Primary Number Line

Introduction to primary number line:

The line is marked with the number is called primary number line. The number line has both positive and negative number. The center point of the primary number line is zero. The zero will not be neither positive nor negative. The positive may or may not have the positive sign on primary number line. But the negative numbers should have negative sign(“-“)

Example for Primary Number Line:

Example 1:

Point the expression x < 3 and x > -2 on the primary number line

Solution:

The expressions x < 3 and x > -2 can be written as -2
Example 2:

Point the expression n > -1 and n < 4on the primary number line

Solution:

The expressions n > -1 and n < 4on can be written as -1 < n < 4. This means, n is greater than -1 but less than 4. Please express your views of this topic second order differential equation by commenting on blog.

Practice Problems for Primary Number Line:

1. Point the expression x < 3 and x > -2 on the primary number line

2. Point the expression x < 5 and x > -5 on the primary number line

3. Point the expression x < 4 and x > -7 on the primary number line

5. Point the expression x < 2 and x > -8 on the primary number line

6. Point the expression x < 9 and x > -11 on the primary number line

7. Point the expression x < 12 and x > -1 on the primary number line

8. Point the expression x < 13 and x > -15 on the primary number line

9. Point the expression x < 4 and x > -8 on the primary number line

10. Point the expression x < 9 and x > -1 on the primary number line

The Bun in Math

Introduction to the bun in math:

Mathematics is the one of the greatest subject in the world, which acts as a fundamental for all subjects. It is generally used to study about the rate of change, its space, and their quantities. In this article, we shall discuss the word problems in math. The following example problems will make the students to get more experts in basic arithmetic problems in math.

Examples for the Bun in Math:

Example problem 1:

In a baker’s shop, there are three buns in the box and two buns in the glass. Find the total amount of buns in baker’s shop.

Solution:

Given that, three buns in the box.

In addition, two buns in the glass.

Therefore the total amount of buns = 3 buns+2 buns

= 5 buns

Finally the total amount of buns in baker’s shop = 5 buns as shown in the following figure.

Example problem 2:

There are 5 buns in each box. How many buns are there in 9 boxes?

Solution:

Given that, one box contains 5 buns.

Therefore 9 boxes contain = 9 x 5 buns

= 45 buns

Totally, there are 45 buns in all boxes.

Example problem 3:

Mani bought 120 grams of buns in a pack. He equally divided the buns in 5 boxes. Calculate the amount of bun in each box.

Solution:

Given that, one pack contains 120 grams of buns.

120 grams is equally divided into 5.

Therefore the amount of bun in each box = `120/5`


= 24 grams.

Finally, each box contains 24grams of bun.

Additional Examples for the Bun in Math:

Example problem 4:

Mike ate `3/6 ` of bun and George ate `2/6` of bun. Calculate the amount of bun that they eat jointly.

Solution:

Given that, Mike ate `3/6` of bun and George ate `2/6` of bun.

Jointly they eat = `3/6+2/6` bun

= `(3+2)/6` bun

=` 5/6` bun.

Finally they jointly eat 5/6 bun.

Example problem 5:

Last month Rajesh sold 100kgs of buns. This month he sold 10 more kgs of bun than last month. What is the percentage of increase in weight of buns?

Solution:

The formula for the percent of increase = (Number of increase) x 100

Original number.

Here increased weight of bun = 10 kgs.

Actual weight of bun in previous month = 100 kgs.

Therefore the percentage of increase of weight of bun `=10xx100/100`

= 10%

That is 10% of buns increased in selling.

Regression Analysis Formula

Introduction to regression analysis formula:

In mathematics, one of the most important topics in statistics is regression. Regression analysis formula is determining the relationship between two variables. Regression analysis formula are used to analysis the several variables. Regression is one of the statistical analysis methods that can be used to assessing the association between the two different variables. Here we are going to discuss about regression analysis formula with suitable example problems.

