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Most Common Number System (Nandan Nayak)

Introduction to most common number system:

In this we have most common number system. Most common system in math includes rational system, decimal numbers, fractional number, whole number, and so on. In this topic we will see some example problems for decimal number, fractional numbers, whole numbers, and so on. And also we have practice problems. Let us start to study about most common number system.

Example problems for most common number system:

Example problem 1: There is a population of 30,000 bacteria in a colony. If the number of bacteria doubles every 25 minutes, what will the population be 50 minutes from now?

Solution:

First, find out how many times the population will double. Divide the number of minutes by how long it takes for the population to double.

50 ? 25 = 2

The population will double 2 times.

Now figure out what the population will be after it doubles 2 times. Multiply the population by 2 a total of 2 times.

30,000 ? 2 ? 2 = 120,000

That calculation could also be written with exponents:

30,000 ? 22 = 120,000

After 50 minutes, the population will be 120,000 bacteria.

Answer: After 50 minutes, the population will be 120,000 bacteria.

Example problem 2: Preston bikes 0.4 kilometers each school day. How far in total will Preston bike over 14 school days?

Solution:

Multiply the kilometers biked each school day by the number of school days.

0.4 ?14 +40 = 56

Count the number of decimal places in the factors. There is 1 decimal place in 0.4.

56. => 5.6

Preston will bike 5.6 kilometers.

Answer: Preston will bike 5.6 kilometers.

Practice problems for most common number system:

Practice problem 1: Crystal is creating potpourri bowls using 18 bags of shredded bark and 15 bags of flower petals. If she wants to make all the potpourri bowls identical, containing the same number of bags of shredded bark and the same number of bags of flower petals, what is the greatest number of potpourri bowls Crystal can create?

Practice problem 2: There is a population of 10,000 bacteria in a colony. If the number of bacteria doubles every 19 minutes, what will the population be 38 minutes from now?

Practice problem 3: A restaurant chef made '1 2/3 ' pints of tomato soup. Each bowl of soup holds '5/6' of a pint. How many bowls of soup will the chef be able to fill?

Solutions for most common number system:

Solution 1: The greatest number of potpourri bowls Crystal can create is 3.

Solution 2: After 38 minutes, the population will be 40,000 bacteria.

Solution 3: The chef will be able to fill 2 bowls.

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Five Number Summary Tutoring (Nandan Nayak)

Introduction to five number summary tutoring:

Five number summary is one of the important topics in mathematics. Five number summary is a sample from which they are derived from a particular group of individuals. Five number summary has a set of observations. In a single variable, it has a set of observations. Five number summary has a different statistics. Here we study about the different statistics involved in five number summary.The online tutoring for the five number summary will give the explanations to the students very interactively through the definitions, steps and examples problems. Therefore, students can learn from online.

Five number summary tutoring:

Different statistics are involved in five number summary are,

Minimum
Maximum
Median
Lower quartile
Upper quartile

Minimum:
Lowest value in the given set of numbers.

Maximum:
Largest value in the given set of numbers.

Median:
Middle value in the given set of numbers.

Lower quartile:
Number between the minimum and median.

Upper quartile:
Number between the maximum and median.

Five number summary tutoring - Steps to solve:

There are different steps to solve the five number summary are,

Observation can be arranged in the ascending order.
The lowest and largest value in the observation can be determined.
The median can be determined. When the observation has odd number of observation than the median is in middle of the observation. Otherwise it is an even number then the median is calculated by the average of the two middle numbers.
The upper quartile can be determined. When the observation minus one is divided by 4 means it is starting with the median and observations in the right side. Otherwise the observation is not divided by four means upper quartile is the median of the observation to the right of the location of overall median.
The lower quartile can be Determined. When the observation set minus one is divided by 4 then it is starting with the median and its observations in the left side. Otherwise the observation is not divided by four means lower quartile is the median of the observation to the left of the location of overall median

Five number summary tutoring - Example problem:

Example 1:

Find the five number summary for the given set of data

{535, 572, 534, 545, 529, 528, and 577}

Solution:

Given set of data

{535, 572, 534, 545, 529, 528, and 577}

{528, 529, 534, 535, 545, 572, 577} [Arrange the set in ascending order]

Minimum and Maximum values in the given set of data are 528 and 577.

Median:

Given observation is odd. So the median is middle of the observation then the median is 535.

Lower quartile:

Given observation is not divisible by four. So the lower quartile is {528, 529, and 534}

Upper quartile:

Given observation is not divisible by four. So the upper quartile is {545, 572, and 577}.

Answer:

Minimum: 528

Maximum: 577

Median: 535

Lower quartile: {528, 529 and 534}

Upper quartile: {545, 572 and 577}

Example 2:

Find the five number summary for the given set of data

{36, 71, 33, 44, 22, 27, 55 and 76}

Solution:

Given set of data

{36, 71, 33, 44, 22, 27, 55 and 76}

{22, 27, 33, 36, 44, 55, 71, 76} [Arrange the set in ascending order]

Minimum and Maximum values in the given set of data are 22 and 76.

Median:

Given observation is even. So the median is median is calculated by the average of the two middle numbers

Median = (36 + 44)/2

= 80/2

Median = 40

Lower quartile:

Given observation is not divisible by four. So the lower quartile is {22, 27, 33 and 36}

Upper quartile:

Given observation is not divisible by four. So the upper quartile is {44, 55, 71 and 76}.

