tangent of circle

Let us study about Tangent of Circle,
Tangent is a line which touches a circle at only one point. At the point of contact with the circle, tangent is at right angles to the radius of the circle. From any point outside a circle, the two tangent lines drawn to the circle is of equal length. Tangent to a circle is a straight line and it won't cross the circle-only touching the circle.

Explanation:

Tangent of a circle is the point where the tangent and the circle intersect with each other.

statistics help

Let us understand what is Statistics,
The science that deals with the collection, classification, analysis, and interpretation of numerical facts or data, and that, by use of mathematical theories of probability, imposes order and regularity on aggregates of more or less disparate elements.

Statistics is a discipline which is concerned with:

* designing experiments and other data collection,
* summarizing information to aid understanding,
* drawing conclusions from data, and
* estimating the present or predicting the future.

The two statements at the beginning illustrate some of these points.

In making predictions, Statistics uses the companion subject of Probability, which models chance mathematically and enables calculations of chance in complicated cases.
I hope the above explanation helped you, now let me explain about elementary statistics.

Least common multiple

Least common multiple :

The least common multiple (LCM) is the smallest multiple that is common to two or more numbers.

Example : What is the least common multiple of 2 and 3?

The smallest multiple common to both 2 and 3 is 6.

Example 2 : What is the least common multiple of 2, 3, and 4?
The least common multiple of 2, 3, and 4 is 12.

Types of Statistics

Let me explain about the types of statistics,
For many people, statistics means numbers—numerical facts, figures, or information. Reports of industry production, baseball batting averages, government deficits, and so forth, are often called statistics. To be precise, these numbers are descriptive statistics because they are numerical data that describe phenomena. Descriptive statistics are as simple as the number of children in each family along a city block or as complex as the annual report released from the U.S. Treasury Department.
Consider two ways of representing descriptive statistics: numerical and pictorial.

Numerical statistics :

Numerical statistics are numbers, but clearly, some numbers are more meaningful than others. For example, if you are offered a purchase price of $1 for an automobile on the condition that you also buy a second automobile, the price of the second automobile would be a major consideration (its price could be $1,000,000 or only $1,000), and thus, the average—or mean—of the two prices would be the important statistic.

Pictorial statistics :

Taking numerical data and presenting it in pictures or graphs is what is known as pictorial statistics. Showing data in the form of a graphic can make complex and confusing information appear more simple and straightforward.
Hope the above explanation was useful to you.

Graphing Linear Inequalities in Two Variables

Let me explain about Graphing Linear Inequalities in Two Variables,
A linear inequality in the two variables x and y looks like

where a, b, and c are constants.
A solution to an inequality is any pair of numbers x and y that satisfy the inequality.
The rules for finding the solution set of a linear inequality are much the same as those for finding the solution to a linear equation.

1. Add or subtract the same expression to both sides.
2. Multiply or divide both sides by the same nonzero quantity; if that quantity is negative, then the inequality must be reversed.

Hope the above explanation helped you.

Explain Mathematical induction

Let us study about mathematical induction,
Mathematical induction, or proof by induction, is a method of mathematical proof typically used to establish that a given statement is true for all natural numbers. It can also be used in more general settings as will be described below. An induction variant is used in computer science to prove that expressions which can be evaluated are equivalent, and this is known as structural induction.
The simplest and most common form of mathematical induction proves that a statement holds for all natural numbers n and consists of two steps:

Showing that the statement holds when n = 0.
Showing that if the statement holds for n = m, then the same statement also holds for n = m + 1.

To understand why the two steps are in fact sufficient, it is helpful to think of the domino effect: if you have a long row of dominos standing on end and you can be sure that
The first domino will fall.
Whenever a domino falls, its next neighbor will also fall.
then you can conclude that all dominos will fall.
Hope the above explanation was helpful.

Triangle Inequalities: Sides and Angles

Let us learn what are Triangle inequalities,
You have just seen that if a triangle has equal sides, the angles opposite these sides are equal, and if a triangle has equal angles, the sides opposite these angles are equal. There are two important theorems involving unequal sides and unequal angles in triangles. They are:

Theorem: If two sides of a triangle are unequal, then the measures of the angles opposite these sides are unequal, and the greater angle is opposite the greater side.

Theorem: If two angles of a triangle are unequal, then the measures of the sides opposite these angles are also unequal, and the longer side is opposite the greater angle.

Example : Figure 1 shows a triangle with angles of different measures. List the sides of this triangle in order from least to greatest.
Figure : List the sides of this triangle in increasing order.

Because 30° < 50° < 100°, then RS < QR < QS.