Solve Math Histograms

Introduction to solve math histogram:

A Histogram is a representation of frequency distribution through the four-sided figure whose width represents class intervals and whose areas are directly proportional to the corresponding frequencies.

Histograms will represent in Two Dimension used to graph continuous data. The histogram is used in continuous data graphing. This will be plotted continuously. Here we are going to solve math histogram

How to Solve Math Histogram:
Building a histogram is very easy. We normally use discrete data's for drawing the histograms. Here we are going to study how to create a histogram

STEP 1 :- If the given frequency distribution which we have is in inclusive form then we have to convert it into an exclusive form.

STEP 2 :- Taking suitable scales are more important,and then mark the class-intervals along x-axis and frequencies on y axis.  Note that the scales chosen for both the axes need not be the same.

STEP 3 :- Construct rectangles with class intervals as bases and the corresponding frequencies as heights. This is how we solve a math histogram.

Example Problems to Study How to Solve Math Histogram:

Prepare a histogram to from the following frequency table.

Class Interval                                     Frequency

0 – 10                                                  13

10 – 20                                                24

20 – 30                                                18

30 – 40                                                10

40 – 50                                                16


The histogram is a frequency density diagram. Histogram will represent will have the rectangular bars, And that will show the class intervals and frequency.

(1) The class intervals is taken on the X-axis and frequencies are taken on the  Y-axis

(2) The scales for both the axes are marked. In the y axis the scales are marked 0, 5, 10, 15, 20, 25,30

(3) while we are marking the class intervals we have to be more perfect, so that we may not make any errors.

(4) Draw rectangle bars with class intervals as bases and the corresponding frequencies as heights.

(5) This is how we build a histogram

Logic General

Introduction of logic general:

The field includes both the mathematical study of logic general and the applications of formal logic to other areas of mathematics. The unifying themes in mathematical logic general include the study of the expressive power of formal systems and the deductive power of formal proof systems.
Mathematical logic general is often divided into the fields of set theory, model theory, recursion theory, and proof theory. These areas share and basic results on logic, particularly first-order logic, and definably.
(Source from Wikipedia)

Mathematical Logic General Divided into Four Important Parts:

1)Set theory

2)Model theory

3)Recursion theory, and

4)Proof theory and constructive mathematics

Logic general for set theory:

If an element x belongs to a set A, we write x ? A. A set containing all the objects likely to be considering in a par8+ticular discussion is called a universal set and is usually denoted by U.

Logic general for proof theory:

A logical argument to be establishes the validity of a proposition or mathematical formula. The proof theory comprised if a set of axioms and premises sequentially to arrive at a formula to be proved in the form of a conclusion.

List of some Logical general operators:

( )           brackets

!  + -        logical not, unary plus, unary minus

* / %         multiply, divide, modulus

+ -          add, subtract

< <=         less than, less than or equal,

> >=         greater than, greater than or equal

==  !=       equal, not equal

&&           logical and

||             logical or

=             assignment

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Examples of Set Theory - Logic General:

Example 1:

Consider the sets:
f, A = { 1, 3 }, B = {1, 5, 9}, C = {1, 3, 5, 7, 9}.
Insert the symbol ? or ? between each of the following pair of sets:
(i) f . . . B (ii) A . . . B (iii) A . . . C (iv) B . . . C

Solution:

(i) f ? B as f is a subset of every set.
(ii) A ? B as 3 ? A and 3 ? B
(iii) A ? C as 1, 3 ? A also belongs to C
(iv) B ? C as each element of B is also an element of C.

Example 2:

Let A, B and C be three sets. If A ? B and B ? C, is it true that A ? C?. If not, give an example.

Solution:

No, Let A = {1}, B = {{1}, 2} and C = {{1}, 2, 3}. Here A ? B as A = {1}

and B ? C. But A ? C as 1 ? A and 1 ? C.
Note that an element of a set can never be a subset of itself.