Answer:

Minimum: 22

Maximum: 76

Median: 40

Lower quartile: {22, 27, 33 and 36}

Upper quartile: {44, 55, 71 and 76}

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Neutron Star Black Hole (Nandan Nayak)

The birth, life and death of a star is determined by interplay of nuclear reactions and the gravitational forces. The nuclear reactions that take place in the interior of the star will create a radiation pressure which in turn tries to push the star outward. However the gravitational forces between the particles of the star will try to pull it inward towards the center.When there is a balance between the outward radiation pressure and the inward gravitational pressure the star attains stability. However, when the nuclear fuel inside the core of a massive star gets exhausted, the star collapses under its own enormous gravitational force., As a result the star shrinks to a smallest size. This collapsed star will be so dense that even light cannot escape from it. Such an entity in the cosmos is called 'Black hole'

Introduction to Neutron Star Black Hole

A star is formed when a large amount of interstellar gas, mostly H2 and He starts to collapse on itself due to the gravitational attraction between the gas atoms or molecules . As the gas contracts it heats up due to atomic collisions. As the gas continues to contract, the collision rate increases to such an extent, that the gas becomes very hot, and the gas atoms are stripped off their electrons, and the matter is in a completely ionized state, containing bare nuclei and electrons. Such a state of matter is called plasma state. Under these conditions, the bare nuclei have enough energy to fuse with each other. Thus hydrogen nuclei fuse in such a manner to form helium with the release of large amount of energy in the form of radiation. The radiation emitted in this process is mostly emitted in the form of visible light, UV light, IR light etc., from its outer surface. This radiation is what causes the star to shine, which makes them visible (Ex : Sun and other visible stars).

Neutron star black hole : Process

The star at the stage is halted from gravitational collapse( contraction) since the gravitational attraction of matter towards the centre of the star is balanced by the out ward radiation pressure. A star will remain stable like this for millions of years, until it runs out of nuclear fuel such as H_ and He. The more massive a star is , faster will be the rate at which it will use its fuel because greater energy is required to balance the greater gravitational attraction owing to greater mass i.e., massive stars burn out quickly. When the nuclear fuel is over, i.e., when the star cools off, the radiation pressure is not sufficient to halt the gravitational collapse. The star then begins to shrink with tremendous increase in the density. The star eventually settles into a white dwarf, Neutron star or Black hole depending upon its initial mass

Neutron Star and Black Hole : Conditions

For a star to become a neutron star, its initial mass must be greater than ten solar masses. (M> 10Ms ). As a star with initial mass M > 10 Ms cools off the large mass of the star causes it to contract abruptly, and when it runs out of fuel it springs back and explodes violently. This explosion flings most of the star matter into space and such a state of star is called a Supernova. A supernova explosion is very bright and outshines the light of an entire galaxy. The mass of the matter left behind is greater than 1.4 Ms . If the mass of the left over matter is between 1.4 Ms and 3 Ms Neutron stars evolve. At this stage the repulsion between electrons will not be able to halt further gravitational collapse. Under such conditions, the protons and electrons present in the star combine to form neutrons. After the formation of neutrons, the outward degeneracy pressure between neutrons prevents further gravitational collapse, and the matter left over is called the Neutron Star.

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Most Common Number System (Nandan Nayak)

Introduction to most common number system:

Example problems for most common number system:

Example problem 1: There is a population of 30,000 bacteria in a colony. If the number of bacteria doubles every 25 minutes, what will the population be 50 minutes from now?

Solution:

First, find out how many times the population will double. Divide the number of minutes by how long it takes for the population to double.

50 ? 25 = 2

The population will double 2 times.

Now figure out what the population will be after it doubles 2 times. Multiply the population by 2 a total of 2 times.

30,000 ? 2 ? 2 = 120,000

That calculation could also be written with exponents:

30,000 ? 22 = 120,000

After 50 minutes, the population will be 120,000 bacteria.

Answer: After 50 minutes, the population will be 120,000 bacteria.

Example problem 2: Preston bikes 0.4 kilometers each school day. How far in total will Preston bike over 14 school days?

Solution:

Multiply the kilometers biked each school day by the number of school days.

0.4 ?14 +40 = 56

Count the number of decimal places in the factors. There is 1 decimal place in 0.4.

56. => 5.6

Preston will bike 5.6 kilometers.

Answer: Preston will bike 5.6 kilometers.

Practice problems for most common number system:

Practice problem 2: There is a population of 10,000 bacteria in a colony. If the number of bacteria doubles every 19 minutes, what will the population be 38 minutes from now?

Practice problem 3: A restaurant chef made '1 2/3 ' pints of tomato soup. Each bowl of soup holds '5/6' of a pint. How many bowls of soup will the chef be able to fill?

Solutions for most common number system:

Solution 1: The greatest number of potpourri bowls Crystal can create is 3.

Solution 2: After 38 minutes, the population will be 40,000 bacteria.

Solution 3: The chef will be able to fill 2 bowls.

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Five Number Summary Tutoring (Nandan Nayak)

Introduction to five number summary tutoring:

Five number summary tutoring:

Different statistics are involved in five number summary are,

Minimum
Maximum
Median
Lower quartile
Upper quartile

Minimum:
Lowest value in the given set of numbers.

Maximum:
Largest value in the given set of numbers.

Median:
Middle value in the given set of numbers.

Lower quartile:
Number between the minimum and median.

Upper quartile:
Number between the maximum and median.

