Learning Sure Event

Introduction to learning sure event:

The word sure event is coming in probability theory.

Probability is the likelihood of occurring of an event. P (A) denotes the probability of an event.

Probabilities of events are always between 0 and 1.

0<=P(A)<=1

We say that an event is a sure event if it is having a probability of occurrence 1.

As we know that the probability varies from 0 to 1.

So if an event has the maximum probability, that is 1;then that event is a sure event.

For example we can consider the case of tossing a coin

In that case the probability of getting a head or tail one.

As one of these event will surely happen. So it is a sure event.

As we talk about sure event we cant avoid the case of impossible events.

Which is the opposite case to the sure event. That is never going to happen.

For example, let us take the example of tossing a die. Here probability of getting an eight is zero

I like to share this Theoretical Probability Definition with you all through my article.

learning sure event-Examples


1) While drawing a dice,probability of getting one event less than 7

here the sample space is (1,2,3,4,5,6)

Probability of the event is P(E) =1

Here E is a sure event.

2)Suppose a bag contains 4 balls of red color.

Here the probability of getting a red ball is P(getting a red ball)=1

Which is also a sure event.

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learning sure event-Practice problems


1.      Find the probability of getting a green ball, from the bag, which contains 5 green balls

2.      Find the probability of getting a white pearl from the bag of 500 white pearls and one cream pearl.

3.      Find the probability of getting a black ball from the pack of white balls.

Answers:

1.      Here the sample space contains only events that contain the occurring of green balls. There is no chance of getting any other ball.

Here the number of events favorable is 5

And total number of events is also 5

So here the probability of getting a green ball is

P (Getting a green ball)=5/5

So it is 1..

2. This is the chance of almost sure event.

Probability of getting the other color pearl is almost 0 here.

3. This is the case of Impossible events.

Here the probability of occurring the event is 0

As it a not possible to get a black ball from the white ball pack

Array Definition Math

Introduction to array definition math:
Array has a list of data. In math array is a rectangular arrangement of elements. The elements are shown in rows and columns. In math array elements are put in the parenthesis or square brackets. In math the arrays are represented by capital letters for example A, B, C……An array is a symbolic way to represent math facts. Using symbols like circle, square or rectangle is one way of writing math facts in array.

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Definition of Array:

Definition of array:

The symbol m `xx` n is used to represent the array in math. The number of columns is represented by first element in the symbol and number of rows is represented by second element in the symbol. For example 2 `xx` 3 mean that array has 2 rows and 3 columns. The structure of array is rectangle. Array is used to be a symbol of the number of data.

Here

First row elements = a1, a2, a3

Second row elements = b1, b2, b3

Third row elements = c1, c2, c3

First column elements = a1, b1, c1

Second column elements = a2, b2, c2

Third column elements = a3, b3, c3

Symbol representation of above array is 3 `xx` 3

Total rows =3

Total column = 3

Types of Array or Matrix:

Types of array or matrix:

Column matrix
Row matrix
Square matrix
Diagonal matrix
Triangular matrix
Scalar matrix
Identity matrix
Zero matrix
Equality of matrix

Definition of column matrix:

Only one column is present in the column matrix.

Definition of row matrix:

Only one row is present in the row matrix.

Definition of square matrix:

If one matrix has equal number of row and column means called as square matrix.

Definition of diagonal matrix:

Other than diagonal elements in the array is zero means called as diagonal matrix.

Definition of triangle matrix:

Triangle matrix must be a square matrix. All the elements in above the diagonal are zero means called as lower triangle matrix. All the elements in below the diagonal are zero means called as upper triangle matrix.

Definition of unit matrix:

Unit matrix must be a square and diagonal matrix. The diagonal elements are one and the remaining elements in the array is zero means call as unit matrix.

Growth Factor in Math

Introduction to growth factor in math:

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

Definition of growth factor in math:

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

Formula to growth factor in math:

When the growth rate is given

Increase in value = P* G*T

P is the principle or original value.

G is the growth rate.

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

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

it is always positive value not the negative one.

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Model problems to growth factor in math:

Problem: 1

Find the growth factor of the original value $500 over a period of 7 years with the growth rate of 6%.

Solution:

The original value is $500

Period of time = 7 years

Growth rate is 6%

The increase value is `(500*7*(6/100))`

=(5*7*6)

= 210

The increased value is $710

Now we have to calculate the growth factor:

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

= `(710/500)`

= 1.42

The growth factor is 1.42

Problem: 2

Find the growth factor of the original value $300 over a period of 9 years with the growth rate of 8%.

