Set Multiple Values

The definition of set is group of object. Collection of whole number, collection of natural numbers, and collection of fraction numbers it is called the some examples of set multiple values. The set symbol is represented the { }. The example of set multiple value is {4, 5, 7, 6}. Next we discuss about this articles set multiple values.

First Problem of Set Multiple Values

Problem 1: set multiple values

If A = {5, 3, 6, 2, 7, 13 ,15} and B  = {5, 3, 6, 2, 7}  find out n(A), n(B), n(A `uu` B)and n(A `nn` B) and to prove n (A `uu`B) = n (A) + n (B) – n (A `nn`B)

Solution:

A = {5, 3, 6, 2, 7, 13, 15}

B = {5, 3, 6, 2, 7}

A `uu` B = {5, 3, 6, 2, 7, 13, 15}

A `nn` B = {5, 3, 6, 2, 7}

n (A) = 7

n (B) = {5},

n (A`uu` B) = {7},

n (A`nn` B} = {5}

n (A) + n (B) – n (A `nn` B)

7 + 5 - 5

= 7

The A `uu` B = 7

So,

n (A`uu` B) = n (A) + n (B) – n (A `nn` B)

Second Problem of Set Multiple Values

Problem 2: set multiple values

If X = {7, 9, 4, 2, 5} and Y = {7, 9, 4, 2, 5, 13, 14} find n(X), n(Y) n(X `uu` Y), n(X `nn` Y) and to verify the identity n (X uu Y) = n (X) + n (Y) – n (X `nn` Y)

Solution:

X = {7, 9, 4, 2, 5}

Y = {7, 9, 4, 2, 5, 13, 14}

{X `uu` Y} = {7, 9, 4, 2, 5, 13, 14}

{X `nn` Y} = {7, 9, 4, 2, 5}

n (X) = {5}

n (Y) = {7}

n(X `uu` Y) = {7}

n(X `nn` Y) = {5}

n (X) + n (Y) – n (X `nn` Y)

= 5 + 7- 5

= 12 - 5

= 7

Here X `uu` Y = 7

So,

n (X`uu` Y) = n (X) + n (Y) – n (X `nn` Y)

Place Value Tenths Hundredths

Place value can describe the value of all numbers .The place value can be used to point out the position of a mathematical system. It is tremendously helps you to read the numerals by its places. Place value is the value which is given to the digit by popular quality .In this article we shall discuss the place value of tenths hundredths.

Place Value Tenths Hundredths:

The place values from one to ten thousand and to ten thousandth are as follows.

For example for the value 11111.11111

1 – Place value one.

10 = place value Ten.

100 – Place value Hundred.

1000 – Place value thousand.

10000 – Place value ten thousand.

1÷10 =0.1- place value tenth.

1÷100= 0.01- place value hundredth.

1÷1000=0.001- place value thousandth.

1÷10000=0.0001- place value ten thousandth.

1÷100000=0.00001- place value hundred thousandth.

Examples Problems on Place Value:

Ex:1 Round the following number to the hundredth place value 746.839256

Sol:

Given that the number 746.839256

From the given number on the left side from the decimal point,

7 indicates Place value Hundred.

4 indicate place value ten.

6 indicate Place value one.

From the given number on the right side from the decimal point,

8 indicate tenth place value.

3 indicate hundredth place value.

9 indicate thousandth place value.

2 indicate ten thousandth place value and so on.

As the question is to encircle the number 746.839256 to the hundredth place value.

The answer is 746.83

Ex:2 Add the numbers 1563.457 and 1999.336 and round the solution to the hundredth place value.

Sol:

Adding the numbers we get




The solution is  3562.793

From the given number on the left side from the decimal point,

3 indicate place value thousand.

5 indicate Place value Hundred.

6 indicate place value ten.

2 indicate Place value one.

From the given number on the right side from the decimal point,

7 indicate tenth place value.

9 indicate hundredth place value.

3 indicate thousandth place value.

As the question is to encircle the number 3562.793 to the tenth place value.

The answer is 3562.8 because the place value nearest to hundredth (7) is greater than 5(9).


Ex:3 Round the following number to the tenth place value 876.473957

Sol:

Given that the number 876.473957

From the given number on the left side from the decimal point,

8 indicates Place value Hundred.

7 indicate place value ten.

6 indicate Place value one.

From the given number on the right side from the decimal point,

4 indicate tenth place value.

7 indicate hundredth place value.

3 indicate thousandth place value.

9 indicate ten thousandth place value and so on.