Five number summary tutoring - Steps to solve:

There are different steps to solve the five number summary are,

Five number summary tutoring - Example problem:

Example 1:

Find the five number summary for the given set of data

{535, 572, 534, 545, 529, 528, and 577}

Solution:

Given set of data

{535, 572, 534, 545, 529, 528, and 577}

{528, 529, 534, 535, 545, 572, 577} [Arrange the set in ascending order]

Minimum and Maximum values in the given set of data are 528 and 577.

Median:

Given observation is odd. So the median is middle of the observation then the median is 535.

Lower quartile:

Given observation is not divisible by four. So the lower quartile is {528, 529, and 534}

Upper quartile:

Given observation is not divisible by four. So the upper quartile is {545, 572, and 577}.

Answer:

Minimum: 528

Maximum: 577

Median: 535

Lower quartile: {528, 529 and 534}

Upper quartile: {545, 572 and 577}

Example 2:

Find the five number summary for the given set of data

{36, 71, 33, 44, 22, 27, 55 and 76}

Solution:

Given set of data

{36, 71, 33, 44, 22, 27, 55 and 76}

{22, 27, 33, 36, 44, 55, 71, 76} [Arrange the set in ascending order]

Minimum and Maximum values in the given set of data are 22 and 76.

Median:

Given observation is even. So the median is median is calculated by the average of the two middle numbers

Median = (36 + 44)/2

= 80/2

Median = 40

Lower quartile:

Given observation is not divisible by four. So the lower quartile is {22, 27, 33 and 36}

Upper quartile:

Given observation is not divisible by four. So the upper quartile is {44, 55, 71 and 76}.

Answer:

Minimum: 22

Maximum: 76

Median: 40

Lower quartile: {22, 27, 33 and 36}

Upper quartile: {44, 55, 71 and 76}

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Number Sense Tutorial (Nandan Nayak)

Introduction to number sense tutorial:

In mathematics, number system is called as system of numeration. Number systems are used to express the quantities for counting, defining order, comparing the quantities, calculating numbers and denoting values. Number system includes natural numbers, integers, rational numbers, algebraic numbers, real numbers, complex numbers, p-adic numbers, surreal numbers and hyper real numbers.

Number sense is explained with examples and practice problems very interactively by tutorial. So students are getting number sense help by tutorial for their studies.

Examples to number sense tutorial:

Example 1:

Add the following decimal numbers 65.45 + 6.892

Solution:

Addition operation for decimal numbers is just like the integers addition. In this problem

65. 45 has two decimal place but 6.892 has three decimal place. Hence, we have to add 0 with the number 65.45, so we get 65.450

That is, 65.45+6.892 = 65.450+6.892

11 1
65.450
+ 6.892
72.342

Example 2:

Find the square root of the following numbers 'sqrt(289)' .

Solution:

'sqrt(189) ' = 'sqrt(17 xx 17)' = 17

Example 3:

Write the standard for the following number 69.089 'xx' '10^3'

Solution:

69.089 'xx' '10^3' which can be written as

69.089 'xx' 10 'xx' 10 'xx' 10

69.089 'xx' 1000 now we have to shift the decimal point to three decimal point. So that we will get

69089

Example 4:

Add the following mixed numbers '8 1/3' and '8 1/4' .

Solution:

We have to convert the following mixed numbers in to improper fraction. For this, denominators are multiplied with the whole number and then add the result of the product with numerator. So that, we will get the improper fraction.

'8 1/3' => '((8 xx 3) + 1)/3' => '(24 + 1)/3' => '25/3'

'8 1/4' => '((8 xx 4) + 1)' => '(32 + 1)/4' = '33/4'

Now we can add both improper fraction

'25/3' + '33/4' here, denominators are not same. So that, we have to find LCM. The LCM is 12

The denominator 3 from the fraction '25/3' is 4 times in the LCM. So we have to multiply the numerator 25 by 4. So we get '100/12'

The denominator 4 from the fraction '33/4' is 3 times in the LCM. So we have to multiply the numerator 33 by 3. So we get '99/12'

'(100 + 99)/12'

'199/12'

Practice Problems to number sense tutorial:

Problem 1:

Add the following decimal numbers 6.45 + 6.82

The answer is 13.27

Problem 2:

Find the square root of the following numbers 'sqrt(324)' .

The answer is 18

Problem 3:

Write the standard for the following number 675.89 'xx' ' 10^3'

The answer is 675890

Problem 4:

Add the following mixed numbers '1 5/3' and '2 6/4' .

The answer is '22/12'

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Approximation Ratio (Nandan Nayak)

Introduction to approximation ratio:

Ratio is processes that are used to define in the form of word to differentiate the word problems in the given question. The ratio is the numerical expression representing a part of a larger whole or proportion. A ratio consists of two numbers separated by a colon. Ratio is numbers can be compared as multiples of one another. The word approximation radio defines the number that is not exact, but closes enough to be used.

Representation of approximation ratio:

The given two numbers is done by a colon. Then they are said to be ratio

Colon is represented as :

Rules to be followed for calculation approximation ratio:

Rule 1: If the value specified after decimal point is five or more than five we can add one to the previous number of the point by rounding the value.

Examples based on approximation ratio definition:

Example 1: Problems based on approximate ratio.

In a pet shop they are puppies and pussy cats, the ratio of puppies and pussy cats are 2:4. If the shop contains 85 pussy cats, how many puppies will be there .Find the approximation ratio?

