Double Counting Online Study

Introduction to double counting online study:

In mathematics the double counting is the counting in two ways is a proof technique that involves counting the size of the set. Double counting is the simple method. Tutor is a person, they are number of the tutors available for online. Online is defined as connecting person through the internet. There are number of the website available in online. In this article we see in detail about double counting online study.

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Example 1: double counting tutoring:


What is the probability of the select ace and queen from punch of card.

Solution:

The probability for ace is occurs `4/52` .

The probability for queen is occurs `4/52`

The combination occurrences of common probability is `1/52`

P (A+B) = P (A) +P (B)-P (AB)

=`4/52+4/52-1/52`

=`8/52-1/52`

=`7/52`

=0.135


Example 2: double counting online study:


A bag contains 6 yellow balls and 6 blue, what is probability for drawn yellow ball, balck ball?

Solution:

Total number of the ball = 12

Yellow ball =5

Blue ball = 15

The probability for yellow ball = `15/30`

The probability for blue ball = `15/30`

P (A + B) = P (A) + P (B) - P (AB)

= `15/30 + 15/30 - 1/30`

= `30/30-1/30`

= 0.97


Example 3: double counting online study:


A bag contains 15 orange ball and 5 green ball, what is the probability for draw orange and green ball.

Solution:

Total number of ball = 20

Number of the orange ball is 15

Number of the blue ball is the 5

Probability of green ball is = `15/20` = 0.75

Probability of blue ball is = `5/20` = 0.25

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Example 4: double counting online study:


What is the probability for selecting either ace otherwise a queen from punch of card.

Solution:

The probability for ace is occurs `4/52.`

The probability for queen is occurs `4/52`

The combination occurrences of common probability is `1/52`

P (A+B) = P (A) +P (B)-P (AB)

=`4/52+4/52-1/52`

=`8/52-1/52`

=`7/52`

=0.13

Math Subtraction Problems Online Study

Introduction to Math Subtraction Problems Online Study:

Many online websites are available today. In those websites, subtracting a number from another number can be explained step by step briefly about the topic for lower grade students to understand clearly. The subtraction is said to be removing a part from the whole. The act of taking one number away from another is known as subtraction in math. For example, subtracting 4 – 2 is 2. Let us see about math subtraction problems online study in this article.Please express your views of this topic 3 digit subtraction with regrouping by commenting on blog.


Worked Examples to Math Subtraction Problems Online Study

Let us learn some of the solved examples explained through online about subtraction in math.

Problem 1:

Solve subtraction of two numbers 63 – (-12).

Solution:

Step 1:

Here, the number 63 is minuend and the number 12 is subtrahend.

Let us write the given number one under the other like,

63 (minuend)

12 (subtrahend)

------------------------

Here, the subtrahend is minus 12 so minus into minus is equal to plus.

Add those numbers and put the sign of larger number to the result.

Step 2:

Add the one’s place and this carry can be added to the tens place.

3 + 2 = 5

Step 3:

Add the tens place,

6 + 1 = 7

Step 4:

Regroup the numbers, we get,

7 + 5 = 75

The larger number is + 63. So, the sign of the result is also + 75.

Therefore, the solution for adding 63 – (-12) is 75.

Problem 2:

Solve subtraction of two numbers – 34 – 45.

Solution:

Step 1:

Here, the number 24 is minuend and the number 45 is subtrahend.

Let us write the given number one under the other like,

24 (minuend)

45 (subtrahend)

---------------------------

Add those numbers and put negative sign before the result.

Step 2:

Add the one’s place,  we get,

4 + 5 = 9

Step 3:

Add the tens place with carry of one’s place,

2 + 4 = 6

Step 4:

Regroup the numbers, we get,

6 + 9 = 69

Therefore, the solution for subtracting – 24 – 45 is 69.


Another Problem to Math Subtraction Problems Online Study


Problem 3:

Solve subtraction of two numbers 23 – 8.

Solution:

Step 1:

Here, the number 23 is minuend and the number 8 is subtrahend.

Let us write the given number one under the other like,

23 (minuend)

08 (subtrahend)

---------------------------

Subtract the two numbers and place the sign of larger number before the answer.

Step 2:

Subtract the one’s place,  we get,

3 – 8 = we cannot subtract 8 from 3. So, we borrow 1 from the minuend tens place 2. So the one's place becomes 13 – 8 = 5 and the tens place of minuend becomes 2 – 1 = 1.

Step 3:

Subtract the tens place, we get,

1 – 0 = 1 (There is no tens place column in the subtrahend place)

Step 4:

Regroup the numbers, we get,

1 + 5 = 15

Therefore, the solution for subtracting 23 – 8 is 15.

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Practice Problems to Math Subtraction Problems Online Study


1. Subtraction of two numbers  – 42 – 12.

Key: - 54

2. Subtraction of two numbers – 23 – (- 13).

Key: - 10

3. Subtraction of two numbers 18 – (- 2).

Key: 20

4. Subtraction of two numbers 43 – 37.

Key: 6

5. Subtraction of two numbers - 26 + 31.

Key: 5

How to Study Successfully

Introduction to how to study successfully:
How to study successfully in math is to learn the  basic formulas and method of solving that math problems, then see the solved problems of that similar type. Now we get an idea of how to solve that math problem then try how to solve that problem step by step. how to study successfully is about a general math, so let us take problems from algebra. In this article let us see problems to how to study successfully.


How to study successfully:

Example 1:

Find the value of the expression 4x + 7 , if x = 7

Solution:

use x = 7 in the given expression 4x + 7

4x+ 7 = 4(7) + 7

= 28 + 7

X  = 35

Here the value of the expression is 35.

Example 2:

If four times of a number is equal to 16. Then find what exactly the number is?

Solution:

let us assume the unknown number as " X "

Given   4 * X = 16.

Move leftside term to right

Then          X = `16/4`

The unknown number x is

X = 4

Example 3:

Find the Coefficients combined in the given equation:

24x2 + 7y + 5xy + 12

Solution:

Here Coefficient of x2 is 24

Coefficient of y is 7

Coefficient of xy is 5

Example 4:

Evaluate 22 - (-3) × 4   + (-6) / 3

Solution :

= 22 - (-3) × 4 + (-6) / 3

= 22 - (-12) + (-2)

= 22 + 12 - 2

= 22 + 10

= 32


How to study successfully:


Example 5:

Find the value of the expression 25x+8 , if x= 3

Solution:

Substitute x = 3 in the given expression 25x+8

25+8 = 25(3)+8

= 75 + 8

X  = 83

Here the value of the expression is 83.

Example 6:

Solve: 8x - 2 = 118

Solution:

Given, 8x - 2 = 118

8x = 118 + 2

8x = 120

x = `120/8`

or    x = 15

Example 7:

Solve the following system:

x + y = 14 - (1)

4x - y = 11 - (2)

Solution:

Solve the (1) equation

y =14 -x

substitute in (2)equation

4x - (14 - x)=11

4x - 14 + x=11

5x=25

x=5

substitute value of x in (1)equation

5 + y=14

y=9

The solution is, (5, 9).

Self Study Math

Introduction:

Let us learn the math by self. Its not a difficult one to study the math by self, we have to concentrate on the problems and show some interest. First of all, we should not think that math is difficult one.

Pre-algebra students with weak arithmetic skills need special instruction.

Repeating students need something new to hold their interest.

Students need Math Study Skills.

Students with disabilities benefit from multi-modality instruction.

Ten Steps to Doing Self Study Math Homework

Review related textbook material.

Review appropriate lecture notes.

Do homework neatly.

Write down every problem step.

Understand reasons for problem steps.

For difficult problems repeat 1 -5 and review similar problems, call another student, use other references, see a tutor or teacher.

Finish by working a problem successfully.

Recall or write down important concepts.

Make up note cards for difficult concepts.

Don’t get behind.


Ten Steps to Doing Online self study math Homework


Review related textbook material.

Review appropriate lecture notes.

Do homework neatly.

Must write down problem and every problem step.

Understand reasons for problem steps instead of using the click and go method.

For difficult problems use the resources provided by the software (videos /tutor line).

Finish by working a problem successfully.

Recall or write down important concepts.

Develop virtual note cards  by using www.studystack.com.

Don’t get behind – you could get block out.

Taking the Test

Ten Steps for Taking a self study math Test :

Memory Data Dump

Preview Test

2nd Memory Data Dump

Test Progress Schedule

Answer Easy Questions

Skip Difficult Questions

Review Skipped Questions

Guess at Remaining Questions

Review All of the Test

Use all the Test Time


Six Types of Test-taking self study math Errors


Misread Directions

Careless Errors

Concept Errors

Application Errors

Test Procedure Errors

Study Errors

Example for self study math:

A coin is tossed 60 times. 25 times tail appears. Find the experimental probability of getting tail.

