Solving Arithmetic Mean

Introduction to arithmetic mean:

     Arithmetic mean is the important concept in mathematical statistics.   Arithmetic mean is also referred to as average or mean.  Arithmetic mean is the ratio between the sum of all values and  number of values.  In this  article we have to learn about how to solving arithmetic mean problems through examples.

Formula to find arithmetic mean = Sum of elements / Total number of elements.

Brief Explanation of Solving Arithmetic Mean

Formula for finding arithmetic mean:

     Arithmetic mean = `(Sumof all the values)/(Number of values)`

     It is simply called as A.M.  Arithmetic mean values are usually mentioned in decimal point values.

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Example Problems on Solving Arithmetic Mean

Example 1:

Solving the arithmetic mean for the following values 78, 89, 24,56,77,14, 19

Solution:

The given values are 78, 89, 24,56,77,14, and 19

Formula for finding the arithmetic mean

Arithmetic mean= `(Sumof all the values)/(Number of values)`

Here the sum of values = 78+ 89+ 24+56+77+14+ 19

Adding this we can get,

Sum=357

Here the number of values=7

Therefore arithmetic mean =`(357)/(7)` = 51

This is the arithmetic mean of the given values.

Example 2:

Solving the arithmetic mean for the consecutive four odd numbers u+21, u+23, u+25, u+27

Solution:

The given values are u+21, u+23, u+25, u+27

Formula for finding the arithmetic mean

Arithmetic mean=`(Sumof all the values)/(Number of values)`

Here the sum of values = u+21+ u+23+ u+25+ u+27

Adding this we can get,

Sum=4u+96

Here the number of values=4

Therefore arithmetic mean =`(4u+96)/(4)` = u+24

This is the arithmetic mean of the given values.

Example 3:

Solving the arithmetic mean for the consecutive numbers y, y+1, y+2, y+3, y+4, y+5, y+6

Solution:

The given values are y, y+1, y+2, y+3, y+4, y+5,y+6

Formula for finding the arithmetic mean

Arithmetic mean= `(Sumof all the values)/(Number of values)`

Here the sum of values = y+ y+1+ y+2+ y+3+ y+4+ y+5+y+6

Adding this we can get,

Sum=7y+21

Here the number of values=7

Therefore arithmetic mean =`(7y+21)/(7)` = y+3

This is the arithmetic mean of the given values.

Proportion Questions

Introduction to proportion questions:
Algebra is with the purpose of separation of mathematics in which calculation are made by using any arbitrary characters to stand for the quantities or things considered. In our day-to-day life, by learning ratio and proportion many a times we compare two quantities of the same type. Thus, in convinced situations, comparisons by division make better sense than comparison by taking the difference. The comparison by division is the Ratio. We denote ratio-using symbol ‘:’. If two ratios are the same, we state that they are in proportion and use the symbol ‘:’ or ‘=’ to equate the two ratios.In this article, we are going to discuss about proportion questions.

Proportion Questions – Definition and Types:

Definition of proposition:

If two ratios are not equal, then we state that they are not in proportion. In a statement of learning proposition, the four quantities involved when taken in order are known as respective terms. First and fourth terms are known as extreme terms. Second and third terms are known as middle terms.

a: b = c : d

There are two types of propositions,

1. Simple proposition:

A proposition consisting of just individual subject and one predicate is called a simple proposition.

Example: The following are simple proposition

1. Ram is blind.

2. The flower is not red.

2.  Compound proposition

A proposition consisting of two or further simple propositions in the form of a single sentence is called a compound proposition.Is this topic free online math tutor hard for you? Watch out for my coming posts.

Example: The following are compound propositions,

Quadrilateral is a square and each side of this quadrilateral is 4cm long.

Proportion Questions – Example Problems:

Question 1:

The income and savings of a family are in the ratio 6: 4. If the income of the family is Rs.7, 500. Find how much is being saved.

Solution:

Let the savings be Rs. m.

The proportion is 6: 4 = 7500: m

(Income: Saving) = (Income: Saving)

`6m = 4 xx 7500`

`(6m) / 6 = (4 xx 7500) / 6`

`m = 30000 / 5`

`m = 6000`

The Savings = Rs.6000 .

Question 2:

Jack works as a dental hygienist. Last week, Jack made `$` 720 for 36 hours of work. How many hours must Jack work in order to make `$` 950?

Solution:

Jack works as a dental hygienist

`($720) / (36hours)` = `($950) / (y hours)`

`(36 hours) xx ($950)` = `(y hours) xx ($720)`

34200 = $720 y

`(34200) / (720)` = y

47.5 = x

Jack 47 hours 5 mins work in order to make $950

Question 3:

If the cost of 11m rope is Rs. 80, find the cost of 6m cloth.

Quantity(in m) Cost (in Rs.)

11                    96

6                      ?

Solution:

The proportion is

11: 6 = 96: ?