Solution:

Given: The pet shop contains 80 pussy cats,

Now, we are going to assign the variable:

Let x = puppies

The item is now found to be written in ratio fraction,

Puppies / pussy cats = '2/4 = x/ 85'

Cross multiplication is to be done.

So, '2 * 85= 4x'

' x= 170/4'

' x = 42.5'

' x=43.'

The value is five after the decimal point we are adding one to the previous number and rounding the value.

Hence the approximation ratio of 43 puppies is present.

Example 2: Problems based on approximation ratio.

In an pond they are fishes and snakes , the ratio of fishes and snakes are found is 6:9 .If the tank contains 25 snakes , how many fishes are there in pond find its approximation ratio?

Solution:

Given: The pond contains 25 snakes,

Now, we are going to assign the variable:

Let x = fishes

The item is now found to be written in ratio fraction,

Fishes / snakes ='6/9=x/25'

Cross multiplication is to be done.

So, '6*25 =9x'

' 150=9x'

'x=150/9'

' x = 16.66'

' x = 17.'

The value is more than five after the decimal point we are adding one to the number before the decimal point.

Hence approximation ratio of 17 fishes is there inside the tank.

Problems to solve based on approximation ratio:

In a zoo they are elephants and horses, the ratio of elephants and horses are found in ratio of 4: 6 .If the zoo contains 25 horses, how many elephants are there find the approximation ratio?
Answer: 17 elephants.

In a forest they are monkeys and lions, the ratio of monkeys and lions, are found in ratio of 2:4.If the circus contains 225 lions, how many monkeys are there?
Answer: 113 monkeys.

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Number Theory Homework Tutoring (Nandan Nayak)

Introduction to number theory homework tutoring:

In this article we will see about number theory homework tutoring. Number theory homework tutoring is nothing but it is also the basic chapters of mathematics. The number theory problems will be simple and easier. Number theory homework tutoring is done by the tutors in online process. Below are some of the solved example problems under this topic of number theory. Number theory homework tutoring will include the problems on the topics like scientific notation, prime factorization etc.

Number theory homework tutoring

Homework tutoring is done by the tutors of tutor vista. There are many tutors of high qualification are always ready to provide tutoring for the students.

Solved problem 1: Write standard form of the given scientific notation 3.432 ? 102

Solution:

Given 3.432 ? 102

To find the standard form just multiply the scientific notation by 10.

10 are raised with the powers of 2. So shift the decimal point two places to the right side. 3.432 --> 343.2

3.432 ? 102 = 343.2

Solved problem 2: Find the least common multiple of 3 and 8

Solution:

Given 3 and 8

To find the least common multiple (LCM), we have to list out the multiples of 3 and 8.

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Multiples of 8: 8, 16, 24, 32, 40, 48

The least common multiple of 3 and 8 is 24. Since 24 is the least common number that comes first in the multiples of both 3 and 8

Solved problem 3: Find the prime numbers in the given series of numbers 14, 16, 19, 21, 25, 29

Solution

Prime numbers are divisible only by 1 and the number itself. It does not have any other multiples. Here we check the given numbers

Multiples of 14 = 1, 2, 7, 14

Multiples of 16 = 1, 2, 4, 8, 16

Multiples of 19 = 1, 19

Multiples of 21 = 1, 3, 7, 21

Multiples of 25 = 1, 5, 25

Multiples of 29 = 1, 29

So here 19 and 29 are the prime numbers of the given series of numbers.

Number theory homework tutoring

Below are some of the practice problems about number theory homework tutoring.

1. Find the prime numbers of the series given below

35, 37, 39, 41, 45

2. Find the LCM of 7 and 9

3. Write the standard form of the scientific notation given 5.243x 102

4. Find the LCM of 11 and 6

5. Find out the prime numbers of the given 42, 63, 70,71

Answer

1. 37, 41

2. 63

3. 524.3

4. 66

5. 71

A number is a mathematical object used in counting and measuring. A notational symbol which represents a number is called a numeral, but in common usage the word number is used for both the abstract object and the symbol, as well as for the word for the number. In addition to their use in counting and measuring, numerals are often used for labels (telephone numbers), for ordering (serial numbers), and for codes (ISBNs).Let us see about the articles is solving math number problems.

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Neutron Star Black Hole (Nandan Nayak)

Introduction to Neutron Star Black Hole

Neutron star black hole : Process

Neutron Star and Black Hole : Conditions

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Magnet Uses (Nandan Nayak)

Introduction to magnet uses:

Magnet is an object that produces a magnetic field. The so called magnetic field is invisible to human eye, but it solely responsible for creating the typical characteristic and property of a magnet, i.e. the invisible force that attracts other various ferromagnetic materials and objects like iron, and attracts and repels other magnets as well. There are permanent magnets that are naturally magnetized and create a consistent magnetic field around them. There are also materials that can be magnetized artificially and hence they get attracted to magnets. These are known as ferromagnetic materials and objects. Another aspect is the electro magnet. An electro magnet is made up of a coil which acts as a magnet when certain electric current passes through it. The magnetic moment determined the overall strength of a magnet while the magnetization determines the local strength of magnetism in a material.

Electro Magnets in details

In simple words, an electro magnet is made up by coiling an electric wire into number of lops called the solenoid. It is when electric current is passed through the wire; it creates a strong magnetic field around it, hence providing it the basic magnetic property of attracting ferromagnetic objects. There are a number of uses of an electro magnet. Electro magnets are used for manufacture of junkyard cranes, particle accelerators, magnetic resonance machines for detecting health problems, for manufacture of electric bells, for manufacture of magnetic locks, for magnetic separation of particles, for manufacture of MRI machines and mass spectrometers and other electro mechanical devices.