As the question is to encircle the number 876.473957to the tenth place value.

The answer is 876.5

Ex:4 Add 388.8018 and 100.1111 and round the solution to tenth place value.

Sol:

Adding 388.8018 and 100.1111 we get,



The solution is  488.9129

From the given number on the left side from the decimal point,

4 indicate Place value Hundred.

8 indicate place value ten.

8 indicate Place value one.

From the given number on the right side from the decimal point,

9 indicate tenth place value.

1 indicate hundredth place value.

2 indicate thousandth place value.

9 indicate ten thousandth place value.

As the question is to encircle the number 488.9129 to the tenth place value.

The answer is 488.9

Practice Problems on Place Value:

Q:1 Round the following number to the hundredth place value 44776.76234

Ans:

The answer is 44776.76

Q:2 Round the following number to the tenth place value 56256353.3564847

Ans:

The answer is 56256353.4

Place Value Number System

The Place Value of a digit in a number system is the digit multiplied by 100, 101, 102, 103, 104, 105, 106, 107, 108, 109,... etc. according as the digit appears in the number system as once, tens, hundreds, thousands, ten thousand, hundred thousand, million, billion, trillion respectively.  Example for place value number system: 3333333333333. This can be represented as three trillion three hundred and thirty three billion three hundred and thirty three million three hundred and thirty three thousand and three hundred and thirty three. Here we are going to see in detail about place value number system.

Ones:

Ones is the word which means the number 1. The place value of ones is one. This is the right most number, For any number the right most number or the first number in the right side will be ones

Example problem:

1)  Find the ones place value in the number 85,494

Solution:

The ones place value in the number 85,494 is 4

2)  Find the ones place value in the number 856,490

Solution:

The ones place value in the number 856,490 is 0

Tens:

Tens is the word which means teh number 10. The place value of tens is two.

Example problem:
1)  Find the tens place value in the number 325,968

Solution:

The tens place value in the number 325,968 is 6

2)  Find the tens place value in the number 16,824

Solution:

The tens place value in the number 16,824 is 0

Hundreds:

Hundred is the word which mean the number 100, the word hundred is also known as centum. The place value of hundreds is three.

Example problem:

1)  Find the hundreds place value in the number 78,256

Solution:

The hundreds place value in the number 78,256 is 2

2)  Find the hundred place value in the number 954,263

Solution:

The hundred place value in the number 954,263 is 2

Thousands:

Thousand is the word which means the number 1,000. The place value of thousand is four. Ten thousand and hundred thousand comes under the category of thousand.

Example problem:

1) Find the thousands place value of the number 479,258

Solution:

The thousands place value of the number 479,258 is 9

2) Find the ten thousands place value of the number 479,258

Solution:

The ten thousands place value of the number 479,258 is 7

3) Find the hundred thousand place value of the number 479,258

Solution:

The hundred thousands place value of the number 479,258 is 4

Millions:

Million is the word which means the number 1,000,000. The place value of million is seven. Ten million and hundred million comes under the category of million.

Example problem:

1)    Find the million place value of 951,654,259

Solution:

The million place value of the number 951,654,259 is 1

2)    Find the ten million place value of 951,654,259

Solution:

The ten million place value of the number 951,654,259 is 5

3)    Find the hundred million place value of 951,654,259

Solution:

The hundred million place value of the number 951,654,259 is 9

Billions:

Billion is the word which means the number 1,000,000,000. The place value of billion is ten. Ten billion and hundred billion comes under the category of billion.

Example problem:

1)    Find the Billion place value of 907,789,246,846

Solution:

The Billion place value of the number 907,789,246,846 is 7

2)    Find the ten Billion place value of 907,789,246,846

Solution:

The ten Billion place value of the number 907,789,246,846 is 0

3)    Find the hundred Billion place value of 907,789,246,846

Solution:

The hundred Billion place value of the number 907,789,246,846 is 9

Trillions

Trillion is the word which means the number 1,000,000,000,000. The place value of trillion is thirteen. Ten Trillion and hundred Trillion comes under the category of Trillion.

Example problem:

1) Find the Trillion place value of 456,758,246,349,246

Solution:

The Trillion place value of the number 456,758,246,349,246 is 6

2)    Find the ten Trillion place value of 456,758,246,349,246

Solution:

The ten Trillion place value of the number 456,758,246,349,246 is 5

3)    Find the hundred Trillion place value of 456,758,246,349,246

Solution:
The hundred Trillion place value of the number 456,758,246,349,246 is 4

Statistics on College Students

Statistics should be help with formal science. These are generating well-organized help of algebraic data among the groups of individuals. In statistics, we are learning help on median, mode, mean and range. Measuring of these problems is extremely easy. For this we are using formulas. Now we will see statistics example problems on the college students.