Product of means = `6 xx 96` = 576

Product of Extremes = `11 xx k`

`11 xx k = 576`

`(11 xx k) / 11` = `576 / 11`

k = `576 / 11`

`k = 52.36 `

The cost of 6 m cloth = Rs. `52.36`

Properties of Arithmetic Mean

Introduction of arithmetic mean properties:

In math and statistics, the arithmetic mean or mean defines group of values is sum of all the values in the group and divide it by the number of items in the group. Based on list or group the name of mean is varied that is if the list defines the statistical population then the mean of the population is known as the population mean. Likewise if the group defines the statistical sample then it is known as sample mean.

Properties of Arithmetic Mean:

Let we see about some of the properties of arithmetic mean.

Arithmetic mean Property 1:

If m1 and m2 are the means of the two lists defined from the values v1 and v2 then the mean m is given by the equation
m = v1m1+v2m2/ v1+v2

Arithmetic mean Property 2:

If each inspection in the data is converted by m, the sum total of all the values unaffected.
That is, m = m1, m2, m3, m4........, mn / v
thus m1,m2,m3,m4........,mn = vm
Replacing each observation by m, we obtains

m+m+m........+m = vm

Arithmetic mean Property 3:

If all value of the variable m is either improved, reduces, divided or multiplied by a constant, the explanation so acquired also improved, reduces, acquire multiplied or acquire divided correspondingly by the similar constant.Please express your views of this topic Solve Equation by commenting on blog.

Arithmetic mean Property 4:

Algebraic sum of the divergence of a group of values from their arithmetic mean is 0.

Example:

Example 1:

Find the mean of the given values 56,35,87,23,63,58,46.

Solution:

We know the formula for find the mean, that is, addition of all the values/ total number of values.

Therefore, 56+35+87+23+63+58+46/7

= 368/7

= 52.571

Example 2:

Find the sum of the deviations of the given different values 5, 10, 15, 20, 25 from their mean.

Solution
Mean of 5, 10, 15, 20, 25 is,

`barx=(5+10+15+20+25)/(5)=(75)/(5)=15`



Therefore the addition of the deviation about mean is 0.

Multiplying Decimals Calculator

Introduction for the multiplying decimals calculator:

Calculator is a device which calculates the required process in that device and also we can substitute the many values in the calculator. Decimals is a number which is indicates the number with the point representation. In decimal number we have the point indication in between the numbers. From left to right we have the point value such as tens, hundreds, thousands etc. For multiplying decimals numbers we have the steps for the multiplication.

Example Problems in Multiplying Decimals Calculator

Example 1:Multiply 0.3 × 0.2

Solution: First enter the two decimal number(0.3 and 0.2) in the first and second box
Now press the enter button
Get the multiplied result(0.006) in the third box.

Multiplier is 0.3 and multiplicand is 0.2
1            
0.3      
× 0.2                      
06                
00  
0.006

Example 2:Multiply 1.256 × 0.32

Solution: First enter the two decimal number(1.256 and 0.32) in the first and second box
Now press the enter button
Get the multiplied result(0.40392) in the third box.
1 1                 
1.256
× 0.32         
1                                    
12512 
3768
0000     
0.40392

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Example 3:  Multiply 0.21256 × 0.1

Solution:
First enter the two decimal number(0.21256 and 0.1) in the first and second box
Now press the enter button
Get the multiplied result(0.021256) in the third box.

0.21256
× 0.1        
021256             
000000 
0.021256                

Example 4: Multiply 0.589 × 0.4

Solution: First enter the two decimal number(0.589 and 0.4) in the first and second box
Now press the enter button
Get the multiplied result(0.2356) in the third box.

0.589
× 0.4        
02356       
0000 
0.2356

Example 5: Multiply 0.54× 1.1

Solution:         
First enter the two decimal number(0.54 and 1.1) in the first and second box
Now press the enter button
Get the multiplied result(0.594) in the third box.

0.54
× 1.1        
054       
054      
0.594       

A Rhombus is a Regular Polygon

Introduction to a rhombus is a regular polygon:

The regular polygon has different types of shapes. A rhombus is one type of regular polygon. A rhombus is closed with four sides and it is like as diamond. It is also referred as quadrilateral shape. Now we are going to see about rhombus in regular polygon.

Explanation for a Rhombus is a Regular Polygon
Some notes for regular polygon rhombus:

The regular polygon rhombus has four equal length sides. A rhombus is considered as parallelogram.The right angles of rhombus is in square shape.

Properties of rhombus regular polygon:

The rhombus has opposite angles are equal.
The diagonals are vertical.
The rhombus has convex property and isotoxal property.
The congruent triangles are used to prove the rhombus is symmetric. The regular polygon rhombus is include properties of parallelogram.

Rhombus regular polygon area calculation:

A rhombus area calculation is done by three methods. They are,

Base times height method – The area of rhombus is ba.
Diagonals method – The area of rhombus is d1d2/2.
Trigonometry method – The area of rhombus is s2 sin a.
In these methods, the base and length of diagonals are used.