Common Uses of a Magnet

There are numerous uses of a magnet. Magnet is used in daily life and also for industrial purposes. It is dynamic and extremely resourceful. Following are some very vital uses of a magnet -

1) Credit Cards and Debit Cards: A wide use of magnets is in the manufacture of credit cards, debit cards and ATM cards. Behind each of these is a magnetic strip. The information is encoded in the magnetic strip and helps to contact the individual's financial institution and connect with their accounts.

2) For manufacture of electric motors and generators: There is a combination of an electro magnet and a permanent magnet found in motors that help to convert electric energy into mechanical energy. The reverse concept is used in generators which coverts mechanical energy into electric energy.

3) Medication: Now days the use of magnets by hospitals has increased substantially. Use of magnets has brought a revolution in the field of surgery and medication. The modern day doctors use the process of Magnetic Resonance Imaging. Through this concept, all the major problems of the patients are diagnosed by the doctors without performing any kind of invasive surgery.

4) For magnetic recording media: Video tapes, Computer Floppies, Hard Disks and etc. use the concept of magnetic reel which helps to encode the information on the magnetic coating which ultimately is transferred in the form of audio and video. This was arguably the revolution as far as the extensive use of magnets is concerned.

5) Miscellaneous: Other very vital uses of magnets are for manufacturing of toys, manufacturing of speakers and micro phones, industrial uses such as lifting heavy iron objects, manufacturing of transformers, for the process of manufacturing of jewellery, for manufacture of chucks that help in the field of metal working etc.

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Learning Logarithmic Function Problem (Nandan Nayak)

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Prepare For 7th Grade Math Practice (Nandan Nayak)

Introduction to prepare for 7th grade math practice:

The preparation of 7th grade math practice includes the topics of Number theory, Operations with integers, Decimal numbers, Operations with decimals, Integers, Operations with fractions, Rational numbers, Pythagorean theorem, Exponents and square roots, Fractions and mixed numbers, Ratios and proportions, Number sequences, Measurement, Charts and graphs, Geometry, Statistics, Transformations, Coordinate graphs, Single-variable equations, Probability. Let, see some of the examples to prepare 7th grade math problems.

Prepare for 7th grade math practice:

Prepare math practice 1:

At a family reunion, each of Connor's aunts and uncles is getting photographed once. The aunts are taking pictures in groups of 2 and the uncles are taking pictures in groups of 8. If Connor has the same total number of aunts and uncles, what is the minimum number of aunts that Connor must have?

Solution:

Write the prime factorization for each number; 2 is a prime number.

You do not need to factor 2.

8 = 2 ? 2 ? 2

Repeat each prime factor the greatest number of times it appears in any of the prime factorizations above.

2 ? 2 ? 2 = 8

The least common multiple of 2 and 8 is 8.

That means that the minimum number of aunts Connor could have is 8, because 4 groups of 2 aunts is a total of 8 aunts and 1 group of 8 uncles is a total of 8 uncles.

The smallest number of aunts is 8.

Prepare math practice 2:

Tatiana placed 9 weights on a scale during science class.

If each weight weighed 0.7 grams, what did the scale read?

Solution:

Multiply the weight of each weight by the number of weights and multiply as you would multiply whole numbers.

0.7
9 ?
________
63

Count the number of decimal places in the factors.

There is 1 decimal place in 0.7.

Move the decimal point 1 place to the left in the answer.

63 ? 6.3

The scale read 6.3 grams.

Prepare math practice 3:

Gabriel owns 10 acres of farmland. He grows beets on 1/5 of the land. On how many acres of land does Gabriel grow beets?

Solution:

Gabriel grows beets on '1/5' of 10 acres of land.

Multiply:

'10xx1/5 =?'

Write 10 is a improper fraction.

'10 = 10/1'

Multiply the numerators and multiply the denominators.

'10/1xx 1/5 = (10xx1)/(1xx5)=10/5'

Simplify the product.

'10/5 = 2'

Gabriel grows beets on 2 acres of land.

Prepare more for 7th grade math practice:

Prepare math practice 4:

Ballet dancers are positioned on stage. If Eve is 9 feet straight behind Curtis and 12 feet directly left of Gun-Woo, how far is Curtis from Gun-Woo?

Solution:

Draw a diagram.

Use the Pythagorean theorem, with a = 9 and b = 12.

a2 + b2= c2

92 + 122= c2

81+144 =c2

225=c2

Sqrt 225 = sqrt c2

15 = c

Curtis is 15 feet from Gun-Woo.

Prepare math practice 5:

A football player named Cole played 40 games last year. This year, he played 5% more games. How many football games did Cole play this year?

Solution:

"5% more" means you should add 5% to the original amount:

100% of original amount + 5% of original amount = 105% of original amount

Write and solve an equation:

Final amount = 105% of original amount

= 105% of 40

= 1.05 ? 40

= 42.

Cole played 42 games this year.

Prepare math practice 6:

Alice's class took a field trip to the art museum. It took them 1 hour to drive to the museum. They stayed at the museum for 3 hours and 15 minutes. When the class left the museum, it was 12:30 P.M. What time did Alice's class leave for the field trip?

Solution:

Add the times to find the total elapsed time.