Statistics Examples for College Students

Example 1:

Find the mean, median for the sequence of numbers, 560,247,281,396,185,160,288.

Solution:

The given numbers are 560,247,281,396,185,160,288.

Mean

Mean is the average of the given number. Calculate the total value of the given sequence.

Sum of the given numbers are = 560+247+281+396+185+160+288

= 2117

Total values are divided by 7 (7 is the total numbers) = `(2117)/(7)`

= 302.43

Median

Middle element of the sorting order of given series is a median.

The sorting order series is 160,185,247,281,288,396,560.

The middle element of the sorting sequence is 281.

So the median is 281.

Example 2:

Find the mode value for the following sequence of numbers, 291,358,640,291,305,291.

Solution:

Given series is, 291,358,640,291,305,291.

Mode is the most repeatedly occurring value of the series.

Here, the number ‘291’ should be occurring three times.

So, the mode value is 291.

Example 3:

Find the range value for the following sequence of numbers, 488,150,362,205,117,250.

Solution:

Given series is, 488,150,362,205,117,250.

Subtract the smallest value from the biggest value of the series is said to be range.

Range = 488 - 117

= 371

Standard Deviation Example for College Students

Let see the learning example for standard deviation in statistics on college students.

Example 4:

Find the standard deviation of the following numbers, 30,59,65,27,16,12,33,22.

Solution:

The given numbers are 30,59,65,27,16,12,33,22.

Establish the mean for the given data.

Mean = `(30+59+65+27+16+12+33+22)/(8)`

= `(264)/(8)`

= 33

Construct the table for finding standard deviation.

x	x-33	(x-33)2
30	-3	9
59	26	676
65	32	1024
27	-6	36
16	-17	289
12	-21	441
33	0	0
22	-11	121
Total		2596

Find (x-m)2 / (n-1) = `(2596)/(8-1)`

= `(2596)/(7)`

= 370.86

Formula of the standard deviation = `sqrt((sum_(i=1)^n (x-m)^2) / (n-1))`

= `sqrt(370.86)`

= 19.26

Thus the standard deviation is 19.26.

These are the few statistics example problems that help on college students.

That’s all about the statistics on college students.

Derivative Calculator Step by Step

In calculus, the rate of change of curve is called derivative. Derivative Calculator is used to find the differentiation of given function. By Using the derivative calculator we can able to find the derivative value easily. Through manual calculator we can able to solve the derivative but it quite difficult to perform the calculation. But through calculator there is no other difficulty rather than entering the question, the answer will produced automatically. we have to enter the question in function place. then enter the value in which we derivative with respect to. then the order of the respected derivative, now click the derivative button. sample derivative calculator is given.

Derivative Calculus Formulas - Derivative Calculator Step by Step:

1. n th power derivative is `d/dx` (xn) = n x(n-1)

2. Exponential derivative `d/dx` (ex) = ex

3. Logarithmic derivative `d/dx` (log x) = `1/x` .

4. Trigonometry derivative `d/dx` (sin x) = cos x

5.Trigonometry derivative `d/dx` (cos x) = - sin x

6.Trigonometry derivative `d/dx` (tan x) = sec2x

7.Trigonometry derivative `d/dx` (sec x) = sec x tan x

8.Exponential derivative `d/dx` (eax) = aeax

9.Product derivative `d/dx` (uv) = u` (dv)/(dx)` + v `(du)/(dx)` .

10.Division derivative `d/dx(u/v)` = ` [v (du)/(dx) - u (dv)/(dx)]/v^2` .

Example Problems - Derivative Calculator Step by Step:

Derivative calculator step by step problem 1:

Find the derivative of given function      x6 + 3x4 + 5x2 + 3x.

Solution:

Given function is    x6 + 3x4 + 5x2 + 3x.

Step 1:      The derivative of given function can be expressed as  `d/dx` (x6 + 3x4 + 5x2 + 3x).

Step 2:      Separate the derivative function is   `d/dx` (x6) + `d/dx`(3x4) + `d/dx` (5x2 ) + `d/dx`(3x).