Formula for Regression Analysis:

Here we study about calculate the regression analysis formulas are,

Formula for regression analysis:

Regression Equation (y) = a + bx

Slope `(b) = (NsumXY-(sumX)(sumY))/(NsumX^2-(NsumX)^2)`

Intercept `(a) = (sumY-b(sumX))/N`


Where,
x and y are the variables.
b = the slope of the regression line is also defined as regression coefficient
a = intercept point of the regression line where is in the y-axis.
N = Number of values or elements
X = First Score
Y = Second Score
`(sumXY)` = Sum of the product of the first scores and Second Scores
`(sumX)` = Sum of First Scores
`(sumY)` = Sum of Second Scores
`(sumX^2)` = Sum of square First Scores.

Example Problem for Regression Analysis Formula:

Problem for regression analysis formula:

Example 1:

Find the regression slope coefficient, intercept value and create a regression equation by using the given table.

X Values	Y Values
5	8
10	16
15	24
20	32
30	40

For the given data set of data, solve the regression slope and intercept values.

Solution:

Let us count the number of values.
N = 5
Determine the values for XY, X2

X Value	Y Value	X*Y	X*X
5	8	40	25
10	16	160	100
15	24	360	225
20	32	640	400
30	40	1200	900
`(sumX = 80)`	`(sumY = 120)`	`(sumXY)= 2400`	`(sumX^2) = 1650`

Determine the following values `(sumX), (sumY), (sumXY), (sumX^2).`
`(sumX) = 80`
`(sumY)= 120`
`(sumXY)= 2400`
`(sumX^2) = 1650`

Plug values in the slope formula,

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Slope `(b) = (NsumXY-(sumX)(sumY))/(NsumX^2-(NsumX)^2)`


`= (5 xx(2400)-(80)xx(120))/((5)xx(1650)-(80)^2)`


`= (12000 - 9600)/(8250-6400)`


`= 2400/1850`

`b= 1.28`

Plug the values in the intercept formula,


Intercept `(a) = (sumY- b(sumX))/N`


`= (120-(1.28xx80))/5`


`= (120 - 103.78)/5`


`= 16.22/5`


`a = 3.24`

Plug the Regression coefficient values and intercept values in the regression equation,
Regression Equation(y) = a + bx
= 3.244 + 1.28x

Answer:

Slope (or) Regression coefficient (b) = 1.28

Intercept (y) = 3.24

Regression equation y = 3.24 + 1.28x

Poisson Distribution Sample Problems

Introduction to Poisson distribution sample problems:

In mathematics, Poisson distribution is a term used to find the number of events happened within a certain time interval. We can also say the Poisson distribution as a discrete probability distribution. A formula is used for finding the Poisson distribution. In this article we are giving some sample problems for Poisson distribution.

Explanation to Poisson Distribution Sample Problems:

The general for calculating the Poisson distribution is as follows.

f(x) = `(e^(-lambda)lambda^x)/(x!)`

Here,

`lambda` – average rate

x – Poisson random variable

e – base value for logarithm having a value = 2.718

Let us see some sample problems using this formula of Poisson distribution.

Example Problems to Poisson Distribution Sample Problems:

Example: 1

In a class room, 2 students are absent today. Find the possibility for exactly 3 students to be absent on tomorrow.Please express your views of this topic irrational numbers examples by commenting on blog.

Solution:

Given:

`lambda` = 2

x = 3

Step 1:

The general formula used for Poisson distribution is,

Poisson distribution =   `((e^(-lambda))(lambda^x))/(x!)`

Step 2:

e-2 = (2.718)-2

= 0.135

Step 3:

`lambda`  = 2

x = 3

`lambda^x` = (2)3 = 8

Step 4:

Substitute the obtained values on the formula.