Solution:

Step 1:

Probability = `("Number of times the event happen") / ("Total number of trials")` .

Step 2:

Number of times tail appeared = 25.

Step 3:

Total number of experiments = 60.

Step 4:

Therefore experimental probability of getting a tail = 25/60= 5/12

Experimental Research Study

Introduction to experimental research study:
A probability experimental is a stipulation where probability affects the outcome. A coin flip is a probability experiment because chance affect whether a coin will ground heads or tails when it is flipped. In probability, an experiment is a procedure with an outcome that deepens leading chance. In this article we are learning about the experiment research study. The experimental research study is a collection research processes. It us used to manipulation and controlled to understand the casual process.


Example 1 –Experimental Research Study:

Now we are going to solve the probability problem for experimental research study.

The three coins are flipped at a time.

What is the probability of get accurately three tails or two heads with one tail?

Solution:

The sample space, when three coins tossed is,

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

n(S) = 8

A be the event of getting three tails,

n (A) = {TTT} = 3

B be the event of getting two heads with one tail,

n (B) = {HHT, HTH, THH} = 3

P (A) = `3/8`

P (B) = `3/8`

P (A or B) = P (A) + P (B)

= `3/8 ` + `3/8`

= `6/8`

= 0.75

Here the expected value is 0.75

Understanding Probability in Math is always challenging for me but thanks to all math help websites to help me out.

Example 2 –Experimental Research Study:


Let see we will sample probability problem for experimental research study.

From the following scores

15.6, 13.5, 20.3, 12.4, 14.9, 8.2, 7.6.

1. above 13.6values

2. below 13.6 values

Probability for finding above 13.6 values:

The given values are 15.6, 13.5, 20.3, 12.4, 14.9, 8.2, 7.6.

Above 13.6 scores = 15.6, 20.3, 14.9.

In the given scores the above 13.6 scores probability values are (15.6, 20.3, 14.9).

Probability for above 13.6 scores =3

Total scores = 7

Probability =`("Above 13.6 values")/("Total given values")`

Total scores = 7

Probability for above 13.6 scores =`3/7`

Answer:

`3/7`

Find the probability for below 13.6 scores:

Solution:

The given scores are,

15.6, 13.5, 20.3, 12.4, 14.9, 8.2, 7.6.

Below 13.6 scores are 13.5, 12.4, 8.2, 7.6.

Formulas for getting probabilities for below 15.1 scores are

Probability =`("Below13.6 values")/("Total given values")`

Here below 13.6 scores values = 4.

Total given scores = 7.

So the probability for below 13.6 scores = `4/7`

= `4/7.`

Answer:

`4/7`

These are experimental research study.

That’s all about experimental research study.

Work Study Homework Ideas

Introduction to work study homework ideas:
The word study homework ideas represent the ideas for the student's homework. Homework is the process of doing some problems of work at home that are not done in the classes.When the students did not practice on the particular exercise or they have inability to do their homework or otherwise if the teacher have no time to do all the problems in the whole, then the teacher in the class need to check their children's homework.

(source from Wikipedia)

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Some examples to explain word study homework ideas:


Let us see some of the word study homework problems.

Solve for the equation 4i + 30= 3i +17

Solution:

4i + 30 - 3i = 3i + 17 - 3i

i + 30 = 17

i + 30 - 30 = 17 - 30

i= -13

In this problem the variable 'i' exist. When the process is ongoing we have the small doubt that either it is the variable or the representation of imaginary number in complex numbers. In execution of the problems we clearly known that it is variable. For practice the teachers give homework to the students with the ideas to study.


Some more problems to explain "word study homework ideas":

Find the mode of the given set of numbers: 11, 11, 12, 14, 13, 12, 11, 12, 12, 14

Solution:

Consider the given numbers we have to arrange that, after arranging we get
11,11, 11, 12,12, 12, 12, 13, 14, 14
Mode for this data is 12 because 12 occurs more frequently than other observations.

In this problem we have different numbers on processing  we have doubt about in what way the prosecution begins in the way of mode, mean. We shortly confused  due to their different operations on same name (slightly moderating their pronunciation).

consider  the margins of victory in the football matches of a league that are following
1, 3, 2, 5, 1, 4, 6, 2, 5, 2, 2, 2, 4, 1, 2, 3, 1, 1, 2, 3, 2, 6, 4, 3, 2, 1, 1, 4, 2, 1, 5, 3, 3, 2, 3, 2, 4, 2, 1, 2
Find the mode for this data.

Solution:

2 has occurred the highest number of times therefore the mode is ' 2'.

Practice problem for the word study homework ideas

consider the following statements we have to tell whether the statement is true or false:
(i) The mode is always one of the numbers in a data.
(ii) The mean can be one of the numbers in a data.
(iii) The median is always one of the numbers in a data.
(iv) A data always has a mode.
(v) The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9.

Study Randomness

Introduction to study randomness:

Randomness is a concept of non-order or non-coherence in a sequence of symbols or steps, such that there is no intelligible pattern or combination. Randomness implies a lack of predictability with the concepts of chance, probability, and information entropy. More formally, in statistics, a random process is a repeating process whose outcomes follow no describable deterministic pattern, but follow a probability distribution.


Studying Events on study randomness:

The studying of randomness are as follows:

Event

An outcome of an experiment is called Event. When two or more events occur in connection with each other the joint occurrence is called a compound event. Events are classified into

1) Independent

2) Dependent

3) Mutually Exclusive event.

Independent: An event A is said to be independent of another event B when the actual happening of A does not influence in any degree the probability of the happening of B.

Dependent: If another probability of the happening of B is dependent or influenced by the previous happening, then B is said to be dependent on A.

Mutually Exclusive: Two events B and A are to be mutually exclusive when through the occurrence of one of them, says A, the other event B cannot take place and vice versa, or when two events cannot happen at the same time.


Applications on study randomness


The studying applications of Randomness are as follows:

1) Games: Randomness is used in many games such as gambling, casino games. Randomness is generating unpredictable numbers. Dice, cards use in games of chance because of randomness.

2) Cryptography: Cryptography concept is developed for secure the data from the attacker or unauthorized users. Cryptography has the two events encryption and decryption using algorithms.

3) Music and art: Randomness is used for generating randomness music. We can use randomness for arranging item to exhibit.

4) Simulation: Simulation is used by many engineering field such as neutron transport in nuclear fission

5) Analysis: Many physics experiments are rely on statistical randomness analysis such as analysing x-rays

6) Statistical sampling: Many statistical process based on Randomness concept.

7) Science: Randomness is used in Physics, Operation research and engineering fields

Study Proposition

Definition of proposition:

A proposition is a standpoint that you will create, defend or destroy. It should be worded as a declarative sentence that definitely expresses your position.

A proposition can be the major point of your position. It can also be a single supportive part. It can also be an opposite proposition that you will disprove.

A statement that affirm or denies something.
The meaning expressed in such a statement, as opposite to the way it is expressed.

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Types of proposition


There are three types of proposition that is fact, value and policy.

Proposition of Fact

A proposition of fact is a statement in which you meeting point largely on belief of the listeners in its truth or falsehood. Your arguments are thus expected at getting your listeners to accept the statement as being true or false.

Proposition of Value

In a proposition of values, you make a report where you are asking your listeners to make an evaluative opinion as to whether the report is morally good or bad, right or wrong. This may be done by comparing two things and asking them which is better.

Propositions of Policy

A proportion of policies advocate a course of exploit In this, you ask your listeners to back a policy or to assign themselves to a particular action.

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Example problems


Example 1:

Given:  x/4 = 75 /100

Solution:

Step 1: We need to find x value.

Step 2: Here we are using cross multiplication method to solve x

Step 3: So, when we cross multiply we get 100x= 300

Step 4: Now we divide using 100 on both the sides

Step 5: The value of x= 3.