1 h + 3 h 15 min = 4 h 15 min

Now find 4 hours and 15 minutes before 12:30 P.M.

Count back by hours to find 4 hours before 12:30 P.M.

This is 8:30 A.M.

Now subtract 15 minutes from 8:30 A.M.

This is 8:15 A.M.

Alice's class left at 8:15 A.M.

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Nature Science Project (Nandan Nayak)

Introduction to nature science project:

Balance in Nature

Whether, it is an ocean, a forest or a pond, there is a chain in which the larger animals eat the smaller ones, in every habitat.

In a particular habitat or a living area, many plants and animals live together. They are all interlinked with each other, and with the environment in which they live. Some habitats may be very small like a pond. While some like oceans or forests may be large. It is very interesting to learn the relationship that all living things share with one another.

Life in any habitat begins with the Sun. Without the Sun, plants will not be able to make food. Using Sun's energy, plants convert water and carbon dioxide into starch that is stored as food. This process is called photosynthesis. It also helps the plants to grow. Since, plants are the only living things that can make their own food, that are called nature's primary producers.

The primary and secondary consumers of science:

Green plants are eaten by many kinds of animals. The rabbit, deer, squirrel as well as all the grazing animals such as cow, sheep and goat are plant eaters. They are known as herbivores.

All these animals, which eat food made by plants, are called primary consumers.

The primary consumers such as a rabbit, a caterpillar or a deer become food for animals like shark in the ocean or a lion in the forest. Animals that feed on the flesh of other animals are called carnivores. Carnivores are also called secondary consumers.

In a habitat, we have a chain of who eats whom. The plants are eaten by herbivores and herbivores are eaten by carnivores. This is not the end of the chain. When the carnivores die that are eaten by scavengers.The relationship between the plants and the animals that eat them is called a food chain. It follows a single path, as animals find food.

E.g. grain, a primary producer, is eaten by a mouse which is a primary consumer. Owl that eats the mouse is the secondary consumer.

The relationship between the various living beings in an ecosystem in the form of a chain, based purely on feeding is known as a food chain. The food chain in carnivores is defined as the food chain contains only three steps for the food chain. The first one is the primary producer and second one is the primary consumer and third one is the secondary consumer.

The solar energy is trapped by the producers.
Plants use this solar energy in reducing carbon from carbon dioxide.
The carbon dioxide is used in manufacturing food in the form of carbohydrates, proteins and fats.

The stored energy is first consumed by herbivores, then by carnivores, then by secondary carnivores.
For example take a food chain in the grassland forest.
In grassland there are lots of grasses.
The grass is eaten by deer (primary consumer).
The deer is eaten by the lion (secondary consumer).
The above food chain tells us that the grass is the starting point of a food chain.
The grass is the producer organism which uses the sunlight energy to prepare food such as carbohydrates by the process of the photosynthesis.
The grass is consumed by the deer which are herbivores.
The deer is consumed by the lion which are herbivores.
Example 2 for food chain carnivores:

The above food chain diagram is also the example for the food chain carnivores.
The above food chain tells us that the trees are the starting point of a food chain.
The tree is the producer organism which uses the sunlight energy to prepare food such as carbohydrates by the process of the photosynthesis.
The tree is consumed by the giraffe which are herbivores.
The giraffe is consumed by the lion which are herbivores.

Food web of nature science:

Though all food chains may appear to be separate, they are actually interconnected in a large and complex food web. Food webs show how plants and animals are interconnected in many ways to help them all survive.

Keeping the Balance

Food chains are a way of keeping the balance in nature. Each link in the food chain is important. Imagine a simple food chain like the following:

grass -------> deer -----------> lion

If tiger is hunted excessively by man and their number goes down, the deer population will increase tremendously. When deer are born in large numbers and live freely they will eat away all plants and grass and a forest might become a desert!

Dependence of Plants and Animals

Each animal and bird species is important to maintain nature's balance. Animals and plants depend on each other. Without plants there would be no food and oxygen. Without animals, plants would not get carbon dioxide for photosynthesis. Many insects play an important role in pollination of seeds. Carnivores help to prevent many herbivores population from increasing excessively. Hawks and eagles clean up by eating dead animals.

Both plants and animals depend on man to let them live. By cutting down forests, we destroy the plants as well as homes of various animals living in them. When humans hunt some animals excessively, their population decreases and at times they disappear completely.

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Introduction to General Relativity (Nandan Nayak)

INTRODUCTION TO GENERAL RELATIVITY

General relativity was devloped by Albert Einstein a century ago. Accoring to general relativity, the observed gravitational attraction between masses depend on space and time also.

Newton's law of universal gravitation was accepted before Einstein's theory of relativity. In Newton's model, gravity is the result of an attractive force between massive objects. Newton's theory of gravitation was also extremely successful at describing motion, But Einstein's description was a much better improvement to Newton's law of gravity. Einstein's description accounted for several effects which were unexplained by Newton's law of gravitation, Minute anomalies in the orbits of Mercury and other planets are considered in Einstein's general theory of relativity. This theory of relativity also predicts the novel effects of gravity like gravitational waves, gravitational lensing and and an effect of graivty on time known as gravitational time dilation.

Einstein's theory of general relativity is four dimensional :

Einstein's theory can be described as four dimensional with time also as one of the coordinate. Normally till Einstein devleoped general theory of relativity noone considered time as a factgor affecting the position. But in Einstein's theory he first took time also as a fourth coordinate and found out that time will appear slower due to some effects.