Transverse Plane

Introduction to transversals plane:

The line, ray or segment which intersects the one or two line or ray or segment in the same plane. The intersected line should not to be parallel.We can also define it as; a line that passes through the one or two lines that are in the same plane (coplanar) is called as transversal line.
Angles:
There are several angles are made by the transversal line which intersect the parallel line.
Corresponding angles

Alternate angles
Alternate Interior angles
Alternate Exterior Angles
Vertical angles
Consecutive interior angles


Transversals Vs Parallel Line Angles:

Corresponding Angles:
When a transversal line intersects the two parallel lines, the angles in the matching corner are called as corresponding angles.The corresponding angles are always having common value.The corresponding angles are the congruent angles that lie on the same side of the transversal line.
Alternate Interior angles:
When a transversal line intersects the two parallel lines, the pair of angles that are on the opposite side of the transversal line but inside of the two lines called as alternate interior angle.The Alternate Interior angles are always having common measurement.
Alternate Exterior Angles:
When a transversal line intersects the two parallel lines, the pair of angles that are on the opposite side of the transversal line but outside of the two lines called as alternate Exterior angle.The Alternate Exterior angles are always having common measurement. Understanding math help online tutor is always challenging for me but thanks to all math help websites to help me out.

Tansversals :vertical and Consecutive Angles:

Vertical angles:
The opposite angles made by the transversal line that intersect the parallel lines are called as vertical angles. These angles are also called as vertically opposite angles.The vertical angles are also having common measurement.
Consecutive interior angles:
The pair of angles on one side of the transversal line but inside of the two lines is called as consecutive interior angles.The sums of the consecutive interior angles are equal to 180 degree.

Parallelogram Diagonals Bisect each Other

Introduction to parallelogram diagonals bisect each other:

Parallelogram figure are one type of quadrilateral. The quadrilaterals are lines of polygons. The parallelogram opposite sides is parallel and then congruent. We are learned parallelogram line opposite angles is congruent. Parallelogram has 2 pairs of equal length sides. The counterpart of solid figure parallelograms is a parallelepiped. In this tutorial is very helpful for students. After joining in this tutorial students are got good marks. Let us we see parallelogram diagonals bisect each other in this article. Understanding how to find the area of a parallelogram is always challenging for me but thanks to all math help websites to help me out.

Brief Description about Parallelogram Diagonals Bisect each Other
Types of parallelograms:

Rectangle

Square

Rhombus

Properties of Parallelogram:

Parallelogram is one type of quadrilateral polygons.

The quadrilateral contrary (opposite) angles are congruent.

parallelogram diagonals bisect each other

Properties of Square lines:

Square type parallelogram containing 4 sides

This parallelogram figures four sides are equal in measure

The opposite sides in this polygon figures are parallel

The diagonals are congruent, and the diagonal are perpendicular and this parallelogram diagonals bisect each other

Properties of Rectangle lines:

Rectangle type parallelogram containing four sides and four angles.

The opposite sides in this Rectangle type parallelogram are congruent

Opposite sides in this shapes are parallel

this parallelogram diagonals bisect each other

Properties of Rhombus lines:

In rhombus all the sides are congruent

Opposite angles in its congruent

The diagonal in its congruent.

This parallelogram diagonal bisects each other.

Simple Math Word Problem

Introduction to simple math word problems:
The math word problems are very helpful to the children. In math word, first we have to understand the given condition then start to solve given conditions. When math is given in the form of word problem, it inspires interest to the children for the reason that children like stories. In this article we will solve the math problem as word with help of example problems for simple math word problems. Having problem with Algebra Simplifying Expressions keep reading my upcoming posts, i will try to help you.

Examples – Simple Math Word Problems:

Let us we will solve the examples for simple math word problems.

Example 1:

There are 20 passengers in bus A and 32 passengers in bus B. How many passengers are there altogether in the two buses?

Solution:

Passengers in bus A = 20

Passengers in bus B = 32

Passengers in bus A + Passengers in bus B

So, 20 + 32 = 52

There are 52 passengers altogether in the two taxis.