`((e^-lambda)(lambda^x))/(x!)`  = `((0.135)(8))/(3!)`

= `1.08/(6)`

= 0.18

Answer: The possibility of getting 3 absentees on tomorrow is 0.18

Example: 2

In a book shop, 2 customers arrived today. Find the possibility for exactly 5 customers to be arrived on tomorrow.

Solution:

Given:

`lambda` = 2

x = 5

Step 1:

The general formula used for Poisson distribution is,

Poisson distribution =   `((e^(-lambda))(lambda^x))/(x!)`

Step 2:

e-2 = (2.718)-2

= 0.135

Step 3:

`lambda`  = 2

x = 5

`lambda^x` = (2)5 = 32

Step 4:

Substitute the obtained values on the formula.

`((e^-lambda)(lambda^x))/(x!)`  = `((0.135)(32))/(5!)`

= `4.32/(120)`

= 036

Answer: The possibility of getting 5 customers on tomorrow is 0.136

Practice Problems to Poisson Distribution Sample Problems:

Problem: 1

In a call center, 2 students are absent today. Find the possibility for exactly 4 students to be absent on tomorrow.

Answer: 0.09

Problem: 2

In a shop, 2 customers arrived today. Find the possibility for exactly 6 customers to be arrived on tomorrow.

Answer: 0.012

Ratio Statistics

Introduction for ratio statistics:

A relation is getting form the comparison of two quantities like in some wisdom is called a ratio. Ratio will be show by the terms of fraction, that is, a:b is equal to `a/b` For example 25 is `1/4` of the hundred, Therefore, the ratio of 25 to 100 is `1/4` . We can write it in ratio as 1:4.

Example Problems for Ratio Statistics:

Example 1: Find the ratio of 90 centimeters to 7 meters in its simplest form.

Solution:

7 m = 7 `xx` 100 cm

Therefore, 7 m = 700 cm

Therefore, the ratio of 90 cm to 7  m = 90cm: 700 cm

Now we have to cancel out the units. So we get

90: 700

Now we have to divide both terms by 10. So we get

9:70

Example 2: Find the ratio of 700 m to 1.7 km in its simplest form.

Solution:

1 km = 1000 m

1.7 km = 1.7 `xx` 1000

Therefore, 1.4 km = 1700 m

Therefore, the ratio of  700 meter to 1.7 km = 700 m : 1700 m

Now we have to cancel out the units. So we get,

700:1700

Now we have to divide both terms by100. So we get

7:17

Example 3: Find the ratio of 20 minutes to 7 hours in its simplest form.

Solution:

1 hour = 60 minutes

7 hours = 7 `xx` 60 minutes

Therefore, 5 hours = 420 minutes

Therefore, the ratio of 20 minutes to 7 hours = 50 min : 420 min

Now we have to cancel out the units. So we get

20: 420

Now we have to divide both terms by 10. So we get

2:42

Now we have to divide both terms by 10. So we get

1:21

Having problem with how to divide mixed numbers keep reading my upcoming posts, i will try to help you.

Practice Problems for Ratio Statistics:

Problem 1 for ratio statistics:

Find the ratio of 900 milliliters to 1.9 liters in its simplest form.

Solution: 9:19

Problem 2 for ratio statistics::

Find the ratio of 900 milligrams to 9 kilograms in its simplest form.

Solution: 1:10

Line Segments in Geometric

Introduction to line segment in geometric:

A line segment is a part of a line that is bounded by two distinct end points and contains every point on the line between its end points. Depending on how the line segment is defined, either of the two end points may or may not be part of the line segment. Two or more line segments may have some of the same relationships as lines, such as being parallel, intersecting, or skew        (source: Wikipedia)

Line Segment in Geometric

Euclidean geometric:

Within the Euclidean geometric, a line is a directly curve.

Line is established to contain assured properties which transmit it to other lines also points.

