:

√225 = √15^2

=(15^2)^1/2

= 15^2/2

= 15

or

√225

5 | 225

5 | 45

3 | 9

3

Therefore √5x5x3x3

= √5^2 x 3^2

= 5 x 3

= 15

In our next blog we shall learn about "factors of 56"

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Line equation and slope form

Let us study about Slope Intercept Form,

A line equation makes the straight line when it is graphed. If the line passes through the points A (x1, y1) and B (x2, y2) and then its slope is,

Slope (m) = (y2 - y1) / (x2 - x1)

The slope is defined as the relation between the perpendicular distance and flat distance between any two points. The slope is denoted by letter ‘m’. The slope is also called as the gradient.

I hope the above explanation was useful.

Advanced event systems

Hi Friends!!!

Let us learn about " Advanced event systems"
Introduction for Advanced Probability:

Mr. Pierce says the theory of probability is simply the science of logic quantitatively treated. Do we know about what is probability? It is a measure of uncertainty of events in a random experiment, and we have also studied the addition rule of probability. And treated probability as a function of outcomes of the experiment, a possible result of a random experiment is called its outcome but now we are going to study about advanced probability.

Advanced Probability Contents:

In this advance probability has so many contents, but we have to see some important topics only, there are given below:

1. Conditional expectation,
2. Poison distribution measures content,
3. Martingales theory and applications content,
4. Continuous-time random process content, and
5. Weak convergence content.

In our next blog we shall learn about "lysosom"

I hope the above explanation was useful.Keep reading and leave your comments.

Explain Additive inverse

Let us study about Additive inverse,

Introduction of addition inverse property:

The Addition Inverse property of a number is the opposite of the number. The sum of any numbers and the addition inverse is always zero.

The addition property is the number that simply to find the opposite number. The additive inverse property is easy to check the real numbers is addition inverse or not.

The real number is ‘ x’ and the addition inverse is ‘-x’ .

I hope the above explanation was useful.

surface area to volume ratio

Hi Friends, Good Evening!!!

Let us learn about "surface area to volume ratio"

Introduction on surface area to volume ratio:

The surface-area-to-volume ratio also called the surface-to-volume ratio and variously denoted sa/vol or SA:V, is the amount of surface area per unit volume of an object or collection of objects. The surface area to volume ratio is measured in units of inverse distance. A cube with sides of length a will have a surface area of 6a² and a volume of a³.

The surface to volume ratio for a cube is thus 6/a. Here we are going to see the formulas for surface area and volume of some regular shapes. Examples to calculate the surface area to volume ratio is given in the following sections.

The surface area in general, is the sum of all the areas of all the figures that cover the surface of the object.

Surface area of cube:

Sum of the areas of all six faces of a cube is its total surface area. Since a cube has all its sides i.e., length, breadth and height equal and each surface is a square.

In words, the surface area of a cube that covers the area of the six squares. The area of one of them is a*a, or a². You can multiply one of them by six since these are all the same, so the surface area of a cube is 6 times one of the sides squared.
In our next blog we shall learn about " what is measurement ? "

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What is Vertical integration

Let us study what is meant by Vertical Integration definition,

This article we are going to explain about vertical integration. The integration is also called anti differentiation. It is the contradictory process of differentiation.
For instance,If we recognize our velocity vector v at some time t then our location vector is given by s where [(ds)/dt] and if we have s=s₀ at t=t₀. In organization, the appearance of vertical integration illustrates a method of control organization.





I hope the above explanation was useful, now let me explain about combination formula

variance formula

Hi Friends, Good Afternoon!!!

Let us learn about "variance formula".

In the variance of a random variable or distribution is the expectation, or mean, of the deviation squared of that variable from its expected value or mean. Thus the variance is a measure of the amount of variation within the values of that variable, taking account of all possible values and their probabilities or weightings.Try to find out "what is probability"

Population Variance Formula Explanation:

The population variance formula for discover the variance for the given population problem

Population Variance formula: Here, N is the size of the population. So X^-an unbiased estimate of µ. The variance of the population

Where µ is the population mean. n values x1, ..., xn from the population, This is merely a individual case of the universal definition of variance introduced above, but controlled to finite populations.

In many functional situations, the true variance of a population is not known a priori and must be computed someway. When making with countless populations, this is generally impossible.

Most of the time it is not possible to obtain data for the entire population. For example, it is impossible to measure the weight of each male in a particular area to determine the average weight and variance for males of a particular area. In such cases, results for the population have to be estimated using samples.

This link will help you to learn how to measure angles.

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Introduction of Conditional Probability

Let us study about conditional probability,
A conditional probability is the probability of an event given that another event has occurred. For example, what is the probability that the total of two dice will be greater than 8 given that the first die is a 6? This can be computed by considering only outcomes for which the first die is a 6. Then, determine the proportion of these outcomes that total more than 8. All the possible outcomes for two dice are shown below:

There are 6 outcomes for which the first die is a 6, and of these, there are four that total more than 8 (6,3; 6,4; 6,5; 6,6). The probability of a total greater than 8 given that the first die is 6 is therefore 4/6 = 2/3.

I hope the explanation was useful, now let me give you some examples of conditional probability.