Examples – Simple Math Word Problems:

A fruit whole seller had 500 apples. He sold 250 apples. How many apples did he have left?

Sol:

The total amount of apples = 500 apples.

Sold apples = 250

Remaining grapes =?

So, 500 – 250 = 250.

He had 250 apples left.

Examples – Simple Math Word Problems:

There are 15 coconuts in each bag. How many are there in 8 bags?

Sol:

So, 15 × 8 = 120.

There are 120 coconuts in 8 bags.

Examples – Simple Math Word Problems:

There are 6 ice creams, 7 fruits and 10 vegetables in a fridge. Calculate how many fruits are placed in the fridge.

Total ice creams = 6.

Total fruits = 7

Total vegetables = 10.

So, the total fruits are placed in fridge is 7. Looking out for more help on binomial probability distribution in algebra by visiting listed websites.

Practice Problems - Simple Math Word Problems:

Example 1:

1. There are 5 passengers in cars A and 4 passengers in cars B. How many passengers are there altogethers in the two cars?

Ans: There are 9 passengers altogether in the two cars.

Example 2:

2. A fruit fruits seller had 10 oranges. He sold 7 oranges. How many oranges did he has left?

Ans: He had 3 oranges left.

Example 3:

3. There are 7 potatoes in each bag. How many are there in 5 bags?

Ans: There are 35 potatoes in 5 bags.

These are example problems for simple math word problems.

That’s all about simple math word problems.

Add Math Question

Introduction to addition math question:

In this article we discuss the addition math question. Addition is way of the arithmetic operations. In math, addition represents the combining groups of numbers to create a large amount of collection data. Addition symbol represented by the plus (+). For example, assume there are 2 + 2 items meaning two items and two other items, add the form of item is four items (Therefore, 2 + 2 = 4). Addition helps to two or more numbers.

Example Problems for Addition Math Question:

Here we willdiscuss the example problems for addition math question,

Addition math question - Example: 1

Find the addition of following numbers: 24 and 13.

Solution:

Step 1:

The given numbers are 24, 13

Step 2:

Add 24 with 13

= 24 + 13

= 37

Step 3:

The final answer is 37

Addition math question - Example: 2

Find the addition of following numbers: 34 and 24

Solution:

Step 1:

The given numbers are 34 and 24

Step 2:

Add 34 with 24

= 34 + 24

= 58

Step 3:

The final answer is 58.

Addition math question - Example: 3

Find the addition of following numbers: 100 and 123.

Solution:

Step 1:

The given numbers are 100, 123

Step 2:

Add 100 with 123

= 100 + 123

= 223

Step 3:

The final answer is 223

Addition math question - Example: 4

Find the addition of following numbers: 200 and 240.

Solution:

Step 1:

The given numbers are 200, 240

Step 2:

Add 200 with 240

= 200 + 240

= 440

Step 3:

The final answer is 440

Addition math question - Example: 5

Find the addition of following numbers: 333 and 100.

Solution:

Step 1:

The given numbers are 333, 100

Step 2:

Add 333 with 100

= 333 + 100

= 433

Step 3:

The final answer is 433

More Example Problems for Addition Math Question:

Addition math question - Example: 6

Find the addition of following numbers: 432 and 222

Solution:

Step 1:

The given numbers are 432, 222

Step 2:

Add 432 with 222

= 432 + 222

= 654

Step 3:

The final answer is 654

Addition math question - Example: 7

Find the addition of following numbers: 555 and 343

Solution:

Step 1:

The given numbers are 555 and 343

Step 2:

Add 555 with 343

= 555 + 343

= 898

Step 3:

The final answer is 898.

Define Domain Math

Introduction to define domain math:

Define domain:

In math, the domain of a function can be defined as the set of all possible input or argument values which allows the functions to be defined. The function provides output value for each input value of the function domain. For example, consider ' f ' be the function between A and B, then A is called the domain of the function ' f '.