For instance for either two different points, here be a unique line having them, in addition to either two different lines meet at most one point within two dimensions, that is the Euclidean plane, two lines which perform not meet are called similar. Within higher dimensions, two lines do not intersect might be similar if they are limited within a plane.Please express your views of this topic Rectangular Coordinate System by commenting on blog.

Any groups of finitely various lines separations the plane into convex polygons.

These separations are recognized like a collection of lines.

Coordinate geometric:

Lines in a Cartesian plane are able to be illustrated algebraically through linear equations in addition to linear functions.

Two dimensions, the distinguishing equation is frequently known through the slope-intercept form

y = mx + c

Examples for Line Segment in Geometric

Example 1:

Given two line equations are y = 6x-2, y =4 x+8.  Find the intersecting point?

Solution:

Point of intersection they will equally contain the similar y-coordinate value.

Set the equations equivalent to all other

6x - 2 = 4x + 8

We can solve:

Rearranging x terms

6x - 4x = 8 + 2

2x = 10

x = 10/2

x = 5

To find y to substitute x value for any given equation

y = 6x - 2

y =  6(5) - 2

= 30 - 2

y = 28

The intersecting point is (5, 28)

Example 2:

Given point of the line is (20, 17) and slope of the line is 7. Find the equation of the line?

Solution:

Given point of the line is (20, 17)

The slope of the line is 7

The equation of the line is y-y0 =m(x-x0)

y - 17 = 7(x - 20)

y - 17 = 7x - 140

7x - y = -140 + 17

7x - y + 123 = 0

Therefore the equation of the line is 7x - y + 123

Weighted Mean Calculator

Introduction to weighted mean calculator:

Weighted mean is nothing but the same as that of arithmetic mean, where as each of the data given is contributed equally to the weighed value. If all the weighted values are equal, then the weighed mean is equal to the arithmetic mean.  Weighted mean basically behaves like a similar fashion to the arithmetic mean. The term weighted mean can also be called as weighted arithmetic mean or weighted harmonic mean . Here we are going to see about the weighted mean calculator and the example problems related to it.

Weighted Mean Calculator:

Here given a calculator for calculating the weighted mean statistics for the given set of data.




Procedure for calculating the weighted mean calculator.

Give the input for the observed field and the weighted value field.

Now click on the calculate button to find the result of the given data set.

Definition of Weighted Mean:

Weighted mean statistics is defined as the summation of the observed values multiplied with the allocated weights which is divided by the summation of the observed values. This is called as the statistics weighted mean.

Formula for the weighted mean statistics is given by,

`""""barx_w = (sum_(i=1)^ n (w_i x_i)) / (sum_(i=1)^n w_i) `

where as

`barx_w`  This is the weighted mean variable

`w_i`  This is the allocated weighted value for the given data.

`x_i`  This is the observed values for the given data.

Steps for solving Statistics weighted mean using calculator:

Calculate the summation for the allocated weighted value and observed value of the given data set.
Calculate the summation for all observed values of the given data set.
Now make the division for the above two calculated values from the given data set.

Weighted Mean Calculator - Example Problems:

weighted mean calculator - Problem:

Calculate the weighted mean for the given data as  the observed values  22, 24, 26, 28 and the allocated weights are 10, 20, 30, 40.

Solution:

Weighted Mean:

Formula for Statistical weighted mean is given by,

`"barx_w = (sum_(i=1)^ n (w_i x_i))/(sum_(i=1)^n w_i) `

= `((10)(22)+(20)(34)+(30)(26)+(40)(28))/ (10+20+30+40) `

= `2800 / 100`

`barx_w`  = 28

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Weighted Mean Calculator - Practice Problems:

Problem 1:

Calculate the weighted mean from the observed values  65, 70, 85, 90 and the allocated weights are 60, 70, 80, 90.

Answer: weighted average = 81.3333

Problem 2:

Calculate the weighted mean for the given data as  the observed values  10, 20, 30, 40 and the allocated weights are 15, 20, 25, 30.

Answer: weighted average = 25