Example 2:

Given: 15/60 =75/p

Solution:

Step 1:  From this question we need to find p value

Step 2: Using cross multiplication we get, 15x= 4500

Step 3: Now we dived e using 15 on both the sides

Step 4: x= 4500/15

Step 5: x= 300

Study About Trigonometry

Introduction to study about trigonometric

Trigonometry (from Ancient Sanskrit "Trikona" or triangle and "Mati" or measure. Also from Greek trigōnon "triangle" + metron "measure") is a branch of mathematics that studies triangles, particularly right triangles. Trigonometry deals with relationships between the sides and the angles of triangles, and with trigonometric functions, which describe those relationships and angles in general, and the motion of waves such as sound and light waves. Trigonometry is usually taught in secondary schools either as a separate course or as part of a precalculus course. A branch of trigonometry, called spherical trigonometry, studies triangles on spheres, and is important in astronomy and navigation. (Source from Wikipedia)

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Study about basic trigonometry ratios:


There are six basic trigonometric ratios they are following,

sin `theta`= opposite /Hypotenuse

cos `theta`= adjacent / Hypotenuse

tan `theta` = opposite /adjacent

cot `theta` = adjacent / opposite

Sec `theta` = hypotenuse / adjacent

Cosec `theta` = hypotenuse / opposite.


Example problem :


Study about trigonometry word problem:

If the distance of a person from a pyramid is 200 m and the angle subtended by the top of the pyramid with the ground is 30o, what is the height of the pyramid in meters?

Solution:

First we have to plot the diagram to represent the given problem, and mark the date carefully.

Choose which trigonometric function represents the ratio of the side.(200)

Let as assume xy=Distance between man and pyramid.(h)

Similarly yz=Height of the pyramid we have to find

Here we have using the trigonometric function tan x here x=30 degree

Therefore tan x =opposite/adjacent

tan x =yz / xy

tan 30 = h/200

Height=tan 30 degree *200

Tan 30 degree=0.577

=0577*200

Therefore height of the pyramid =115.47

Understanding solving word math problems is always challenging for me but thanks to all math help websites to help me out.

Study about application of trigonometric:

Trigonometric used large number of application. It is mainly used in astronomy and geography.

Similarly trigonometric used many fields they are,

Electronics
Statics
Number theory
Acoustics
Computer graphics.
Meteorology
Economics
Navigation and aircraft

Study For Patterns Exam

Study for patterns:

A pattern, from the French patron, is a type of theme of recurring events or objects, sometimes referred to as elements of a set. These elements repeat in a predictable manner. It can be a template or model which can be used to generate things or parts of a thing, especially if the things that are created have enough in common for the underlying pattern to be inferred, in which case the things are said to exhibit the unique pattern.

Source: Wikipedia

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More about patterns for exam:


Study for patterns exam, you need to know the numeric patterns. Number patterns in algebra are patterns made from numbers. Study for patterns exam, we need know the basic operations like addition, subtraction, multiplication and division. So you can prepare numbers can be in a list. Any math operation used to make the patterns.

Study for patterns exam, we know about more information about patterns. Many of the patterns in algebra you see will use addition. The same number will be added to each number in the list to make the next number in the list in study for patterns exam.

Example study for patterns exam:

1, 3, 5, 7, 9, 11, 13…

The pattern in algebra is to add 2 every time. The next number is 15, then 17.


Example study for patterns exam:


Example 1:

2,5,8,11,14,17…

Solution:

The pattern in algebra is to add 3 every time. The next number is 20, then 23.

Example 2:

2,4,6,8,9,10,12,14,…

Solution:

If you guessed that the rule is counting by 2 using even numbers, you are correct.

Example 3:

1,1,2,3,5,8,13,21,34,55,…

Solution:

Look carefully and think!!!

If you concluded that the answer to this pattern in algebra is that you need to add number together to get the next number in line, you are correct.

1+1=2,2+1=3,3+2=5,5+3=8,…

This is a famous pattern in algebra or sequence known as the Fibonacci sequence.

Understanding pre algebra formulas is always challenging for me but thanks to all math help websites to help me out.

Practice problem study for pattern exam:

Problem 1:

A store gives a door prize to its third customer and to every fifth customer after that. Which of the following customers will get a door prize?

The 62nd

The 71st

The 79th

The 98th

Answer: D

Problem 2:

To find the next two number of pattern with proper explanation                                                                                            1,3,5,6,9,11,13,15,…

Answer: 17,19

Study Calculus Placement Exam

Introduction to Study Calculus Placement Exam

This is for the students who are preparing to take one or two Advance Placement Examinations in Mathematics offered by the College Entrance Examination Board, and for their teachers.

The Courses

Calculus AB and BC are both full-year courses in the calculus of function of a single variable. Both courses emphasize:

Student understanding of concepts and applications of calculus over manipulation and memorization
Developing the student’s ability to express function, concepts problems, and conclusion analytically, graphically, numerically, and verbally, and to understand how these are related.
Using a graphing calculator as a tool for mathematical investigations and problem-solving.

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Studying Topics on Calculus Placement Exam


Both courses are intended for students who have already studied college-preparatory mathematics. The main difference between the two is that BC calculus tests some more theoretical aspects of calculus and it covers a few additional topics. The AB exam usually tests straight forward problems in each topic. The BC asks harder questions but neither is tricky.

The Calculus AB and BC Examinations and the course descriptions are prepared by committees of teachers from colleges or universities and from secondary schools. The examinations are intended to determine the extent to which a student has mastered the subject matter of the course.

Each examination is 3 hours and 15 minutes long.

Understanding Asymptotes of Rational Functions is always challenging for me but thanks to all math help websites to help me out.

The Calculus Placement Exam


First, In Part A there are 28 multiple choice questions for which 55 minutes are allowed. Calculators are not permitted. In Part B there are 17 multiple choice questions for which 50 minutes are allowed and a graphing calculator is permitted.

Second, the free response section ahs twp parts each have three questions each of which requires you to write out the solutions and the steps by which you solved it. You are permitted to use calculators for the first three questions and 45 minutes are allowed for each part.

Study Arithmetic Test Prep

Introduction to study of arithmetic test prep:

Here we will study arithmetic progression for test prep

An Arithmetic Progression study prep, or AP, is a series where each new term after the first is obtained by adding a constant d, called the common difference study, to the preceding term.If the starting term of the sequence is 'a', then the arithmetic progression  is, a + d, a + 2d, a + 3d, . . .where the nth term is a + (n - 1)d.Few test problems prep for study arithmetic is given in the following sections.


Study example problems for arithmetic test prep:


Arithmetic Sequence Problem:

Problem:Find the sum of all positive integers, from 7 to 1764 inclusive, which are divisible by 7.

Solution:study the Sequence of first few elements positive integers divisible by 7 are given by 7, 14, 21...
The above sequence has a first element equal to 7 and a common difference d = 7. We need to know the rank of the term 1764. We use the following formula for the nth term
an = a1 + (n - 1 )d

1765 = a1 + (n - 1 )d
Substitute a1 and d by their values

1764 = 7 + 7(n - 1)
Solve for n to obtain ,      n = 252
1764 is the 252th term, we can use the following formula to find sum
sn = `(n(a_(1) +a_(n)))/(2)`
s252 = `(252 (7 + 1764)) / 2`
= 223146

Study to solve arithmetic word problem for test prep:

Problem:Three apples and four oranges cost $400. The cost of the orange is half the cost of the apple. What is the cost of apple?

Solution: Take cost of the apple is x and cost of the orange is y then test.
From the statement has given we can test as follows
3x + 4y = 400              (1)
x (`1/2` ) = y or x = 2y    (2)
Solving these two equations and test
3(2y) + 4y = 400
6y + 4y = 400
y = 40
Substitute  value and study  y in equation (2) and test
x = 80
Therefore, cost of the apple is $80.

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Study practice problems for Arithmetic Test prep:


Pro1: Find a21 given that a4 = 12 and a9 = 27

Ans: a20 = 63

Pro 2:A factory makes 4249 number of bulbs. There were three kinds of bulbs – serial, power saver, and fancy. The number of fancy was 715 more than the number of power saver. The number of serial was 5 times the number of power saver. How many fancy did the company make test?

Ans: 607

Study Collection of Data

INTRODUCTION:

Statistics is used to make effective use of numerical data for groups of individuals or experiments. It deals with collection of data, analysis and interpretation of data.

It improves quality of data by the design of experiments and survey sampling. It applies in government, business, variety of academic disciplines and social sciences.

It has several methods and which can be used to describe or summarize a collection of data. It is called descriptive statistics which very useful in research.

Source:- Wikipedia

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Overview for collection of data


Data collection techniques use us to systematically collect information about our objects of study like people, phenomena and about the settings which they occur.

If the data are collected randomly, it will be very difficult to answer our research questions in a way.

There are various data collection techniques can be used now days. They are,

Using available information
Observation
Face to face interview
Administering questionnaires
Group discussions
Projective techniques, scaling, mapping.