E=mc^2 equivalence of mass and energy

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Equivalance theory of mass and energy:

Though the concept of relativity was in vogue before Einstein's time, It became popular and approved after Einstein's theory only.

The main theory in this is that the speed of light in a vacuum is constant and an absolute physical boundar for motion. We common people never realise this because normally the speed we travel is negligible compared to speed of light. For objects travelling near light speed, the theory of relativity states that objects will move slower and shorten in length from the point of view of observer on earth. We should make it clear that time dilation and length short is only apparent and not real. In other words, there is no change in actual time or length. It seems apparent relative to the place from where we are seeing. This is the very important point in General theory of relativity.

First point is it applies when travelling in a very high speed almost equal to that of light. Hence we should not compare this theory in normal life with negligible speeds and come to conclusion there is no apparent change in time of length.

Second point is there is no actual or real change in time or length, It is apparent from the view of observer because of relativity.

The famous equation of Einstein E =mc2 which reveals the equivalence of mass and energy.

Theory of relativity - Fundamental points

The theory of relativity consists of two main points.

1. The first is the Special theory of relativity. It deals with the question of whether rest and motion are relative or absolute. According to Einstein's special theory of relative, the relationship between rest and motion are relative and not absolute. the Special Theory of Relativity, which essentially deals with the question of whether rest and motion are relative or absolute, and with the consequences of Einstein's conjecture that they are relative and not absolute.

2. The second is the General Theory of Relatitivy, which primarily applies to particles when they accelerate, mainly due to gravitation. The theory of Einstein acts as a radical revision of Newton's theory for fast moving and/or very massive bodies. In other words, we can say that this is an expansion of Newton's theory on understanding some of the key principles involved. Newton's theory of gravity operated through empty space, but did not explain as far as how the distance and mass of a given object could be transmitted through space. Einstein's general theory of relativity second part provides explanation for this.

The second part of the theory of relativity states that objects continue to move in straight line in space time, but we observe the motion as acceleration because nature of space time is curved.

ACCURACY OF Einstein's theory of relativity:

Einstein's general theory of relativity have been confirmed to be accurate to a very high degree over a period of time. Also the data has been proved to corroborate many other important key predictions.

How it was proved in 1919?

Total solar eclipse which was inaccessible due to brightness of sun was analysed by astrronomers straight near the edge of the sun. This was possible because the light of stars is indeed deflected by the sun as the light passes near the sun on its way to earth. It also predicted the rate at which two neutron stars orbiting one another will move toward each other. Thus the general theory of relativity was proved to be the best confirmed principles in all of physics.

general theory of relativity - amazing results

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How really amazing General theory of relativity is:

Here the fourth dimension coordinate that is time is linked or related to matter and space. A continuum is created by dimensions of matter, time and space. Time itself cannot exist without matter and space. So we can infer that the uncaused first cause must exist outside of the four dimensions of space and time, and possess eternal, personal, and intelligent qualities in order to possess the capabilities of intentionally space, matter -- and indeed even time itself -- into being. This is really amazing to persons having average brains and limitations like us.

The existence of time implies eternity (with beginning and end) and the existance of space implies infinity. Hence the theory itself is a combination of infinity and eternity. To understand this, we have to take so much pain. Really we have to wonder how Einstein, an ordinary human being, by birth, thought and found all these things accurately. The nobel prize awarded to him was very less compared to the volume of theory he proved.

Conclusion:

The article we discussed is only introduction to general theory of relativity. Full applications and concepts will be very useful and interesting. The general theory of relativity thus is a theory which expands Newton's previous findings about gravitation without contradicting his findings. Also here time, space and matter are considered to provide a continuum. Also when speed nearly equals that of light, time appears to go slower while length appears shorter.

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Five Number Summary Online (Nandan Nayak)

Introduction to five number summary online help:

Online:

The specific meaning of the term online is nothing but the connecting two states. Online is mostly used in computer technology and telecommunications. Online can be referred the World Wide Web or it may be Internet.

Five number summary online help:

Different statistics are involved in five number summary are,

Minimum
Maximum
Median
Lower quartile
Upper quartile

Minimum:
Lowest value in the given set of numbers.

Maximum:
Largest value in the given set of numbers.

Median:
Middle value in the given set of numbers.

Lower quartile:
Number between the minimum and median.

Upper quartile:
Number between the maximum and median.

Five number summary online help - Steps to solve:

There are different steps to solve the five number summary are,

The upper quartile can be determined. When the observation minus one is divided by 4 means it is starting with the median and observations in the right side. Otherwise the observation is not divided by four means upper quartile is the median of the observation to the right of the location of overall median.
The lower quartile can be Determined. When the observation set minus one is divided by 4 then it is starting with the median and its observations in the left side. Otherwise the observation is not divided by four means lower quartile is the median of the observation to the left of the location of overall median

Five number summary online help - Example problem:

Example 1:

Help to find the five number summary for the given set of data

{235, 222, 244, 255, 217, 228, and 267}

Solution:

Given set of data

{235, 222, 244, 255, 217, 228, and 267}

{217, 222, 228, 235, 244, 255, 267} [Arrange the set in ascending order]

Minimum and Maximum values in the given set of data are 217 and 267.

Median:

Given observation is odd. So the median is middle of the observation then the median is 235.

Lower quartile:

Given observation is not divisible by four. So the lower quartile is {217, 222, and 228}

Upper quartile:

Given observation is not divisible by four. So the upper quartile is {244, 255, and 267}.