Solution:

The original value is $300

Period of time = 9 years

Growth rate is 8%

The increase value is `(300*9*(7/100))`

(3*9*7)

= 147

The increased value is $447

Now we have to calculate the growth factor:

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

= `(447/300)`

= 1.49

The growth factor is 1.49

Problem: 3 find the growth factor of the numbers behind the numbers 12.5,50, 100, 200, 400.

Solution:

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

(50/12.5) = 2
(100/50) =2
(200/ 100)= 2
(400/200)=2

Here the growth factors between the numbers are 2

the growth factor of the numbers is 2

5th Grade Math Functions

Introduction to 5th grade math functions:

The mathematical concept of a function expresses the intuitive idea that one quantity (the argument of the function, also known as the input) completely determines another quantity (the value, or the output). A function assigns a unique value to each input of a specified type. The argument and the value may be real numbers. (Source: Wikipedia)

Is this topic Simple Interest Problems hard for you? Watch out for my coming posts.

5th grade math functions - Example problems:


Here we will discuss about the 5th grade math functions,

5th grade math function - Example problem: 1

Find the simple interest on a sum of Rs. 5000 for 5 years at the rate of 14% per annual.

Solution:

The given principal amount = Rs. 5000

Interest rate = 14% per annual.

Interest on Rs. 100 for 1 year = Rs. 50

Interest on Rs.2500 for 1 year = Rs. 500

Therefore,

Interest on Rs. 2500 for 3 year = 5 * 500

= Rs. 2500

[Answer: The Simple interest value is Rs. 2500]

5th grade math function - Example problem: 2

Write the given number 9564 in expanded form.

Solution:

The given number is 9564

It can be written as,

9564 = 9000 + 500 + 60 + 4

Rearrange the above numbers as,

9564 = (9 * 1000) + (5 * 100) + (6 * 10) + (4 * 1)

Answer: 9564 = (9 * 1000) + (5 * 100) + (6 * 10) + (4 * 1)

5th grade math function - Example problem: 3

Find the sum of the two algebraic functions (x + 52x ^5 - 15) and (11x - 52)

Solution:

The given two functions are (x + 52x ^5 - 15) and (11x - 52)

Add the given two functions, we get

= (x + 52x ^5 - 15) + (11x - 52)

Expand the above functions, we get

= (x + 52x ^5 - 15 + 11x - 52)

= 52x3 + 12x - 67

Answer:  (x + 52x ^5 - 15) + (11x - 52) = 52x ^5 + 12x - 67

5th grade math functions - Practice problems:

1. Find the expand form for the given number 75689.

[Answer: 75689 = (7 * 10000) + (5 * 1000) + (6 * 100) + (8 * 10) + (9 * 1)]

2. Find the simple interest on sum of 6000 for 4 years at the rate of 10%.

[Answer: The simple interest value is 2400]

3. Add the given two algebraic functions f(x) = 89x + 15 and g(x) = 8x2 - 26

[Answer: 8x2 + 89x – 11]

6th Grade Math Problems

Introduction:

This article deals with the math subject topics that are covered under the 6th(sixth) gradewith sample problems. The basics of all topics in mathematics are covered in the 6th grade and the student is prepared to cope with advanced concepts in mathematics in higher classes.

6th grade math topics:

The 6th (sixth) grade math subject includes the topics like basics of the,

Number system (whole numbers, decimal numbers, rational numbers, integers, fractions and ordering the numbers)
Measurement (metric system, temperature, mass, volume, length, time, area, surface area, and perimeter)
Basic geometry (understandings the elementary shapes, ideas and geometric figures)
Basic Algebra
Data handling in statistics and Symmetry
Ratio and Proportion.
These all are the important and basic topics for the 6th grad math topics.

Explanatory:

1. Number system:

In number system they have to know about how to recognize the numbers from 0 to ‘n’ (minimum 1000000) and, to write an order, represent, comparing, locate the numbers and identify the numbers.

And fully know about the decimal, whole, rational numbers, understanding the mixed numbers, fraction numbers from based on the concepts.

2. Measurements:

In measurement topic completely understanding of all the measurements like mm, cm, meter, km, feet, inches, yards, miles and units. And calculate the area, volume an etc…

3. Geometry:

To know about the geometric figures, concepts, ideas, and dimensional shapes and know about how to draw, calculate and understanding.

4. Basic algebra:

Algebra is the basic chapter for understanding all the other chapters and it has covers many topics. It is very useful for create, analyze, identify.

5. Statistics:

This statistics chapter covers the basics about the data, probability, distributions and statistics.