Here, we are going to see few example and practice problems of domain which help you for learning domain function in math.

Example Problems to Define Domain in Math:

Define domain math with example problem 1:

Find the domain of the function y = x^2 + 7.

Solution:

Step 1: Given function

y = x^2 + 7 .

Step 2: To find domain

In the given function, the term x^2 is never negative and therefore x^2 + 7 never less than seven.

Hence, the domain is all real numbers greater than 7.

Step 3: Solution

The domain of the given function is all real numbers y ≥ 7.

Define domain math with example problem 2:

Find domain of the function y = |x + 13|.

Solution:

Step 1: Given function

y = |x + 13| .

Step 2: To find domain

We know that the modulus function gives us only positive values.

That is, the domain of modulus function is (0, ∞).


Step 3: Solution

Hence, the domain of the given function is (0, ∞).

Define domain math with example problem 3:

Find domain of the function y = `(11x - 4)/(x^2 + 7x + 12)`

Solution:

Step 1: Given function

y = `(11x - 4)/(x^2 + 7x + 12)`

Step 2: Set the denominator of the given function y = `(11x - 4)/(x^2 + 7x + 12)` to zero and solve for x

x^2 + 7x + 12 = 0

The above equation can be written as

x^2 + 4x + 3x + 12 = 0

By taking common terms outside, we get

x(x + 4) + 3(x + 4) = 0

(x + 3)(x + 4) =0

By factoring each term, we get

x = - 3, x = - 4

Step 3: Solution

Therefore, the domain of a given function is all real numbers except for x = - 3 or -4

Practice Problems to Define Domain in Math:

1) Find domain of the function y = x^2 + 15

2) Find domain of the function y = |7x - 11|

3) Find domain of the function y = `(5x + 9)/(x^2 + 5x + 4)`

Solutions:

1) The domain of the given function is all real numbers greater than 15.

2) The domain of the given function is (0, ∞).

3) The domain of a given function is all real numbers except for x = - 1 or - 4.

Determinant Linear Independence

Introduction to determinant linear independence:

In mathematics, determinants are linearly independent if none of the determinants can be obtained from the others.
When determinants are linearly independent, then each determinant contains new information about the variables.
For example,
A = `[[0],[0],[2]]` B = `[[2],[-4],[2]]` C = `[[0],[4],[-4]]` D = `[[8],[4],[3]]` .

Here, the determinants A, B and C are linearly independence determinant but the determinant of D is not since determinant of D is equals to 9A + 4B + 5C. Following example and practice problems will help you to study about linearly independence determinant. I like to share this Determinant Calculator with you all through my article.

Example Problems of Linear Independence Determinant:

Example problem 1:

Show that the determinant `[[7,2],[6,4]]` is linearly dependence or not using Wronskian determinant method.

Solution:

Step 1: Given determinant

`[[7,2],[6,4]]` .

Step 2: Condition of Wronskian determinant

If the value of the determinant is equal to 0, then the determinant is linearly dependent.

If the value of the determinant is not equal to 0, then the determinant is linearly independent.

Step 3: Calculate the value of the determinant.

`[[7,2],[6,4]]` = (7 * 4) - (2 * 6)

= 16

Since the value of the determinant is not equal to 0, the given determinant is linearly independence.

Step 4: Solution

Hence, the given determinant `[[7,2],[6,4]]` is linearly independence.

Example problem 2:

Show that the determinant `[[4,2],[2,1]]` is linearly dependence or not using Wronskian determinant method.

Solution:

Step 1: Given determinant

`[[4,2],[2,1]]` .

Step 2: Condition of Wronskian determinant

If the value of the determinant is equal to 0, then the determinant is linearly dependent.

If the value of the determinant is not equal to 0, then the determinant is linearly independent.

Step 3: Calculate the value of the determinant.

`[[4,2],[2,1]]` = (4 * 1) - (2 * 2)

= 0

Since the value of the determinant is equal to 0, the given determinant is linearly dependence.

