Math Magic

**Making Predictions Activities**

Let we will looking about the concept of prediction and statistics. Predictive analytics includes a diversity of the methods from statistics, data mining and game theory. They are used in examine current and chronological facts to make the forecast on future events.

Prediction:

- The predictive models develop prototypes are found in the past and transactional data to recognize risks and opportunities.
- These models also can capture the relationships between many factors to permit appraisal of risk or possible linked over a scrupulous set of conditions.

**Types of predictive analytics:**

There are three types of predictive analytics.

**Predictive models:**

- These models are used to examine past performance to review.
- They are how possibly a customer is to reveal a particular activities in the future in order to get better marketing effectiveness.
- This Is also includes models which are seek out request data samples to answer questions about customer performance.

**Descriptive models:**

- These models should be enumerate relationships in data in a system.
- That are mostly used to categorize customers or forecasts into groups.
- The focus of a predicting single customer performance expressive models recognize identify many distinct relationships among customers or products.

**Decision models:**

- Decision models evaluating the relationship among all the elements of a decision.
- These models should be used in optimization and maximizing certain results.

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Math Help

**Sine Formula**

Formula for sin(A+B)

**Introduction**

What is the formula for sin(A+B)?

Is sin(A+B)=sin A + sin B?

This applet shows the formula for sin(A+B) & cos(A+B).

How to make use of the applet

Change angles A & B by pressing “+” & “-” buttons.

The lengths of two arrows appear by checking “Character” box.

You will understand the green arrow is the sum of red arrow & the blue arrow. That indicates the formula for sin(A+B).

**Sum & Difference Formulas**

sin(A+B)=sin A cos B + cos A sin B

sin(A-B)=sin A cos B - cos A sin B

cos(A+B)=cos A cos B - sin A sin B

cos(A-B)=cos A cos B + sin A sin B

The “sine rule”

A common use of the trig functions, as you might have noticed from the geological contexts, is to work out lengths and angles in triangles that occur in physical problems.

Math Help

**Define Median**

The median of a distribution with a discrete random variable depends on whether the number of terms in the distribution is even or odd. If the number of terms is odd, the median is the value of the term in the middle.

**What is a median**

The middle number (in a sorted list of numbers). Half the numbers in the list are less, and half the numbers are greater.

To find the Median, place the numbers are given in value order and find the middle number.

Example: find the Median of {12, 3 and 5}. Put them in order: {3, 5, 12}, the middle number is 5, so the median is 5.

If there’s two middle numbers(as happens when there’s an even amount of numbers) then average those two numbers.

Example: find the Median of {12, 3, 5 and 2}. Put them in order: {2, 3, 5, 12}, the middle numbers are 3 and 5, the average of 3 and 5 is 4, so the median is 4.

Math skill tutor

Let us study about the skill tutor math. The word tutor refers to a person who is teaching others about their doubts in various subjects through online which is a network connection that is made available all over the world.

The term skills tutor math is said to be as the method where we learn about various math problems with the clear explanations of their steps used to solve it. Examples are discussed.

Also get help with combination formula

Execute the division technique to calculate the ratio values for the number 13 by 52.

** Step 1: **Given numbers: 13 and 52

**Step 2: **Follow the steps as given below to determine the ratio:

=

=

**Step 3: **Thus we have the calculate ratio of the given numbers 13 and 52 is 1:4.

Our next blog will be on Note on Logical Questions

How to do Fractions

**Introduction:**

A part of a whole when it is divided into equal parts is a fraction.Set of Fraction is a subset of the set of Rational Numbers.

Learning how to solve fractions is an important aspect of solving mathematical problems. Students across grades struggle with solving various types of fraction problems which include quadratic and graphing linear equations, polynomials and algebraic equations.

**How to Do Fractions Simplifying:**

- In order to know, how to do fractions we first need to find the common factor of both the numerator and denominator (A common factor is any number that divides both the numerator and denominator). Like 3 divides 6 and 21.
- Then continue dividing the fraction with the common factor till there are no more common factors in the numerator and denominator.
- Now the fraction is called as simplified fraction as no common factors remaining which can divide both the numerator and denominator.

**Simplifying****:**

Lets take 12/14. Here both 12 and 14 are divisible by 2 so lets divide the fraction with 2.