Step 3:      Now we know the n th power derivative rule. That is `d/dx` (xn) = n x(n-1)

Step 4:       In the first term n = 6, So derivative of   `d/dx` (x6) = 6 x(6-1)  = 6x5

Step 5:    Differentiate all the term, we get    =   `d/dx` (x6) + `d/dx`(3x4) + `d/dx` (5x2 ) + `d/dx`(3x).

=  6 x(6-1)  +  (3)(4) x(4-1)  + (5)(2) x(2-1)  + (3)(1) x(1-1)

=  6x5 + 12x3 + 10 x + 3

Answer:  6x5 + 12x3 + 10 x + 3.


Derivative calculator step by step problem 2:

Find the derivative of given function       5x2 -  3tanx .

Solution:

Given function is   5x2 -  3tanx .

Step 1:      The derivative of given function can be expressed as  `d/dx` (5x2 -  3tanx ).

Step 2:      Separate the derivative function is    `d/dx` (5x2 ) - `d/dx`(3 tan x).

Step 3:      Now we know the n th power derivative rule. That is `d/dx` (xn) = n x(n-1)

Step 4:       In the first term n = 2, So derivative of   `d/dx` (x2) = 2 x(2-1)  = 2x

Step 5:    Differentiate all the term, we get    =   `d/dx` (x2) - `d/dx`(3 tan x).

=  2x  - 3 sec2x .

=  2x  - 3 sec2x .

Answer:   2x  - 3 sec2x .

Study Online Limits of Trigonometric Functions

In online, trigonometric function are recognized as circular function of an angle. They are organizing to transmit the position of a triangle toward the lengths of the surface of a triangle. Let x, an angle in radians `x->0` `sin x->0`, so `lim_ (x->0)(sinx)` is of the in-between type of type 0. In online we acquire more information regarding all the problems contain step by step solution. Various websites are present in study online limits of trigonometric functions.

Study Online Limits of Trigonometric Functions:

The general rule of limit trigonometric function:

`"lim_(x->a) `  =>    `lim_(x->a) f(x) =0 `

Trigonometric functions acquire in a large variety of uses to include found indefinite lengths as well angles in triangles often right triangles.

Function of an angle expressed though ratios of the length of the surface of right-angled triangle contain the angle.

Trigonometric function is the proportion of the exterior of the right triangle. Function of an angle articulated while ratios of the length of the sides of right-angled triangle have the angle



Trigonometric function:

Sin = `(opposite)/("hypotenuse")`
Cos =` (adjacent)/("hypotenuse")`
tan =`(opposite) / (adjacent)`
cot  = `(adjacent) / (opposite)`
sec = `("hypotenuse") / (adjacent)`
csc =`("hypotenuse")/(opposite)`

There are three reciprocal function in trigonometric.

Csc x = `1/(sinx) `

Sec x =`1/(cosx) `

cot x =`1/(tanx) `

Examples for Study Online Limits of Trigonometric Functions:

Example 1 for  study online limits of trigonometric functions:

How to find `lim_(x->o) (sin 8x)/(8x)`

Solution:

Step 1: the given function is  `lim_(x->o) (sin 8x)/(8x)`

Step 2: let t = 4x we have `t->0` when `x->0`

Step 3:  `lim_(x->o) (sin 8x)/(8x)`

=    `lim_(t->o) (sin t)/(t)`

= 1.

So the solution is     `lim_(x->o) (sin 8x)/(8x)`      = 1.

Example 2 for study online limits of trigonometric functions:

How to find  `lim_(x->4) (sin (x-4))/(x^2-9x+20)`

Solution:

Step 1: The given function is `lim_(x->4) (sin (x-4))/(x^2-9x+20)`

Step 2:   `lim_(x->4) (sin (x-4))/(x^2-9x+20)`

`lim_(x->4) (sin (x-4))/((x-5)(x-4))`

Step 3:     `lim_(x->4)(sin(x-4)/(x-4)*1/(x-5))`

Step 4:  `1*-1 =-1`

So the solution is    `lim_(x->4) (sin (x-4))/(x^2-9x+20) = -1`

Example 3 for  study online limits of trigonometric functions:

How to find `lim_(x->pi/3) (sin x)`

Solution:

Step 1: the given function is `lim_(x->pi/3) (sin x)`

Step 2:   `lim_(x->pi/3) (sin x)` <br>

Step 3:   = 0.8660

So the solution is     `lim_(x->pi/3) (sin x) = 0.8660`

Example 4 for study online limits of trigonometric functions:

How to find  `lim_(x->-4) (sin (x+4))/(x^2+6x+8)`

Solution:

