Help with statistics basics

Introduction to Statistics:

In this article let me help you on statistics basics. Online tutors are the individuals who will help the scholars in studies and report the new additional skills by using a step-by-step method. Online tutors are explaining the issues to the scholars. So the scholars can clear the doubts within a minute. Statistics is the most important idea in maths. Statistics is the appropriate science. Now let me show you a example on statistics. This will help you on understanding better.

Example:
Find out the Median for the following sequence. 24,28,32,37,42.

Solution:

First sort the above numbers. They get 24,28,32,37,42.

The middle element is 32. This could also help us on speed maths

Therefore median=32.

Introduction to Quadratic Equations Formula

Introduction to Quadratic Equations:

In this section let me help on quadratic equation formula. A quadratic functions in the variable of x is an equations of the general form ax2 + b x + c = 0, Where "a","b","c" are real numbers, a not equal to Zero. 2x2 + x – 300 = 0 is a quadratic equations.

The Simplifying Quadratic equations, the general form is ax2 + bx + c, where "a", "b", and "c" are just numbers; they are known as the "numerical coefficients". The Formula is derived by the process of completing the square.

Example:

Solve (x + 1)(x – 3) = 0.


solution:-

(x + 1)(x – 3) = 0
x + 1 = 0 or x – 3 = 0
x = –1 or x = 3


The solution is x = –1, 3

Help on Adjacent Angles

Adjacent Angles

Definition of Adjacent Angles

In this lesson let me help you on adjacent angles. The word “adjacent” means “next” or “neighboring”.

Adjacent angles are angles just next to each other. Adjacent angles share a common vertex and a common side, but do not overlap.

Examples of Adjacent Angles

In the figure shown, a and b are adjacent angles. They have a common vertex O and a common side OA.


Solved Example on Adjacent Angles

Example 1

Name all pairs of angles in the diagram that are adjacent. Solution: This can also help us on big words and definitions
Adjacent angles are angles just next to each other. Adjacent angles share a common vertex and a common side, but do not overlap.

Ða and Ðb, Ðb and Ðc, Ðc and Ðd, Ðd and Ðe, Ðe and Ða are the pairs of adjacent angels in the diagram shown above.

Note on types of functions

In this section let me help you on types of functions. To know types of function, first one has to consider two sets with values(briefly explained below) and representation of function is done by values bounded in a oval shaped boundary as shown in diagrams below.

Considering two functions A and B

* One-one function

* Many-one function

* Onto function

* Into function

And below are the functions explained in detail with mapping function representation.

Example Problems for Function:

This can also help you on adjoint matrix.

Q 1 : f(x) = 3x + 4 substitute the value for x = 4

Sol : Given f(x) = 3x + 4

Substitute the value in equation x = 4

Here the notation value has substituted

f(2) = 3(4) + 4

Here we have multiplied by 3( 4 ) = 12

f(2) = 12 + 4

f(2) = 16

Help on Inequality Solver

Introduction to inequality solver:

In mathematics, an inequality is the statement about the relative size or order of two objects or about whether they are the same or not

* The notation a <>

* The notation a > b represents that a is greater than b.

* The notation a ≠ b represents that a not equal to b, but does not say that one is greater than the other or even that they can be compared in size.

the above statemnet denotes, a is not equal to b. These relations are called as strict inequalities. The notation a <>

These inequalities are involved in various expressions which are expressed in following statements. This will also help us on product rule

1. Numerical inequalities
2. Literal inequalities
3. Double inequalities
4. Strict inequalities
5. Slack inequalities
6. Linear inequalities

What is prime number?

Introduction about search what is a prime number:

In this section let me help you go through on what is a prime number.In mathematics, a prime number (or a prime) is a natural number that has exactly two different natural number divisors: 1 and itself. The first twenty-five prime numbers are:

Prime Numbers:- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Condition: - If x is the prime number then the next factors of the number x is 1 and X only. Let us see what are prime numbers in math. (Source: Wikipedia)

Search What is a Prime Number:

* Prime number means it must be divisible by one and itself only. Other than this no more factor for prime numbers.

* Take any one number and then divide it by 2, 3, 4.... This will also help us on knowledge from study

* Suppose if any number gives more than 2 factors, that is not a prime number. Otherwise it is known as prime number.

* If the number has more than two factors then it is considered as composite number. This is the way to search a prime number.

Note on Linear Functions

Linear Function is defined as follows, considering two sets A and B. We form the Cartesian Product, we form relations. From all the relations, we can select a few which satisfy the rule that each element of the set A is related to only one element of the set B.

When a relation satisfies this rule, it is called a fuction.

In this chapter, we will study how a function is a relation, but a relation may not be a function.

Hence the function calculator sections helps to differentiate relation and a function.

Characteristics of Functions

1. Two functions f,g are equal if and only if they have same domain and range and f(x)=g(x) for every x ? A. This will also help us on linear equation form

2. f: A ---> B is one-one(Injection) if and only if for all a0 ,a1 ? A, “f(a0)=f(a1) implies that a0=a1 “

3. f: A ---> B is onto(Surjection) if and only if f(A)=B. also for every b ? B, there exists an element a ? A such that f(a)=b.

4. f: A ---> B is Bijection if f is one-one and f is onto.then number of elements in A is equal to number of elements in B.

Properties of logarithms

Introduction:

We use logarithms to mark terms linking various forms of powers in a different form. If you can job self-assuredly with powers in dissimilar analysis you should have no problems conduct logarithms.

mmediately as calculation is the opposite process of addition, and taking a square root is the opposite action of squaring, exponentiation logarithms are inverse operations. Decision an antilog is the opposite operation of judgment a log, so is an additional name for exponentiation.

Three Properties of Logarithms

Following are the three properties of Logarithms.

Multiplication property:

The first property of logarithms is declare what is the rule when you multiply two values with the same base together

(x² * x³) Recall that logarithm is exponents, and when you multiply, you are going to add the logarithms.

log_c xy = log_c x + log_c y.

Example problem:

1. Log₅50

Log₅(25 * 2 )= log₅ 25+log₅ 2

2. Log₅ 80

Log₅(40 * 2 )= log₅ 40+log₅ 2.

Division property:

The second property of logarithms are the law what time you divide two values by resources of the similar base is the way to subtract the exponents. Therefore, the law for division is the method to subtract the logarithms.

The log of a calculate is the dissimilarity of the logs.

Log_c (x/y) = log_c x – log_c y.

Example problem:

1) Log₅ 60

Log₅(20/3) = log₅ 20- log₅ 3

2). Log₅ 120

Log₅(60/2) = log₅ 60 – log₅ 2

Raising to a Power property:

The third property of logarithms are what time you increase a quantity to a power, the law is that you multiply the exponents jointly. In logarithms properties the exponent scheduled the argument is the coefficient of the log.

log_c x^r = r * log_c x.

Example problem:

Log₅100²=2 log₅100

= 2 log₅(10*10)

= 2 (log₅10 + log₅10)

= 2(2 log₅10)

Log₅100²= 4 log₅10