So we get 12/14 = 6/7 Now 6/7 does not have any common factors so 6/7 is the simplified fraction

So both 18 and 42 are divisible with 2,3,6

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Explain Trigonometric Inverse Functions

**Introduction:**

Before finding the differentiation of trigonometric inverse functions, recall how the inverse trigonometric functions are defined and what the domain and range of each inverse trigonometric function. For ready reference, the domain and range of these functions and relations are tabulated below.Before finding the differentiation of inverse trigonometric functions, recall how the inverse trigonometric functions are defined and what the domain and range of each inverse trigonometric functions. For ready reference, the domain and range of these functions are tabulated below.

Whenever we say differentiability of these functions we consider them in their respective domains.

## Derivative of sin-1x

Let y = sin^{-}^{1} x, then sin y = x.

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Explain partial derivative calculator

**Introduction:**

Calculates the derivative of an expression **…** displays a pop-up menu which can be used to select a variable for partial derivatives. Calculates the derivative of an expression specified using a simple partial derivative calculator**…** is equivalent to partial derivative operator.

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant. Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function f with respect to the discrete variable x is variously denoted by

` f’_x` , ` f_x` , `del_x f` , or `(del f)/(delx)`

For example , supppose *f *is a function in x and y then it will be denoted by* f(x,y).*

So, partial derivative of *f* with respect to x will be $\frac{∂f}{∂x}$ keeping y terms as constant. Read as curly f / curly x or del f / del x

Note that its not dx , instead its ∂x.

$\frac{∂f}{∂x}$ is also known as f_{x}

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Understanding Linear equations in two variables

**Introduction:**

Solving an equation means finding replacement values for the variable that make a true sentence. The solutions of an equation with two variables are ordered pairs. An equation with two variables usually has an infinite number of solutions.

A simple linear equations in two variables is a statement of equality between two algebraic expressions involving an unknown quantity called the variable. In a linear equation the power of the variable is always equal to 1. The two sides of an equation are called Left-Hand Side (LHS) and Right Hand Side (RHS).They are written on either side of = sign. The process of finding the value of the unknown quantity for which the equation is true, is called solving the equation. The value so found is called the root or solution of the equation.

**Graphing linear Equations:**

To graph a linear equation with two variables, use the following procedure:

Graphing • Choose any convenient values for x.

Linear • Substitute each x-value in the equation and solve to find each corresponding y-value. Write these

Equations solutions as (x, y) pairs.

• Graph at least 3 of the ordered pairs and draw the straight line that passes through them.

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Probability Example

**Introduction:**

An **experiment** is a situation involving chance or probability that leads to results called outcomes. An **outcome** is the result of a single trial of an experiment. An **event** is one or more outcomes of an experiment. **Probability** is the measure of how likely an event is. Lets work on probability examples.

**Example:**

1) A spinner has 4 equal sectors colored yellow, blue, green and red. What are the chances of landing on blue after spinning the spinner? What are the chances of landing on red?

**Solution:** The chances of landing on blue are 1 in 4, or one fourth

The chances of landing on red are 1 in 4, or one fourth.

In the problem above, the experiment is spinning the spinner.

The possible outcomes are landing on yellow, blue, green or red.

One event of this experiment is landing on blue.

The probability of landing on blue is one fourth.

By Solving Probability examples, you can also learn and will help you to solve on conditional probability examples.

Hope you liked the above explanation. We will learn further on conditional probability. Please leave your comments, if you have any doubts.

Multiplication Chart

**Introduction on Multiplication Chart:**

In math, multiplication is the arithmetical operation of calculating one value with another value. Each chart is formatted for printing on a single sheet of paper although some can be pasted together to form larger charts if desired This is one kind of operations in basic arithmetic mean. Multiplication is nothing but the repeated addition. For example: 5 * 4 = 20, it can be represented as 4 + 4 + 4 + 4 + 4 = 20, therefore we can add the number 4 simultaneously 5 times in-order to multiply 5 * 4.. Math multiplication chart is useful in making the multiplication process more easy.

If we need any multiplied answer we can easily find the answer from this chart. For example 11 x 9 = 99. This is represented in the chart. By using the chart, multiplication process made more easy. This is the use of the multiplication chart.

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