Methods of Data collection


There are four main methods for collection of data. They are following,

Census                          -  It is a study which collects data from every one of a population.  It requires cost and time.
Sample survey               -  It is a study which collects data from a subset of a population.
Experiment                    - It is a controlled study for understanding cause and effect relationships. Here the researcher controls how subjects are assigned to groups and how many treatments each group receives. Compares some dependent variable.
Observational study       -  Similar to experiments, It also used to understand cause and effect relationships, but here the researcher is no need to control how subjects are assigned and treatments each group receives.

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Each Method of data collection has own advantages and disadvantages. They are following,

Resources                                                   - when the population is too large, a sample survey has a big advantage over a census.
The Generalize of data collection           -  It requires random selection to a larger population. It uses to the appropriateness of      applying findings from a larger population.
The Causal inference of data collection   -  Here cause and effect relationships can be tested when subjects are randomly assigned to groups.

Study About Axes

Introduction to Study About Axes:

Study about axes is of great importance in co-ordinate geometry.Co-ordinate geometry is mainly based on the X and Y axes.study about axes include ,the study of the x and y axes ,in co-ordinate plane.The X and Y axes are the lines placed in the plane perpendicular to each other. Normally the X axis is the line horizontal and Y axis is the line in vertical.

Study about axes may also include the plotting of points in the co-ordinate plane.Normally the x co-ordinate is placed first in the set of ordered pairs.And the Y co-ordinate is placed in second. so a ordered pair will be in the form(x,y).

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Each reference line is called a coordinate axis or  axis of the system, and the point where they meet is its origin. The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as a signed distances from the origin

One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, one can specify a point in a space of any dimension n by use of n Cartesian coordinates, the signed distances from n mutually perpendicular hyperplanes

While talking about study of axes,the quadrants are of great omportance.Mainly there are 4 quadrants.1st,2nd,3rd,and 4th quadrants.In the 1st quadrant both the x and y co-ordinates will be positive.Example:(1,2) is apoint on 1st quadrant.

In the second quadrant  X is negative and y is positive.Example :(-1,3)

In the 3rd quadrant both X and Y co-ordinates are negative. Example:(-4,-2)

In the 4th quadrant X is positive and Y is negative. Example:(4,-8)


Study of axes - Example


Example1:

Plot the point (2,3)

Here the x co-ordinate of the point is 2 and y co-ordinate of the point is 3.so the point we have to mark 2 units away from x  axis and  3 units away from y axis.

Plot the point (-2,3)

Here the point will be in the second quadrant. it will be again 2 units away from the y axis to the left and 3 units from the x axis.

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Importance of Study of axes in co-ordinate geometry


Study of axes in co-ordinate geometry helps us to get the relative position of points in  a plane.and it will also helps us to find the distance between the points in the plane.

Study About Countable

Introduction to study about countable:
Countable is natural number sets.It is denote how many number of variables are present.If there is no countable values means it is called as uncountable.In countable set, we can count the numbers  only once.Injective function is exist in set.It is called countable set.It is defined by f:S`->` N.N={0,1,2,….}.Some theorems are used to derive the contable set.

Theorem: In this theorem, consider a set as S and following conditions should be equal.

1). S is countable. That is f:S`->` N.

2). If subjective function is exist in set or empty means  g:N`->` S.

3). If bisection is exist in set of finite means  h:N`->` S.

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study about countable-Formal introduction


For more information, we study the the some theorems.

Study the countable by formal introduction:

Theorem 1: Cartesian product of finitely many countable sets is countable.

Repeated mapping is generate the finite vectors to natural numbers.Natural numbers easily  map the positive rational numbers.One or more than mapping method is used.

Theorem 2: This define countable set is consider allevery subset.

Prime number set is countable. For example, 2 maps to 1 and 3 maps to 2.

Theorem 3: Rational numbers are countable.

All fractions set are defined.Integers are represented by a and b.For example, 0 maps to (0,1,0) and 3 amps to(3,1,0).

Theorem 4: Natural number sequence is finite length set.It has length sequence 1,2,3.

Theorem 5: All finite subsets are countable.Order the elements when we have a finite subset.

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Study the properties of countable:

Basic theorem: It has three conditions.The basic theorem differentiate the sets as finite and infinite.

Corollary: Consider S and T sets.

1). F:S`->` T is injective ,where countable is T and then countable is S.

2). G:S`->` T is surjective and countable is S and then countable is T.

Study the Cantor’s enumeration is defined collection of countable sets.It is also called denumerable set.If we want to resolve the problem means we can use at most countable.We can study the orders of countable by using some methods.Well orders is used to ordered totally.It has another ways that is normal order of integers of rational numbers.

Study About Grade Measure

Introduction of study about grade measure:
Grade measurement is the geodetic determination of the local radius of curvature of the figure of the Earth by determining the difference in astronomical latitude between two locations on the same meridian, the metric distance between which is known.

The first known grade measurement was performed by Eratosthenes (240 BC) between Alexandria and Syene in what is now Egypt, determining the radius of the Earth with remarkable correctness. The Dutch geodesist Snellius (~1620) repeated the experiment between Alkmaar and Bergen op Zoom using more modern geodetic instrumentation.

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More about the grade measure:


In trigonometry, following three systems are used for measuring an angle according to different units employed:

Sexagesimal system.

Centesimal system

Circular system.

Centesimal system is used to measure a grade.

Centesimal system:

In this system, an angle is measured in terms of grades, minutes and seconds. Thus we have

1 right angle    =          100 grades (100g).

So        90 angle           =          100 grades (100g).

1 angle             =          1.111 grade (1.111g).

1 grade             =          100 minutes (100’).

1 minute          =          100 seconds (100’’).

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Example problem for grade measure:


Find the degree grade corresponding to the following time and angle measures:

a)      270 angle

b)      1 hour 40 minutes

c)      3 hour 20 minutes

d)     1 hour 40 minutes

e)      120 angle

Pro 1:    270o angle = grade?

Sol :     270 angle         =270 x 1.111  (where 1 = 1.111)

=299.97

After routing resultant number, we get

=300

270o angle or right angle = 300 grade (200g)

Pro 2 :      3 hour 20 minutes

Sol :               1 hour = 60 minutes

So 3 hour 20 minutes = 180 minutes+20 minutes

We know 1 grade = 100 minutes, so we can rewrite the given as

3 hour 20 minutes = 180 minutes + 40 minutes

= `300/100` grade

= 3 grades

=3 grades (3g)

3 hour 20 minutes is equal to 3 grades (1g)

Pro 3:          1 hour 40 minutes

Sol :            1 hour = 60 minutes

So 1 hour 40 minutes = 60 minutes+40 minutes

We know 1 grade = 100 minutes, so we can rewrite the given as

1 hour 40 minutes = 60 minutes + 40 minutes

= 100/100 grade

= 1 grade

=1 grade (1g)

1 hour 40 minutes is equal to 1 grade (1g)

Pro 4:       Find the 120 angle into grades?

Sol :       120 angle         =120*1.111

=133.32

After routing resultant number, we get

=133 grades (133g)

120 angles are equal to 133 grades (133g)

Study About Compression

Introduction to study compression:-

In this article we are going to study about compression and its techniques. In graphing, a technique which is used to get smaller graph towards x axis or y  axis is recognized as compression technique. Compression technique is use to compact the given graphical equation. Compression comes below the topic of transformations. A compression technique is of two types, they are Horizontal compression, Vertical compression.

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Study about compression types:-


Horizontal Compression:-

•    Horizontal compression is one of the solidity technique uses to compress the graphical equation. In horizontal compression, the solidity is done towards y – axis.

•    If the function is y = f (x), the horizontal stretching or compressing of the function is the function f (ax).

•    If 0 < b < 1, the graph is stretched horizontally by a reason of a units.

•    If b > 1, the graph is compression horizontally by a reason of “b” unit.

•    If “b” is to be negative, the horizontal compression or stretch of the graph is done by a reflection of the graph across the y-axis. Horizontal compression techniques decrease the graph from its unique position.

Vertical Compression:-

•    Vertical compression is one of the compression technique uses to compress the graphical equation. In vertical compression, the solidity is done towards x – axis.

•    If the function is y = f (x), the vertical stretch or compressing of the occupation is the function f (ax).

•    If 0 < b < 1, the graph is stretched vertically by “b” units.

•    If b > 1, the graph is compressed vertically by “b” units.

•    If “b” is to be negative, the vertical compression or stretch of the graph is done by a reflection of the graph across the x-axis. Vertical compression technique reduces the graph from its innovative position.