Answer:

Minimum: 217

Maximum: 267

Median: 235

Lower quartile: {217, 222 and 228}

Upper quartile: {244, 255 and 267}

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Why is Geometry Important in Life (Nandan Nayak)

Introduction:

Geometry is important in life because it is the learning of space and spatial dealings is an important and necessary area of the mathematics curriculum at every evaluation levels. The geometry theories are important in life ability in much profession. The geometry offers the student with a vehicle for ornamental logical reasoning and deductive thoughts for modeling abstract problems. The study of geometry is important in life because it's increasing the logical analysis and deductive thinking, which assists us expand both mentally and mathematically.

Definition for why is geometry important in life:

This article going to explain about why geometry is important in life. Geometry is a multifaceted science, and a lot of people do not have an everyday need for its most advanced formulas. Understanding fundamental geometry is essential for day to day life, because we never know when the capability to recognize an angle or figure out the region of a room will come in handy.

Importance of geometry in life:

The world is constructing of shape and space, and geometry is its mathematics.
It is relaxed geometry is good preparation. Students have difficulty with thought if they lack adequate experience with more tangible materials and activities.
Geometry has more applications than just inside the field itself. Often students can resolve problems from other fields more easily when they represent the problems geometrically.
Uses of geometry:

Geometry is the establishments of physical mathematics presents approximately surround us. A home, a bike and everything can made by physical constraints is geometrically formed.
Geometry allows us to precisely compute physical seats and we can relate this to the convenience of mankind.
Anything can be manufacturing use of geometrical constraints like Architecture, design, engineering and building.

Example:

Let us see one example regarding why geometry important in our life. If you want to paint a room in your accommodation, you should know how much square feet of room you are going to cover by paint in order to know how much paint to buy. You should know how much square feet of lawn you contain to buy the correct amount of fertilizer or grass seed. If you required constructing a shed you would have to know how much lumber to buy so you should know the number of the square feet for the walls and the floor.

Geometry architecture is a one of the foundation of all technologies and science using the language of geometry pictures, diagrams and design. Geometry was fully depends on structure ,size and shape of the object. In every day geometry was very important in architectural through more technologies In a daily life geometry was used in th technology of computer graphics, structural engineering, Robotics technology, Machine imaging, Architectural application and animation application.

In this article why is geometry important in architecture, We see about application of geometry architecture in daily life and technology sides.

Basic concepts of geometry important in architecture:

General application of geometry or important of geometry :

Generally geometry was used for identifying size, shape and measurement of an object.
Fining volume, surface area, area ,perimeter of the room a and also properties about shaped objects in building construction.
Also used for more technologies for example : computer graphics and CAD
Computer graphics:

In computer graphics geometry was used to design the building with help of more software technologies. And also how to transferred the object position.

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Exam of Logarithms in General (Nandan Nayak)

Introduction to exam of logarithms in general:

Exam of logarithm in general involves the learning and understanding of the following concepts of logarithms:-

Conversion of exponential to logarithmic form

The three laws of logarithms

The base changing formula

After learning the above topics of logarithms, the exam of logarithms in general preparation can be considered almost complete at the basic level. Essentially, one gains the application knowledge of logarithmic laws and concepts that enable one to simplify and solve logarithmic equations. The above basic logarithmic concepts help us to prove advanced logarithmic statements.

The above mentioned concepts on logarithms are briefly explained below as preparation for exam on logarithms in general.

Conversion of exponential to logarithmic forms in general:

The logarithm of a number is equal to the exponent to which the base of that logarithm must be raised in order to obtain that number.

Logarithms can be considered as a different type of representation of exponential statements.

For example, the exponential statement '6^2 = 36' can be expressed in the logarithmic form as follows:-

log '(6) 36 = 2'

In the above conversion from exponential to logarithmic form, we note the following rules:-

Base of the logarithm and the exponential form is the same.

The result in the exponential form is made the object in the logarithmic form.

The exponent in the exponential form is made the result in the logarithmic form.

The three laws of logarithms:

The three standard laws of logarithms can be stated as follows:-

First law of logarithms - the product law

The logarithm of a product of two or more numbers is equal to the sum of the logarithms of each of the numbers in the product. Thus, if 'a' and 'b' are two non-negative real numbers, and 'c' is the base of the logarithms, then,

'log (c) ab = log (c) a + log (c) b'

This law highlights that logarithms reduce multiplication to addition.
Second law of logarithms - the quotient law

The logarithm of the quotient of two numbers is equal to the difference of the logarithms of each of the two numbers. Thus, if 'a 'and 'b' are two non-negative real numbers, and 'c' is the base of the logarithms, then,

'log (c) a/b = log (c) a - log (c) b'

This law highlights that logarithms reduce division to subtraction.
Third law of logarithms - the power law

This law defines the logarithm of an exponential expression. The logarithm of an exponential expression is equal to the product of the exponent in the exponential expression and the logarithm of the base of that exponential expression.

'Log (c) a^b = b * log (c) a'

This law highlights that logarithms reduce exponents to products.

The base changing formula

The base changing formula helps us to change the base of logarithms, which is a very essential function in solving logarithmic equations. It helps to simplify logarithmic equations. By using the base changing formula, one can change the base of a logarithm to any other number or variable.

'Log (a) b = (log (c) b)/(log (c) a)'

In the above statement, the base of the logarithm is being changed from 'a' to 'c'.

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