Perimeter of regular polygon rhombus:

The total distance of outside rhombus is called as perimeter. The perimeter of rhombus is 4S. Here, the ‘S’ is length of side.Understanding free tutoring online is always challenging for me but thanks to all math help websites to help me out.

More about a Rhombus is a Regular Polygon

Example problems for regular polygon rhombus:

Problem 1: What is the area of regular polygon rhombus with b = 6 and a = 7.

Answer:

The side length is given as 6 and altitude is 7.

Therefore, the rhombus area is ba = 6 x 7 = 42.

Problem2: Determine the perimeter of regular polygon rhombus with side length 8.

Answer:

The side length is 8.

A rhombus perimeter is 4S = 4 x 8 = 32.

Exercise problems for a rhombus is a regular polygon:

1. What is the area of rhombus with b = 10 and a = 6.

Answer: Area = 60.

2. Find the perimeter of regular polygon rhombus with 4 side length.

Answer: The perimeter is 16.

Probability Math Version

Introduction to Probability Math Version

In math version, probability is a method of expressing knowledge or attitude that an occurrence will happen. In mathematics the idea has been given a right sense in probability theory, that is used broadly in such areas of learn as mathematics, finance, statistics etc. Now we will see the examples of probability.I like to share this Calculating Probability with you all through my article.

Examples - Probability Math Version

The following difficult examples are used to understand the probability concepts.

Example 1

The set A has the numbers from 15 to 23. Find the probability for the following outcomes?

i) Select the numbers below 20.

ii) Select the numbers between 15 to 20.

Solution

The set A={15,16,17,18,19,20,21,22,23}

i) Take P(A) is the probability for select the numbers below 20.

Total numbers n(S)=9

Here the following numbers are the below 20 n(A)={15,16,17,18,19}=5

So P(A)=`(n(A))/(n(S))`

=`5/9` .

ii) Take P(B) is the probability for  select the numbers between 15 and 20.

Total outcomes n(S)= 9

The following numbers are available n(B)= {16,17,18,19}=4

So P(B)=`(n(B))/(n(S))`

= `4/9` .

Example 2

James has 5 white balls, Mercy has 10 blue balls and Tom has the 6 yellow color balls. Find the probability for select James white balls.

Solution

James white color balls n(A)=5

Mercy’s blue color balls n(B)=10

Tom’s yellow color balls  n(C)=6

Total number of balls n(S)=5+10+6

=21.

Take P(A) is the probability for select James white balls.

P(A) =`(n(A))/(n(S))`

=`5/21` .

Example 3

Solve the probability for select the letter ‘R’ from the word ‘ALGEBRA?

Solution

Given word is ALGEBRA.

Total letters n(S)=7

Number of ‘R’ letter n(A)=1

So the probability=`1/7` . 

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Practice Problems- Probability Math Version

1.What is the probability for select the letter ‘E’ from the word ‘SET THEORY’?

Answer:

Probability=`2/9` .

2.What is the probability for select the even numbers from 1 to 6?

Answer:

Probability=`1/2` .

These example problems are used to learn the probability concepts in math version.

One to One Function Calculator

Introduction to One to one function calculator:

In this article we are discussing about one to one function problems solving by calculator.  A function for which each number of the range of the function corresponds to approximately one number of the domain, One to one is often written 1 – 1. In this calculator first enter the problems. Finally press the solve button we get the solutions.

One to One Function Calculator – Example Problems:




Example 1:

Is g(x) = 2x - 1 one to one function?

Solution:

Now we plug if x = p and x = q

g(p) = g(q) implies that  p = q

So,   2p - 1 = 2q - 1

Add 1 on both side of the function. We get,

2p = 2q

Divide by 2 on both sides of the function. Finally we get p = q.

So Thus the given function is one to one function

Example 2:

Is f(x) = 4x + 3 one to one function?

Solution:

Now we plug if x = p and x = q

f(p) = f(q) implies that  p = q

So,   4p + 3 = 4q + 3

Subtract 4 on both sides of the function. We get,

4p = 4q

Divide by 4 on both sides of the function. Finally we get p = q.

So Thus the given function is one to one function.

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Additional One to One Function Calculator – Example Problems:

Example 3:

Is f(x) = 5x + 4 one to one function?

Solution:

Now we plug if x = p and x = q

f(p) = f(q) implies that  p = q

So,   5p + 4 = 5q + 4

Subtract 4 on both sides of the function. We get,

5p = 5q

Divide by 5 on both sides of the equation. Finally we get p = q.

So Thus the given function is one to one function

Example 4:

Is f(x) = 6x + 5 one to one function?

Solution:

Now we plug if x = p and x = q

f(p) = f(q) implies that  p = q

So,   6p + 5 = 6q + 5

Subtract 4 on both sides of the function. We get,

6p = 6q

Divide by 6 on both sides of the function. Finally we get p = q.

So Thus the given function is one to one function