Topic:Probability

Probability, is a way of expressing knowledge or belief that an event will occur or has occurred.

Here is some probability problems ,which help you to understand the concept much better.

Questions & Answers

1- Mr. Johnson taught a music class for 25 students under the age of ten. He randomlychose one of them. What was the probability that the student was under twelve?

Ans:-

The probability that the student was under twelve was 25/25, so P = 1.

2- The compact disk Jane bought had 12 songs. The first four were rock music. Tracks
number 5 through 12 were ballads. She selected the random function in her Compact
Disk Player. What is the probability of first listening to a balla?

Ans:-

The probability of listening to a ballad is 8/12, so P = 0.67.

I hope it helped you ,for more math help ,you can reply me.

Problem on Solving a Function and Show Graphical Representation for the Function

Relations and functions are the dependent concepts of math where the value of a variable is dependent on the other variable in the given function. It is expressed in terms of graphical representation as shown in the below example

Topic : Solving a Function and expressing graphically

In the given function variable 'x' is the independent value and y is the dependent one.

Problem : a) If y = √x −1, Find the values for x = 0, 1, 2, 3, 4.Round to three decimal places where necessary.
b) Explain why no negative values are chosen as values to substitute
in for x.
c) Draw a graphical representation for the values.

(a)Solution :

When x = 0
y = √x – 1
= √0 – 1
= 0 – 1
= -1

When x = 1
y = √x – 1
= √1 – 1
= 1 – 1 and y = -1 - 1
= 0 and y = -2

When x = 2
y = √x – 1
= √2 – 1
= 1.414 – 1 and y = -1.414 - 1
= 0.414 and y = -2.414

When x = 3
y = √x – 1
= √3 – 1
= 1.732 – 1 and y = -1.732 - 1
= 0.732 and y = -2.732

When x = 4
y = √x – 1
= √4 – 1
= 2 – 1 and y = -2 - 1
= 1 and y = -3

(b) Solution :
No negative values are chosen for x because square root of a negative
number is imaginary and is not defined in real space.

(c) Solution :

For more help contact geometry help or algebra help.

A Question on Rightangle Triangle and Find length of a Side

On a Right angled triangle, number of theorem are derived. One such theorem is Mid point Theorem, with below example theorem is very well explained.

Topic : Right angle Triangle and Mid Point Theorem

Problem : Given angle C is a right angle, E is a midpoint of AC, F is the midpoint of BC, AF = √41, BE = 2√26, Find AB

Solution :













From the figure,
In ∆ACF
AC² + CF² = AF² (by Pythagoras Theorem)
AC² + (CB/2)² = (√41)² (as CF is half of CB)
AC² + CB²/4 = 41

Now in ∆ECB
EC² + CB² = EB²
(AC/2)² + CB² = (2√26)² (as EC is half of AC)
AC²/4 + CB² = 104

Now adding both the equations, we get
AC² + CB²/4 + AC²/4 + CB² = 41 + 104
(1+1/4)AC² + (1+1/4)CB² = 145
5AC²/4 + 5CB²/4 = 145
5/4(AC² + CB²) = 145
Now, in ∆ACB, AC² + CB² = AB²

So we get, 5/4 AB² = 145
AB² = 145 * 4/5
AB² = 116
AB = √116
AB = 2√29

Hope the above elaborated explanation will help you to understand mid point theorem and help you to solve similar kind of problems.

If you have any queries please write to us and geometry help will respond to your queries.

Question on Listing Polygon Names

Topic : Polygon

Question : List the names of Ploygons

Solution :

Sides ------ Name
n ----------N-gon
3 ----------Triangle
4 ----------Quadrilateral
5 ----------Pentagon
6 ----------Hexagon
7 ----------Heptagon
8 ----------Octagon
10 ---------Decagon
12 ---------Dodecagon

Question to Prove a Theorem

Topic : Theorem

Theorem : Prove that if gcd(a,p²)=p and gcd(b,p²)=p² then gcd(ab,p^4)=p³. where a and b are integers and p is a prime number.

Solution :
GCD (a, p²) = p
implies that a ia a multiple of p or p is a divisor of a.
So let a = kp
where k is a constant
Similarly GCD(b, p²)=p²
implies that b is the multiple of p² or p² is a divisor of b
So let b = mp²
where m is a constant
So a = kp and b = mp²
ab = kp . mp²
ab = kmp³
implies that ab is a multiple of p³ and km is the constant
So greatest common dividor of kmp³ and p^4 is p³
Hence GCD (ab, p^4) = p³
Hence proved.

Problem on Factorization and Simplification

Topic : Simplification

Problem : Solve

Solution :

Simple Linear Equation to Find the Value of a Variable

Topic : Linear Equation
Problem : Solve 0.7n - 1.5 + 7.3n = 14.5

Solution :
0.7n - 1.5 + 7.3n = 14.5
8.0n - 1.5 = 14.5
8.0n = 14.5 + 1.5
8.0n = 16.0
n = 16.0/8.0
n = 2.0
= n = 2