Math problems for 6th grade:

Example 1: Can you instantly find the greatest and the smallest numbers in each row?

1. 352, 856, 89,21,1548, 659, 256.

2. 32, 58, 6985, 20, 568, 125,129.

Solution:

1. 352, 856, 89,21,1548, 659, 256

The greatest number is 1548,

The smallest number is 21.

Solution:

2. 32, 58, 6985, 20, 568, 125,129.

The greatest number is 6985,

The smallest number is 20.

Example 2:  one side of the square is 6cm. Calculate the area of square?

Solution:

One side of the square is 6cm.

Square has totally 4 equal sides,

Area of square formula is = a ^2

We know a = 6cm

So, a ^2 = 6*6

= 36 cm

Answer is = area of square has 36 cm.

These are the problems on 6th grade math problems.

Learning Circles

Introduction About Learning Circles:

By learning, Circle consists of set of points from middle point. The point from the all points on a circle are equidistant is called the center of the circle, and the distance from that point to the circle is called the radius of the circle. illustration of circles is in single letter, its center. Circle has center point C and a radius of length r.


Properties of circle:


Let we see about the properties of learning circles:

The arc of a circle contains two points on the circle and all of the points on the circle that lie between those two points.
Chord is a segment and having end points which is on a circle.
Diameter of circle:
Length of the diameter = 2 × length of the radius.

Circumference of a Circle:
Circumference = 3 × diameter (approx.).

These are the properties of learning circles.


Formula:


Formulas of learning circles:

The area of circle:

Area of circle = 'pi' * r^2

where, r is the radius of the circle.

The diameter of circle:

Diameter of circle = 2 * r.

where,  r is radius of the circle.

The circumference of circle:

Circumference of circle = 2* 'pi' *r (or) 'pi' *d.

where,r is the radius of the circle.

d is the diameter of the circle.

Example 1:

Find the area, diameter and circumference of circle with radius of 4cm.

Solution:

1.The area of circle:

Area of circle = ∏ *r*r.

=(3.14)*4*4.

= 50.24 cm^2.

2.The diameter of circle:

Diameter of circle = 2*r.
= 2* 4.
= 8cm.

3.The circumference of circle:


Circumference of circle = ∏ * d.
= (3.14)* 8.
= 25.12cm.
Example 2:

Find the area, diameter and circumference of circle with radius of 7cm.

Solution:

1.The area of circle:

Area of circle = ∏ *r*r.

=(3.14)*7*7.

= 153.86 cm^2.

2.The diameter of circle:

Diameter of circle = 2*r.
= 2* 7.
= 14 cm.
3.The circumference of circle:

Circumference of circle = ∏ * d.
= (3.14)* 14.
= 43.96 cm.

Learning Articles with Histograms

Introduction to learning with histograms:

A graphical representation, in which learning the articles of histogram were identified as a bar graph for a particular measure of two frequencies and it has format of table that has shown in the bar graph and the graph represents the shapes that are given in the format. The height of a box and the measure is equal to the base side of the frequent data and the interval. A histogram is a graph demonstration of bar graph. Here shown about the types of distribution in the histogram.

learning part in articles with Histogram:

Horizontal X-Axis:

In the horizontal X-axis the bar chart gives the scale valve, which are the dimensions that fit into the data. These dimensions were normally well-known to the periods. Plot the horizontal X-axis points in the bar chart with respect to the values of Vertical Y-axis.

Vertical Y-Axis:

The straight bar or Vertical Y-axis in the bar chart gives the scale value, which shows you the several times the values within a period occurred. In several times it called as "frequency" in Y-axis.

Legend:

The legend provides extra information about the documents where the data came from and how the measurements were gathered.

Bars:

The bars consists of two main characteristics in the histogram, they are height and width. The height represents the several times the values within a period occurred. The width represents the length of the period covered by the bar. It is the same for all bars.

Title:

The title part in the histogram briefly explains the information about the things that are used in the bar chart.

learning Uses of articles with Histogram:

This histogram shows moreover a perfect distribution that covers about the graph, which displays all the brilliancy levels that contained in the scene found from the darkest to the brightest. The values are arranged with the values at the bottom of the graph from left to right. It gives an idea about the histogram and its use.

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Learning Conditions for the articles with Histogram:

The data’s can be marked clearly on the graph by measuring the data values accurately the scale and period.
The scale should contain all the data values. The period divides the scale into equal parts.
Learning Applications of articles with Histograms:

Clear review of total data sets that graphically shown in the bar chart.
Evaluate the measurements to the given specifications.
Share the information to the team.
Assist in administrative.