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Example problems about study compression:-


Study compression problem1:-

Write the graph of

f(x) = 3x ^2

With a vertical compression by a cause of 1/2

Solution:-

For the given function, f(x), draw the graph,

Take f(x) = y

y = 3x ^2

For the given function the graph will be a parabolic function,

y= 3x ^2/2

2y = 3x ^2

This graph is compressed by a cause of 1/2. The compression of original graph is done towards x – axis by a factor of 1/2.

Study compression problem2:-

Write the graph of

f(x) = 2x ^2

With a horizontal compression by a cause of 1/2

Solution:-

For the given function, f(x), draw the graph,

Take f(x) = y

y = 2x ^2

For the given function the graph will be a parabolic function,

y/2 = 2x ^2

y = 4x ^2

This graph is compressed by a cause of 1/2. The compression of original graph is done towards y – axis by a cause of 1/2.

Study About Composite

Introduction:

A complete integer that has factors other than 1 and the digit itself is one of study about the Composite Number.  A study about composite quantity is a positive numeral which has a cooperative divisor other than itself. In other words, the study about composite numbers consider if n > 0 is numeral and there is some integers 1 < a, b < n such that n = a × b then n is composite. By classification, each integer is better than one either a prime number or a composite number.


Definition:


The study about composite numbers is one of the sessions in the mathematics. The digit one is a unit and it is specified as neither prime number nor composite. For illustration, the integer 14 is composite number because it can be factorized as 2×7. Equally, the study integers 2 and 3 are not yet a composite numbers because each of them can only separated by one itself. Composite are the study about the numbers are the numbers other than prime numbers.


Classification of composite numbers:


1. By counting the number of prime factors we can ale to classify the composite numbers.

2. A composite number with two or further prime factors is a semi prime.

3. A composite number with three different prime factors is called as sphenoid number.

4. One more way is to classify the composite facts is by with the amount of the divisors.

5. Every composite numbers consists of at least two or three divisors.


Examples:


Some of the examples of composite numbers are given below,

4 – Factors of   4 are 2 and 2,4and1.

6 – Factors of   6 are 3 and 2, 6 and 1.

8 – Factors of   8 are 4 and 2, 8 and 1.

9 – Factors of   9 are 3 and 3,9 and 1.

10 – Factors of 10 are 5 and 2,10 and 1.

12 – Factors of 12 are 6 and 2,4 and 3,12 and 1.

14 – Factors of 14 are 7 and 2, 14 and 1.

15– Factors of 15 are 5 and 3, 15 and 1.

16 – Factors of 16 are 8 and 2, 4 and 4, 16 and 1…..

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Practice problem:

Identify the composite number from the following.

Choices:

A.5

B.19

C.27

D.59

Correct answer: c

Step 1: Here, only 27 have factors other than 1 and itself.

Step 2: The factors of 27 are 1, 3, 9, and 27. So, 27 is a composite number.

Study Algebra Edition

Introduction to study algebra edition:

Algebra comes from the Arabic word al-gebra. It represents as the “reunion of the broken words”. In mathematics, Letters like a, b, c, x are been used to represent the numbers, values, complex numbers, integers and these unite with the general operations to form the algebraic expressions. If two algebraic expressions are equated we get the algebraic equations.


Learn study algebra edition:


The algebra edition mainly divides in to two topics they are Algebra1, Algebra2.The algebra 1 further classified into exponents, graphing linear equations, and quadratic equations and factoring. The algebra 2 consists of probability, inequality, trigonometry, parabolas and logarithmic functions. Algebra edition includes all the topics mentioned above.

Algebra 1:

Algebra1 is one of the most important branches in mathematics. Algebraic expression is the collection or of algebraic terms like constants and variables linked by mathematical symbols .In algebra 1 the unknown variables are represented by using letters.

Algebra 2:

Algebra2 get online help of solving equations, graphs and function, quadratic equations, slope of a line, trigonometric identities, etc.

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Example problems for study algebra edition:


Problem 1:

Solve the equations: x + 2y + 3z = 14, 3x + y + 2z = 11, 2x + 3y + z = 11.

Solution:

x + 2y + 3z = 14 (1)

3x + y + 2z = 11 (2)

2x + 3y + z = 11 (3)

Consider the equations (1) and (3)

(1) ?           x + 2y + 3z = 14

(3) × 3 ? 6x + 9y + 3z = 33       (subtracting)

–5x – 7y = –19

5x + 7y = 19 (4)

Consider the equations (2) and (3)

(2) ?           3x + y + 2z = 11

(3) × 2 ?   4x + 6y + 2z = 22    (subtracting)

–x – 5y = –11

x + 5y = 11 (5)

Consider the equations (4) and (5)

(4) ?          5x + 7y  = 19

(5) × 5 ?   5x + 25y = 55   (subtracting)

–18y = –36

?   y = 2

Substitute y = 2 in (5) we get

x + 5(2) = 11

x + 10 = 11

x + 10 - 10 = 11 - 10

? x = 1

Substitute x = 1, y = 2 in (3) we get

2(1) + 3(2) + z = 11

2 + 6 + z = 11

8 - 8 + z = 11 - 8

? z = 3

The solution is x = 1, y = 2, z = 3.


Problem 2:

Solve the equation 7x – 12 = 3x – 24

Solution:

7x – 12 = 3x – 24                    (Adding 12 on both sides)

7x – 12 + 12= 3x – 24 + 12

7x = 3x – 12                                     (Subtract 3x on both sides)

7x – 3x = 3x – 3x – 12

4x = -12                                   (Divide by 4 on both sides)

`4x / 4 = - 12 / 4`

x = -3

So, the answer for x is -3.

Study algebra calculus

Introduction to study algebra calculus:

It is the study of algebra calculus is the course that involves relations and its use. This is the Algebra along with the Elementary Algebra course provides a solid foundation to higher mathematics course such as College Algebra, Pre-Calculus and Calculus. To be proficient with the mathematics, we highly recommend you to examine the examples and properties discussed in this course and ponder any of the subtleties encountered in any mathematics problems. I like to share this Definition of Inverse Function with you all through my article.


Definition of study algebra calculus:


Study algebra calculus is the 'Rates of Change'. Calculus as the we know it today was developed in the later half of the seventeenth century by two mathematicians, Gottfried Leibniz and Isaac Newton. There are two main branches of the calculus: Differential Calculus and the Integral Calculus. Differential calculus and the determines the rate of change of a quantity, integral calculus finds the quantity where the rate of change it is known as the algebra calculus.

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Examples on study algebra calculus


When you are studying is the rates of change in mathematics, you are in the branch of mathematics called algebra calculus.

Midpoint Formula:

The Midpoint formula is used when you need of the point that is exactly between two other points. The midpoint formula is a applied when you need to find is a line that bisects a specific line segment. Essentially, the 'middle point' is called the "midpoint".

The midpoint of M of the line segment from p1(x1,y1) to p2(x2,y2)

x1 + y1     x2 + y2

---------  ,    ----------

2                2

Slope Formula:
Sometimes called 'Rise over Run'.

The formula for a slope of the straight line going through the points (x1, y1) and (x 2, y 2) is given by:

y2 - y1

M  =  ----------

x2 - x1

The subscripts refer to the two points.
( m = rise / run )
Parallel lines have equal slope.
Perpendicular lines have negative reciprocal slopes.

Study 7th Grade Pre Algebra

Introduction to pre algebra:

Algebra: Algebra deals with the symbols,usually letters of the alphabet, are used to represent numbers and quantities.

Algebraic expression: a quantity that combines variables, numbers, and operation symbols.

Area: the space occupied inside a two-dimensional shape.

Equation: a mathematical statement in which two or more expressions are set equal to each other.

Inequality: a mathematical statement comparing two or more expressions using <, >, ≤, and ≥.

Like terms: two or more terms that have the same variable raised to the same power.

Linear equation: an equation that represents a line.

Polynomial: an expression made up of terms containing variables with whole number exponents.

Probability: a number from 0 to 1 that gives how likely anevent is to happen.

Real number: any number that can be represented with a point on the real number line.

Solution of an Equation: the value that makes an equation true when the variable is replaced by the value.

Term: a variable, number, or the product of a number and a variable

Variable: a symbol that is used to represent a quantity.

Volume: the amount of space enclosed in a solid object.

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Pre algebra includes different topics:


Natural numbers, arithmetic
Integers, fractions, decimals and negative numbers
factorization of natural numbers
Properties of operations such as associative property, distributive property and commutative property
Roots and powers
Evaluating expressions, such as operator precedence and use of parentheses
Basics of equations, that includes rules for invariant manipulation of equations
Variables and expressions.