Step 4: Solution

Hence, the given determinant `[[4,2],[2,1]]` is linearly dependence. Is this topic free math problem solver online hard for you? Watch out for my coming posts.

Practice Problems of Linear Independence Determinant:

1) Show that the determinant `[[6,2],[3,4]]` is linearly dependence or not using Wronskian determinant method.

2) Show that the determinant `[[3,6],[6,12]]` is linearly dependence or not using Wronskian determinant method.

Solutions:

1) The given determinant `[[6,2],[3,4]]` is linearly independence.

2) The given determinant `[[3,6],[6,12]]` is linearly dependence.

Real World Math Applications

Introduction to real world math applications :

Mathematics is the systematic study of numbers, quantity, shapes and space. Mathematics contains a special system of symbols and rules for organizing them. It is a broad-ranging field of study in which it can be used as the calculation tool for computing quantities. . Mathematics is a part of science which can be used throughout the world. The real world math applications are in the fields such as in natural science, finance, engineering, music, medicine, cooking and the social sciences.

Applications of Mathematics in Real World :

In our real world, mathematics can be used in many fields.The geometrical shapes can be seen in nature, the examples are spider’s web, shape of an orange and symmetry of leaf.

Here are the examples that mathematics can be used in everyday’s life such as walking in  the road , purchasing things, mobile charging, movement of the pendulum in the clock, collection of data.

Applications of  Math in Different Fields :

Mathematics can be used in many fields in our real world. They are as follows:

Finance
Robotics and Radar design.
Manufacturing
Music
Telephone network designs.
Medical imaging
Architecture
Cooking
Chemistry

Example Problems  for Math Applications:

Finance :

In our real-life math is using in a variety of investments such as  simple and compound interests, bank deposits, CD's, stocks, bonds, and mutual funds.

1.If  you loaned $500 to your  friend for one month and charged her 1% interest .Calculate the simple interest and compound interest.

Simple interest =$5 at the end of the month.

compound interest =  $505 at the end of the first day.

Home Decoration:

Most of the home decorators complete work within a budget.

2. To  buy new carpeting for your home in the rooms such as  living room, bedroom, and hallway, but not in the bathroom. find the total area of carpeting.

The total length  is 12 + 10 = 22 feet.

The total width is 7 + 5 = 12 feet.

The total area is   = 22  x 12 =  264 – (7* 5) = 229 square feet.

Exponents and Their Various Types

A number can have a power on it. It signifies that the number must be multiplied equal to the number of times of the power. The power can be any number like 1, 2, 3, and so on. The number can also be negative. When the number is 1, it is called the number is to the power of 1. When the number is 2, it is said that the number is squared. When the number is 3, it is said that the number is cubed. When the number is squared it is multiplied by itself two times. When the number is cubed it is multiplied by itself three times. This is the difference between the powers 2 and 3. This is the basic difference. The power just signifies the number of times the number must be multiplied with itself. The process of multiplication remains intact. The term zero exponents is got when the power is zero. The zero exponent definition says that the power is zero in this case. In this case the number is multiplied by itself zero times and the answer obtained is one. So, a number raised to zeroth power gives the answer 1. I like to share this Absolute Value Function with you all through my article.

This is the zero exponent property and can be very helpful in understanding the concept. The zero exponent examples will make the concept more clear and understandable. A number can be taken and raised to the power zero to explain this. If ‘2’ is raised to the power of 5, the answer obtained is 32. If it is raised to the power of 4, the answer obtained is 16. If it is raised to the power of 3, the answer that is got is 8. Further if it is raised to the power of 2, then the answer obtained is 4. Next the number is raised to the power of 1 and the answer obtained is the same number. In this the number is 2. The answers obtained have been decreasing by a factor of 2.Finally the number is raised to the power of zero and the answer obtained is one. This explains that a number being raised to zeroth power gives the answer one. One thing to be noted here is that the answer will be one only if the number chosen is not zero. When a number is raised to the power of zero then the number must not be zero.