Rational Numbers

Let us study about rational numbers,
A rational number is a number that can be expressed as a fraction p/q where p and q are integers and . A rational number p/q is said to have numerator p and denominator q. Numbers that are not rational are called irrational numbers. The real line consists of the union of the rational and irrational numbers. The set of rational numbers is of measure zero on the real line, so it is "small" compared to the irrationals and the continuum.

The set of all rational numbers is referred to as the "rationals," and forms a field that is denoted Q. Here, the symbol Q derives from the German word Quotient, which can be translated as "ratio," and first appeared in Bourbaki's Algèbre (reprinted as Bourbaki 1998, p. 671).

Any rational number is trivially also an algebraic number.
I hope the above explanation was useful.

An arc of a circle

Hi Friends
Good Afternoon!!! Can you give me examples for things which are round?(moon, cycle wheel, coin, foot ball and so on. Let us learn about "An arc of a circle" .

Any part of a circle is called an arc of the circle. We usually name an arc by 3 points.

Arc: a curved line which is a part of the circumference of a circle. In other words we can say that, a circular arc is a segment of the circumference of a circle.

Arcs are grouped into two descriptive categories:
1) minor arc
2) major arc

In our next blog we shall learn about "Area of a circle"

I hope the above explanation was useful. Keep reading and leave your comments.

What Is A Monomial?

my dear friends...i enjoy writing for you guys everyday and therefore i just think of the topics that i can share with all of you.

Let us understand about Monomial.

Monomial:

An algebraic expression which contains only one term is called a monomial.

Example: -7z, 8xy, 9 a³b²

Coefficient of a term:

Any factor or group of factors of a product is known as the coefficient of remaining factors.

Example:

In product 12ab,

12 is numeral coefficient of ab

12a is the coefficient of b

ab is the coefficient of 12 and so on

Note: when the coefficient is unity, that is 1 (one), it is usually omitted, 1x is written as x

The example above has the steps mentioned above.Let me know how informative you found this post and if you want to share some ideas let me know.

what is statistics

Let us study about statistics,
Statistics as a discipline is the development and application of methods to collect, analyze and interpret data. Modern statistical methods involve the design and analysis of experiments and surveys, the quantification of biological, social and scientific phenomenon and the application of statistical principles to understand more about the world around us. Since data are used in most areas of human endeavor, the theory and methods of modern statistics have been applied to a wide variety of fields. Some areas that use modern statistical methods are the medical, biological and social sciences, economics, finance, marketing research, manufacturing and management, government, research institutes and many more. Exciting new areas are opening up, due to developments in areas such as biotechnology, survey research and computing.

The Department of Statistics is involved in research, teaching, and statistical consulting for the entire University. Because of its activities, the collaborative work with other disciplines give graduate students a wide range of opportunities to work with individuals in these disciplines and to learn practical applications of statistical principles from direct experience.
I hope the above explanation was useful, now let me explain about Probability.

Frequency Distribution

Let us study about Frequency Distribution,
Frequency distributions are like frequency polygons; however, instead of straight lines, a frequency distribution uses a smooth curve to connect the points and, similar to a graph, is plotted on two axes: The horizontal axis from left to right (or x axis) indicates the different possible values of some variable (a phenomenon where observations vary from trial to trial). The vertical axis from bottom to top (or y axis) measures frequency or how many times a particular value occurs.

For example, in Figure 1 , the x axis might indicate annual income (the values would be in thousands of dollars); the y axis might indicate frequency (millions of people or percentage of working population). Notice that in Figure 1 the highest percentage of the working population would thus have an annual income in the middle of the dollar values. The lowest percentages would be at the extremes of the values: nearly 0 and extremely high.

Figure 1

A symmetric bell curve.

Notice that this frequency curve displays perfect symmetry; that is, one half (the left side) is the mirror image of the other half (the right side). A bell-shaped or mound-shaped curve is also normal, giving it special properties.
I hope the above explanation was useful.

Dot Plot

Let me explain what is meant by "Dot Plot",
Dot plots are similar to bar graphs. Typically used for a small set of values, a dot plot uses a dot for each unit of measurement; thus, the undergraduate expense data in Table 1 could be represented by a dot plot like that shown in Figure 1 .


Figure 1 : Dot plot of the expenditures of a college undergraduate for the past year.
Hope the above explanation was useful.

Decimal Fraction

Let Us Learn About Decimal Fraction

A fraction whose denominator is 10, 100, 1000 and so on is called a decimal fraction.

For examples 3/10, 7/100, 15/1000, 135/10000 so on.........

Let us convert a fraction in to decimal

1) 3/10 = 0.3

2) 7/100 = 0.07

3) 15/1000 = 0.015

4) 135/10000 = 0.1350

Example

Solve multiply decimal fraction (233.85/102.3) * (35.62/45.22)

Solution:

Given that (233.85/102.3) * (35.62/45.22)

The question defines the 233.85 divided by 102.3 and multiplication of 35.62 divided by 45.22

So the two fraction need to multiply here,

= ( 233.85) * (35.62)/(102.3) *(45.22)

= 8329.737/4626.006

= 1.8006

The answer is = 1.8006

Try to convert the following fraction into decimal.

a) 1/2 =

b) 1/5 =

c) 1/32 =

d) 13/16 =

In our next blog we shall learn on Mixed Fraction.


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