Example:


Evaluate the expression for the given values.
2m – 3n + 7 for m = 8 and n = 5
Solution:
2m – 3n + 7 = 2(8) – 3(5) + 7
= 16 – 15 + 7
= 8

2) Evaluate 3x+ 4y - 12 for x =2 and y = - 3

Solution:

=  3(2)+4(-3) -12

= 6-12 -12

= 6 - 24

= -18

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Practice problems for pre algebra:


Evaluate the expression for the given values, 5x – 2y + 13 for x = 3 and y = 7
Evaluate the expression for the given values, 2p – 3q + 56 for p = 7 and q = 3
Evaluate the expression for the given values, 8m – 13n – 18 for m = 7 and n = 5.

Study About Geometric Problems

Introduction to study about geometric problems:

Geometry (Ancient Greek: γεωμετρία; geo- "earth", -metria "measurement") "Earth-measuring" is a part of mathematics concerned with questions of size, shape, relative position of figures, and the properties of space. Geometry is one of the oldest sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.


Formulas on study about geometric problems:


To study about the formulas of geometric which are givenas below:

Rectangle formulas:

Rectangle Perimeter = l + l + w + w = 2 × l + 2 × w = 2+2w

Area of the Rectangle = l × w

Square formulas:

Perimeter of the square = c + c + c + c = 4 × c = 4c

Area of the square = c* c = c 2

Parallelogram formulas:

Perimeter of the Parallelogram= c + c + d + d = 2 × c + 2 × d = 2c + 2d

Area of the Parallelogram = b × h

Rhombus formulas:

Perimeter of the Rhombus = c + c + c + c = 4 × c = 4c

Area of the Rhombus = b × h

Triangle formulas:

Perimeter of the Triangle = c + d + e

Area of the Triangle = (b × h)/2

Trapezoid formulas:

Perimeter of the Trapezoid = c +d + e + f
Area of the Trapezoid = (c+d) * h / 2

Circle formulas:

Perimeter of Circle = 2 × pi × R or Perimeter = pi × d

Area of the Circle = pi × R 2 or Area = (pi × d2)/4


Problems on study about geometric problems:


Study geometric Square problem:

Problem 1:

Calculate the area and perimeter of square when side length is 8cm?

Solution:

Area of square = (side*side)

=8*8

=>64cm2

Perimeter of square= 4* side

=4*8

= 32cm

Study geometric Rectangle problem:

Problem 2:

Find the area and perimeter of rectangle with length 9cm,width 7 cm?

Solution:

Area of rectangle = Length x width

= 9*7

= 63cm2

Perimeter of rectangle=2(Length +width)

=2(9+7)

= 32cm

Study geometric Triangle problem:

Problem 3:

Find the area and perimeter of triangle Base=8, Height=9, other two sides are 10,11?

Solution:

Area=1/2/(8*9)

=72/2

= 36cm2

Perimeter= (sum of three sides)

= (8+10+11)

= 29 cm

Study About Study Geometry

Introduction to study about study geometry:

Let us study about geometry,

Geometry can be defined as the system of concepts, in which a few ideas were initialized to derive the big ones. These kinds of systems are said to be deductive systems. It tells you the deduction concepts and consequence logic's, which can be applied throughout your life time. In this article, you can learn about the basic terms of geometry. I like to share this Surface Area Cube with you all through my article.

This definition is used in study of geometry.


Study about Basics of Geometry:


Some basics are there to study geometry,

Point:

A point can be defined as the basic object of geometry.

Line:

A line can be defined as the connection of many points. The line having only one dimension, i.e. length. It doesn't have any other dimensions. The two end points name can be used as the line name. Otherwise, it can be named by a single lower case alphabet.

Collinear points:

Collinear points are the points, which lie on the same line. If the point doesn’t lie on the line, then those points are said to be non collinear points.

Plane:

In study of geometry, a plane can be defined as the infinite set of points combined to form a flat surface; it can be extended infinitely in any directions. A plane having infinite length and width, but no height. It’s normally a four side geometric figure. It can be represented by a single upper case letter.

Some basics are there to study geometry,

Point:

A point can be defined as the basic object of geometry. It can be represented by a capital letter or a dot. A point have no dimensions, it just denote a position.

Line:

A line can be defined as the connection of many points. The line having only one dimension, i.e., length. It doesn't have no other dimensions. The two end points name can be used as the line name. Otherwise, it can be named by a single lower case alphabet.

Collinear points:

Collinear points are the points, which lie on the same line. If the points doesn't lie on the line, then those points are said to be non collinear points.

Plane:

In study of geometry,  a plane can be defined as the infinite set of points combined to form a flat surface, it can be extended infinitely in any directions. A plane having infinite length and width, but no height. Its normally a four sided geometric figure. It can be represented by a single upper case letter.

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Study about Other Important Geometry Terms


Some geometry terms are used in study of geometry,

Midpoint:

A midpoint can be defined as a point, which separates a line segment equally from both the end points.

Ray:

A ray can be defined as a line having one fixed end point and an infinite extension on the other end. It is denoted by two upper case letters with an arrow mark on top.

Angles:

An Angle can be formed by two rays having common end point. These rays are said to be the sides of an angle. An Angle is measured by a unit called as degrees. An Angle varies from 0° to 180°.

Right angle:

If an angle is 90°, then the angle is said to be right angle.

Obtuse angle:

If an angle is more than 90° but less than 180°, then the angle is said to be an obtuse angle.

Straight angle:

If an angle is 180°, then the angle is said to be a straight angle.

Study About Tangent

Introduction to study about tangent
A line or plane which touches a curve or surface. If a circle and a line in the same plane contact each other at only one point then the line is called a tangent to the circle. If a tangent to a circle in a plane is also a tangent to another circle in the same plane then, it is called a common tangent to the circles. If the centers of the circles are on the same side of the tangent, it is called external common tangent. If the centers are on opposite sides of the tangent, it is called internal common tangent. If a sphere and a plane contact at only one point, the plane is called tangent plane to the sphere. The point of contact is called point of tangency. Here we are going to study about the properties and theorems about tangents. Having problem with Finding the Volume of a Cylinder keep reading my upcoming posts, i will try to help you.

Tangent chord theorem

Tthe measure of an angle determined by the chord of a circle and the tangents at one of its end points is equal to half of the degree measure of the intercepting arc of that angle.


Formulas to study about tangent:


The following are very common formulas to study about tangent

tan θ = (side adjacent of length side) / (opposite of length).

tan θ = sin θ/ cos θ  = 1/ cot θ

tan2 θ = sec2 θ - 1

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Properties to study about tangent:


A line which touches a circle at exactly one point is called a tangent line and the point where it touches the circle is called the point of contact.
A tangent is the limiting position of a secant when the two points of intersection coincide.
A tangent is the limiting position of a secant when the two points of intersection coincide.
A radius, through the point of contact of tangent to a circle, is perpendicular to the tangent at that point.
From an external point, two tangents can be drawn to a circle.
The lengths of two tangents from an external point are equal.
The tangents drawn from an external point to a circle are equally inclined to the line joining the point to the centre of the circle.
The angles formed in the alternate segments by a chord through the point of contact of a tangent to a circle is equal to the angle between the chord and the tangent.

Discount Rates

This topic has a legendary background. In grand olden days people were using camels to carry heavy loads. When the camel is resting, a heavy load will be placed on its body to its great disliking. After all done, the master will take out a small straw from the load to the notice of the animal and will throw it away. The camel will be extremely happy that the load is much lighter now. I like to share this Discount Rate Formula with you all through my article.

In present days, the above technique is practiced by almost all sellers in the world. Even a billionaire will not accept a sale without discount. Thus, ‘discount’ is a concept that has occupied a place in math. The discount rates are normally expressed as a percentage of the original price. Thus, fundamentally, one has to know the concept of percentages to calculate discount rate. By calculating discount rate, we also come to know how to find discount.

Let us discuss the matter with some practical examples.

In a textile show room, tee shirts are tagged with labels saying that ‘Original price $15, the discount only for today is 10%’. (The today usually remains ever!). Now let us do the math exercise. With the concept on percentages, 10% means a fraction of 10/100. That is, the rate of discount is $10 for every purchase with original price of $100.In other words the rate is 0.1 times the original price. Thus, the discount on the tee shirt originally costing $15 is 0.1 times $15 which works out as $1.5. So what you finally need to pay is $15 - $1.5 = $13.5.