Step 1: The given function is   `lim_(x->-4) (sin (x+4))/(x^2+6x+8)`

Step 2:   `lim_(x->-4) (sin (x+4))/(x^2+6x+8)`

`lim_(x->-4) (sin (x+4))/((x+2)(x+4))`

Step 3:     `lim_(x->-4)(sin(x+4)/(x+4)*1/(x+2))`

Step 4:  `1*-1/2 `

Step 5:      =   `-1/2`

So the solution is   `-1/2`

Absolute Property Solutions

Basically absolute values mean a value without considering its sign. Here we are going to find the solutions of absolute properties. If we are having any number x mean absolute value of x is denoted like |x| and its value is +x. Likewise for |-x| = x. Here we are going to learn the properties of the absolute value and its solutions. If we know the properties of the absolute value it is easy to do the operations on the absolute values.

Absolute Property Solutions:

The first property is non negative property.

Absolute property solutions - Non negativity property:

Absolute value of the numbers is always greater than 0. if we are having a negative number its absolute value is a positive number.

Example:

What is the absolute value of the number -1.2?

Solution:

The given number is -1.2

We have to find the absolute value of the number -1.2

So |-1.2| = +1

So always |x| > 0

Absolute property solutions - Positive definiteness:

The second property is positive definiteness.

The absolute value of the number 0 is always 0. If |x| = 0 then x = 0 (always)

Example:

What is the absolute value of 0?

Solution:

Basically an absolute value is having two values. But for 0 the absolute value is |0| = 0

Absolute property solutions - Multiplicative property:

Multiplication of any two given absolute values equals to the individual absolute value multiplication.

|x y | = |x| |y|

Example:

|-5 x 3| = |-15| = + 15

|-5| x |3| = +5 x +3 = + 15

So both the values are same.

More Absolute Property Solutions:

Absolute property solutions - Subtraction addition property:

Addition of any two given absolute values is always less than the value of its individual addition.

|x + y| ≤ |x| + |y|

Example:

|4 + -3| = |1| = 1

|4| + |-3| = 4 + 3 = 7

1 < 7

Absolute property solutions - Symmetry property:

Symmetry property mean |-x| = |x|

Absolute value of the –x and absolute value of x is always same.

Example:

|-4| = |4| = +4

Absolute property solutions - Identity of indiscernible property:

The difference of any two absolute values of the number is 0 then these two absolute values are same.

|x - y| = 0 then x = y

Example:

Find the absolute value of |5 – (-5)|

Solution:

Absolute value of |5| = +5

Absolute value of |-5| = +5

So |5 – (-5)| = 0

Absolute property solutions - Preservation of division:

The division of any two absolute values and its individual absolute value division are equal.

|x / y | = |x| / |y| (where y ≠0)

Decimal to Percentage Conversion

The conversion of one model to another is the most important thing in the world, which one can never
deny. The above sentence is so assertive because of the underlying fact that learning is important at
every aspect, since it is important for the take away we get out of something. Conversion basically gives
a general perception that it is usually simplified to a simpler form to get a better understanding, so it is a
positive word which gives a positive meaning. This concept is all the same like above, decimal or fraction
conversion into the other.

The process of  Decimal to Percent conversion is done when one is good in basics and fundamentals of
mathematics. First of all one has to be good in decimal which will help in identification of the number
when posed for solving. Decimal can also be called as fraction, when a fraction is simplified the result
will be a decimal. The above will help in solving the question Convert Decimal to Percent. The process of
conversion is not rocket science, it is as simple as solving the basic addition and subtraction.

Converting Decimals to Percents basically involves basic multiplication. The multiplication of the decimal for the conversion is 100 and the symbol used for percent-age is %. This symbol signifies the percentage.

This conversion can be explained clearly using the following example; the question will be given as
convert 0.6 Decimal to Percentage, the answer for the question will be 60%, which is simplified by
multiplying the number 0.6 by 100. The answer will be 60% when multiplied. This can be further
explained by considering another example, convert 0.75 Decimals to Percents, the answer for this
example will 75%, which is resulted after multiplying 0.75 by 100.

Now it is time to think about some of the real life scenarios, where we will need this concept for
applying. Of course every single thing that one studies or learnt should be applied sometime or
somewhere at some point of his / her life, if one does not uses or applies it, there is no point in learning
things. It is mostly used while forecasting the sales of any firm because it is always essential to use
percentile rather than using decimals while portraying the results, which will make the one to whom the
results are presented understand the numbers which resulted.