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This is not the case only with show rooms or malls. Even in online transactions we come across the ‘discount rates’. The agent of the seller on chat will mention ‘today we are offering heavy discounts’. In all likelihood, the quoted sentence will be a copy paste from a prepared notepad which may be as old as Bible. In these cases they will not even tax your brain. The complete quote will be like this. ‘Original price $100, offer applicable only on this chat is $79.99 ($80 may seem to be very heavy for the customers even though the difference is just one cent!), amounting to more than 20% discount’. Well, leaving the humorous part of the story, mathematically there is no flaw in this offer. Because the amount of discount is $20.01 and when you work back for the rate of discount, it comes to 20.01%.
Basically this is the concept on discount rates.

Online Study

Introduction to line online study:

In Euclidean geometry, a line is a straight curve. The general form of a line is represented by a equation

Ax + By + C = 0

The above equation of a line can be written as

y = (-`A/B` )x + (-`C/B` )

Plug - A/B  = m and   - C/B = b in the above equation, it becomes

y = mx + b

The above equation is called as slope intercept form of line equation.

Where, m is the slope and

b is the y-intercept

In online, we can study more about this line equation in detail. The example and practice problems are given below which shows how online will helps for your study.

(Source: Wikipedia)

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Example problems of line online:


The following example problems will helps you  to study about line in online.

Example 1:

Find x-intercept of a line y = 4x + 12

Solution:

Step 1: Given line equation

y = 4x + 12

Step 2: Substitute y = 0 in the equation  y = 4x + 12  to find x-intercept.

0 = 4x + 12

Step 3: Solve the above equation for x

Subtract 12 on both side of the equation to cancel 12 from the right hand side of the equation,

-12 = 4x

Multiplying by 4 on both side, we get

- 3 = x

Therefore,

x = - 3

Step 4: Solution

The x-intercept of the given line is (-3, 0)

The following example problems will helps you  to study about line in online.

Example 2:

Find y-intercept of a line 3y = 4x + 12

Solution:

Step 1: Given line equation

3y = 4x + 12

Step 2: Substitute x = 0 in the given equation to find y-intercept.

3y = 4(0) + 12

Step 3: Solve the above equation for y

3y = 0 + 12

Multiplying by 3 on both side, we get

y = 4

Step 4: Solution

The x-intercept of the given line is (0, 4)

Example 3:

Write the following line equation x + 5y = 6 into slope intercept form.

Solution:

Step 1: Given line equation

x + 5y = 6

Step 2: Subtract x on both sides to cancel x from the left hand side of the equation

5y = 6 - x

Step 3: Multiply by 5 on both sides, we get

y = `6/5` - `x/5`

On rearranging, we get

y = - `1/5` x + `6/5`

Step 4: Solution

The slope intercept form of given line equation is y = - `1/5 ` x+ `6/5`

I have recently faced lot of problem while learning Obtuse Angle Examples, But thank to online resources of math which helped me to learn myself easily on net.

Practice problems of line online:


1) Find x-intercept of a line y = 8x - 7

2) Find y-intercept of a line 5y = 6x + 15

3) Write the following line equation - x + y = 8 into slope intercept form.

Solution:

1) (7/8, 0)

2) (0, 3)

3) x + 8

Learning Geometric Progression

Introduction to Learning Geometric progression

Learning geometric progression is very easy and can be done very quickly . Geometric progression is a type of progression where the consecutive digits have a common ratio between them . This means that if a G.P (geometric progression ) is present with general term a(i) then for terms  a(i+1) = a(i)* r  , where r is the common ration of the G.P.


MORE OF LEARNING GEOMETRIC PROGRESSION


Take an example .

Lets understand the Geometric Progression in more detail.

Let a Geometric Progression has its first element as 4 and the common ratio be ‘3 ‘. So the next term will be multiplying  first term 4 with common ration 3

i.e 2nd term = 4*3 = 12

Similiarly to find the 3rd term  we multiply the second term by 3 so

3rd term =  12*3 = 36

So we can go on like this .

So the general formula will be that to find ‘nth’ member of the Geometric Progression we can write the formula

a(n)th  term = (first term) * ((common ratio)^(n-1))

so for this example    the a(n) will be  = 4* ((3)^(n-1))

I have recently faced lot of problem while learning Line Parallel, But thank to online resources of math which helped me to learn myself easily on net.

PROPERTIES OF G.P


In the previous section , the method of finding the Geometric Progression if the initial element and the common ratio is given. Now in this section we will find out how to check it a series of number are in  Geometric Progression.

Lets us suppose that we have three numbers  a, b, c and we have to find that they are in G.P or not. The rule is that  if they are in G.P then

b^2  = a*c

this means that if 2, 4, 8, 16 is a series given then  to find that if it is in common ratio .

4^2  =  8*2    (for 2,4,8)

And  8^2 = 4*16   (for 4,6,8 )

So 2,4,6,8 is in Geometric Progression

Metric Units Math

Introduction to metric units math:

In mathematics, metric units system is one of the important topics. It is used for measuring purpose of an international decimalized system of measurement. In all over world, it is the most common system for measuring different units. For personal, commercial and scientific purposes, it can be used widely. From the base units, it can be used to derive larger and smaller units which may be standard set of prefixes in powers of ten. I like to share this Multiply Fractions Calculator with you all through my article.



Metric units for mass and time in math:


Metric units for mass:

Basic unit for mass is gram.

Some metric units for mass are

1 kilogram = 1000 grams
1 hectogram = 100 grams
1 decagram = 10 grams
1 decigram = 1/10 (or) 0.01 gram
1 centigram = 1/100 (or) 0.001 gram
1 milligram = 1/1000 (or) 0.0001 gram

Some symbolized metric units for mass are

1 kilogram = 1 kg
1 milligram = 1 mg
1 centigram = 1 cg
1 gram = 1 g
1 decigram = 1 dg

Metric units for Time:

Some of the metric units for time are

1 minute = 60 seconds
1 hour = 60 minutes (or) 3600 seconds
1 day = 24 hours (or) 1440 minutes (or) 86400 seconds
1 week = 7 days
1 year = 12 months (or) 52 weeks

Metric units for Length and temparature in math:


Metric units for Length:

Basic unit of length is meter.

Some metric units for length are

1 kilometer = 1000 meters

1 hectometer = 100 meters

1 decameter = 10 meters

1 decimeter = 1/10 (or) 0.01 meter

1 centimeter = 1/100 (or) 0.001 meter

1 millimeter = 1/1000 (or) 0.0001 meter

Some symbolized metric units for length is

1 millimeter = 1 mm

1 centimeter = 1 cm

1 meter = 1 m

1 decimeter = 1 dm

1 kilometer = 1 km

Metric units for Celsius to Fahrenheit:

For converting Celsius to Fahrenheit, multiply the given Celsius temperatures in to 9/5 then we get the Fahrenheit temperature. Celsius is denoted by C

Fahrenheit = 9 /5 Celsius temperature

Metric units for Fahrenheit to Celsius:

For converting Fahrenheit to Celsius, multiply the given Fahrenheit temperatures in to 5/9 then we get the Celsius temperature. Fahrenheit is denoted by F

Celsius = 5/9 Fahrenheit temperature

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Metric units for Volume in math:


Basic unit of a volume is liter.

Some metric units for volume is

1 kiloliter = 1000 liters
1 hectoliter = 100 liters
1 decaliter = 10 liters
1 deciliter = 1/10 (or) 0.01 liter
1 centiliter = 1/100 (or) 0.001 liter
1 milliliter = 1/100 (or) 0.0001 liter

Some symbolize metric units for volume is

1 kiloliter = 1 kl
1 liter = 1 l
1 deciliter = 1 dl
1 centiliter = 1 cl
1 milliliter = 1 ml

Metric units for U .S system of volume:

Basic unit for U.S system of volume is teaspoon

Some of the U. S systems of metric units for volume are

Tablespoons = 3 teaspoons
Fluid ounces = 2 tablespoons (or) 6 teaspoons
Cups = 8 fluid ounces (or) 16 tablespoons
Pints = 2 cups (or) 16 fluid ounces
Quarts = 2 pints (or) 4 cups
Gallons = 4 quarts (or) 8 pints (or) 16 cups.

Study About Adjacent

Introduction to study about adjacent

Adjacent is an adjective meaning contiguous, adjoining or abutting. In geometry, adjacent is when sides meet to make an angle. In trigonometry the adjacent side of a right angled triangle is the cathetus next to the angle in question. In graph theory adjacent nodes in a graph are linked by an edge. (Source: From Wikipedia)

Here we are going to study about adjacent. I like to share this Adjacent Angles Definition with you all through my article.


Study about adjacent sides

Here we are going to study about adjacent sides of polygons. In a two dimensional shapes, like triangle, square or rectangle, two sides which share a common vertex and angle is called as adjacent sides.

If the adjacent sides of a polygon are in same length, then it is called as a square. In a rectangle, the adjacent sides are not equal but, opposite sides are equal. The angle between adjacent sides in a square and a rectangle is 90 degrees.

If the adjacent sides of a triangle are equal and it is called as an isosceles triangle.

Example problem

If the lengths of adjacent sides of a rectangle is x and x+5 meters respectively. The perimeter of the rectangle is 34 meter. Find the area of the rectangle.

Solution

The perimeter of the rectangle = 2(l + b)

Here the length and breadth of the rectangle is given by it's adjacent sides, x and x+5.

so, 34 = 2(x + x + 5)

34 = 2(2x + 5)

34 = 4x + 10

34 - 10 = 4x - 10

24 = 4x

x = 6

So, the adjacent sides of the rectangle are 6 and 11 meter respectively.

Area of the rectangle = lb square meter

= 6 * 11 square meter

= 66 square meter.

So the area of the given rectangle is 66 square meter. Understanding Find an Angle is always challenging for me but thanks to all math help websites to help me out.


Study about adjacent angles


Here we are going to study about adjacent angles.

Adjacent angles are nothing but, two are more angles which shares a common vertex.
If the sum of two adjacent angles is 90 degree, then the angles are called as complementary angles.
If the sum of two adjacent angles is 180 degree, then the angles are called as supplementary angles.
Example problem

If two adjacent angles are complement to each other, and one angle measures 48 degree, find another angle.

Solution

Given that the adjacent angles are complement, that is the sum of the adjacent angles is 90 degrees.

One angle measures 48 degree.

Measure of another angle = 90 - 48

= 42 degree.

Algebra Study Guide

Introduction to algebra study guide:

Algebra, a branch of mathematics deals with the expressions of various order, their operations, relations and construction and concepts of expressions.Algebra is the combination of numerical numbers, alpha-numeric variables, expressions and etc., the basic aim of the algebra is balancing the algebraic equations on both sides.In algebra study guide you can learn about the various expressions and order of expressions, with their standard forms. I like to share this Adding Polynomials with you all through my article.



General concepts of Algebra – algebra study guide:


Quartic function:


The Quartic function can be defined as the algebraic expression of fourth order. That is the highest power in the equation is equals to 4.

It is an algebraic equation with order number 4.

The general form is given by,

f(x) = ax^4 + bx^3 + cx^2 + e.

thus, the quartic expression from algebra study guide.

Quintic equation:

The Quintic equation can be defined as the algebraic expression of fifth order. That is the highest power in the equation is equals to 5.

It is an algebraic equation with order number 5.

The general form is given by,

ax5 + bx4 + cx3 + dx2 + ex + f = 0.


Understanding Binary Division is always challenging for me but thanks to all math help websites to help me out.

Polynomial:

The Polynomial expression can be defined as the algebraic expression of second order. That is the highest power in the equation is equals to 2.

The polynomial equation is of the form,

x^2 – 10x + 7 = 0

Note:

The addition or multiplication of any two polynomial results another polynomial.

These are the various forms of algebraic equations from algebra study guide.

Experiment Learning

Introduction experiment learning:-

In this article we are learning about the experiment concept. A learning probability experiment is a condition where chances affect the outcome (the result of a learning experiment). A coin flip is a learning probability experiment because chance affect whether a coin will ground heads or tails when it is flipped. In learning probability, an experiment is a procedure with an outcome that deepens leading chance. Some learning examples of such experiments are given below. Is this topic Experimental Probability Definition hard for you? Watch out for my coming posts.


Example for learning experiment:-


Learning Experiment 1:-

Toss the coin. But the coin is fair, (that is balanced or unbiased) the chance of in receipt of a head is one chance in two. The chance of in receipt of a tail is also one in two.

Solution:-

In conditions of probability, we say that each outcome is evenly likely to occur and that the probability of tossing a head is one dived by two.

Learning Experiment 2:-

Ten cards number one to ten are placed in pack and then a card is drawn at random. It is even that is some of the ten cards will be selected.

Solution:-

There are four prime numbers and so the chance of choose a card bearing a prime number is four in ten hence, the probability of select a prime number is four dived by ten or two divide by five.

Learning Experiment 3:-

A die is fearful and the number on the highest face in noted. It is uniformly likely that any of the 8 numbers will show on the top. In other words the likely outcomes are 1, 2, 3, 4, 5, 6,7and. The set of these outcomes is called the example space for the experiment.

Solution:-

There are 4 odd numbers and 4 even numbers. so the chance of an odd number being on the peak face of the die is 4 in 8 (as there are 8 numbers in the sample space). So we say that the probability of obtain an odd number on the summit is 4 in 8:   P (odd number) =4/8.

Learning Experiment 4:-

Believe one more random experiment. This time two dice are thrown at once ant the numbers on the top are noted. There are 16 probable outcomes that are; there are 16 elements in the sample space.

Solution:-

By inspecting the following table, we see that there are 4 chances of getting a double. So the probability of getting on the uppermost faces is 4 in 16 P (double) =4/16.

I have recently faced lot of problem while learning online math tutoring for free, But thank to online resources of math which helped me to learn myself easily on net.


Practices problem for learning experiment:-


Learning Experiment Problem1:-

During Coin tossing, Toss a fair coin once and ask what the probability of heads is?

Answer:- one dived by two.

Learning Experiment Problem 2:-

A pack contains 124 birth certificates, of which 48 are of male births and 78 of female births. Suppose that a credential is drawn at random from this pack. What is the probability that the certificate tired will be that of a male birth?

Answer:- The probability of drawing a female’s credential is P (F)=78/124.

Learn Harmonic Mean Online

Introduction to learn harmonic mean online:
Harmonic mean is used to find the average of the given terms. Harmonic mean is defined as the number of given value divided by the inverse of the each values given. For calculating the harmonic mean, we are using one of the formula. By using the formula, we are calculating the harmonic mean.


Explanation to learn harmonic mean online

The explanations to learn harmonic mean is as follows,

Online has number of examples about the harmonic mean with suitable solutions.
All the examples given in online are worked out with step by step solutions.
Also the practice problems for the harmonic mean are very helpful to the students.
The formula given for calculating the harmonic mean is as follows,

Harmonic Mean =  `N/( (1/a_1) + (1/a_2) + (1/a_3) + .......(1/a_n))`

Where,

N = Number of terms in the given functions.
`1/a_1`   = Inverse of each terms in the given functions. Understanding Interesting Data Sets is always challenging for me but thanks to all math help websites to help me out.

Example problems to learn harmonic mean online

Problem to learn in online:

Problem 1:  2, 4, 8, 16. What is the value of the harmonic mean?.

Solution:

Step 1: Given:

Data  = 2, 4, 8, 16

N = 4

Step 2: Formula:

Harmonic Mean =  `N/( (1/a_1) + (1/a_2) + (1/a_3)....(1/a_n))`

Step 3: Simplify:

Harmonic Mean =  `N/( (1/a_1) + (1/a_2) + (1/a_3) + (1/a_4) )`

= `4/ ( (1/2) + ( 1/4) + (1/8) + (1/16))`

Step 4: Solve:

=  `4/((8 + 4 + 2 + 1)/16)`

= `64/(8 + 4 + 2 + 1)`

= `64/15`

= 4.2666

Result: Harmonic Mean = 4.2666

Thus, this is the required answer for the above given harmonic function.

Problem 2: 1, 3, 6, 8, 12. What is the value of the harmonic mean?.

Solution:

Step 1: Given:

Data  = 1, 3, 6, 8, 12

N = 5

Step 2: Formula:

Harmonic Mean =  `N/( (1/a_1) + (1/a_2) + (1/a_3)....(1/a_n))`

Step 3: Simplify:

Harmonic Mean =  `N/( (1/a_1) + (1/a_2) + (1/a_3) + (1/a_4) )`

= `5/ ( (1/1) + ( 1/3) + (1/6) + (1/8) + (1/12))`

Step 4: Solve:

=  `5/((24 + 8 + 4 + 3+ 2)/24)`

= `5/((41/24))`

= `120/41`

= 2.9268

Result: Harmonic Mean = 2.9268


Practice problems to learn harmonic mean online

Practice problems to learn in online:

Problem 1: 2, 6, 12, 24, 26. What is the value of the harmonic mean?

Answer: 6.027

Problem 2: 3, 5, 7, 9, 12. What is the value of the harmonic mean?

Answer: 5.742