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Go online to this statistics calculator and get your answers from it:

https://www.hackmath.net/en/calculator/statistics

14 / {14 + 12} =14 / 26 =0.5385 x 100 =53.85%

I would go with "Mothers' Day" because it is a celebration of ALL mothers, not just yours or mine.

1 hour 30 minutes =1 1/2 =1.5 hours

1.5 / 24 =0.0625 x 100 =6.25% of the day, or 1/16 of the day.

If you mean writing as a single log .......

(log 2)(log 4)   =

(log 2) (log 2^2 ) =

(log 2 )  *  [ 2 ( log 2)  ]

2 (log 2)^2

Another, albeit, intuitive way!

In a 5-12-13 triangle, 5=(12+13)/5. Its perimeter is 30, area =(5 x 12)/2 =30 sq.units.
The right triangle with a perimeter of 1 is similar to the 5-12-13 triangle. Its sides are then
1/30 of the 5-12-13, so its area is proportional by (1/30)^2. Its area is therefore =area(5-12-13) / 30^2
=30 /30^2 =1/30 sq.units.

The formula is:  y = 2^x

First night:         y = 2¹  =  2

Second night:    y = 2²  =  4

Ninth night:        y = 2⁹  =  512

That is correct. Thank you!

The first  is using  degrees......the second, radians

let the base = b
let the hypotenuse = c
a=(b+c) / 5, or 
5a =(b+c), but we have:.................(1)
a+b+c=1, we sub as
a+5a = 1, and we have:
a = 1/6, now will sub this into (1) above:
5/6 - b = c, Now to solve for b, will use Pytho. theorem:
a^2 + b^2 =c^2...........................(2)
(1/6)^2 + b^2 =(5/6 - b)^2 simplifying this we get:
(10/6)b = 24/36
b = 2/5, we now have:
Area = ab/2
(1/6)(2/5)(1/2) =1/30 sq.units.

The leg of a right triangle is equal to 1/5 the sum of other sides. The triangle has a perimeter of 1. What is the triangle's area? Thank you.

Let the sides be  a, b and c      where a and b are the legs and c is the hypotenuse

Let  a  =  ( b + c) / 5     so    5a   = b + c

And since the perimeter   =  1, we have that

a +  b + c  =  1                

a +  5a   = 1

6a  =  1    →   a  =  1/6 units

And we have that  5(1/6)=  b + c   →  5/6  = b + c  →  c = (5/6) - b

So.....using the Pythagorean Theorem, we have that

a^2 + b^2  =  c^2

(1/6)^2  + b^2   = [ (5/6)  - b ] ^2

(1/36) + b^2   =  b^2  - (10/6)b + 25/36    simplify

(1/36)    = 25/36 - (5/3)b      rearrange as

(5/3)b   =   25/36  -  1/36

(5/3)b  =  24/36

(5/3)b  =  2/3

5b =  2

b = 2/5 

So.......the area  = (1/2)(product of the legs) =  (1/2)(a)(b)   =  (1/2)(1/6)(2/5)   =  1/30 units^2

The sequence continues as : 1, 15/8, 21/5, 85/16, 341/35, 1365/128, 5461/315, 4369/256, 1387/55, 69905/3072..........etc.
The easiest way to see a pattern in such a sequences is to look at the numerator(the top number) and the denominator(the bottom number) separately. If you do that, you will see that the numerator seems to use this formula: (2^(2n) - 1), and the denominator seems to use this formula: (n + 2)!!. !! is called "the double factorial function". Example: 10!! =10 x 8 x 6 x 4 x 2 =3,840. 0!! is defined as 1.
So, your formula appears to be: (2^(2n) - 1) / (n + 2)!!, which is the genarating function.
Notice that the improper fractions are all reduced to their absolute minimum.

SEE THE ANSWER BELOW UNDER YOUR FIRST POSTING !!

2ⁿ - 1  =  118 000

--->     2ⁿ  =  118 001

--->     log( 2ⁿ )  =  log( 118 001 )

--->     n·log( 2 )  =  log( 118  001 )

--->     n  =  log( 118 001 ) / log ( 2 )

--->     n  =  16.848 ...   

--->     n  =  17

Since  2⁵ - 1  =  31     and     2¹¹ - 1  =  2047, the size are between  31  and  2047.

It takes at most  n  checks to find an item in a field of  2ⁿ - 1  items.

When  n = 6,  2⁶ - 1  =  63

When  n = 7,  2⁷ - 1  =  127

So, if you have 106 words, it will take a binary search at most 7 checks.

The sum of this inifnite series  =

4 / ( 1 - 3/a)        where  4  is the first term  and  (3/a)  is the common ratio

Simplifying this, we have

4a /  [ a - 3]

Note.........that  since a is positive, the first value of a that produces a perfect square is when a  = 4

4(4) / [ 4 - 3 ]  =  16 / 1    =  16    which is a perfect square

I don't think that is even a sequence.

You say "Show that N is a factor of 2^(p+1)" ??. Are you sure it is not the reverse? That is:

Show that 2^(p+1) is a factor of N?

Since the two triangles created are similar, each dimension of the larger triangle created will be  (17/8)  that of the smaller triangle

Call h the height of the smaller triangle......so its   area  =  (1/2)*8*h  =  4h  (1)

And the area of the larger triangle  = (1/2)* 17 * (17/8) h   =   (289 / 16)h    (2)

So  the area  of the trapezoid  =  (2) - (1)   =  (289/16) h - 4h   =  [ 289 - 64 ] / 16 * h =

[225 / 16] h

So.....the ratio of the smaller triangle to the trapezoid  =  [4h] /  ( [ 225/ 16] h )  =  64 / 225

Just as Melody found....!!!!

math is amazing

By your post i can assume you're about 14 or 13 years old, exploring the wide imaginary world called math.

Other people told you you're wrong, "You cant multiply infinity" "infinity is not as number", the usual stuff. Then you defended your post because you are "visualizing the concept of infinity as the theoretical "number" of possibilities for a number or decimal, or "numerical infinity"".
 

But i think they are missing the point.
 

But that part will come later- first we need to go back.

30 minutes before writing this post, i came across your post. I started reading, and i got furious. "How could you write those thing?!" i thought to myself. "Is this guy out of his mind?! what is he doing?! you cant use infinity like that, you just cant!!"

you reminded me of a guy i came across on the internet- a fanatic guy that didnt finish highschool. That guy, seemed to appear in every math forum that mentioned his name. Whats interesting about him, is he had some interesting claims like the claim we can only infer things about math by trying those things in the real world- He came up with a really weird theory, using unprofessional, invented words to express some of his ideas- one of them, that was a direct result of his previous theorem- was that pie is not constant. The way he "proved" it was probably drawing circles in his office.

He had some other, weird ideas. But the most irritating thing about him, was he was never wrong. Every time someone tried to tell him why, He posted something he already posted, or explained why he's right using his broken logic.

I remember one of those people told him that math is not about measure, and that geometry is a mathematical thing that cant be proven using real life, but using math. The guy's response was "if this is the way of mathematics, this is not my way", and that mathematics and the "geometric reality" are different.

He wasnt a university student, but that didnt stop him from arguing with professors and genuises.

And you remind me of him in a certain way. the way you try to create your own math.

But i guess that's fine, because you are young and cant really start learning advanced mathematics. We all stumble sometimes, especially when we are thirsty for knowledge but cant get it.

Oh right, i almost forgot! i promised my part about why they're wrong-

What the other people that answered your question didnt understand is, the problem with your post is NOT the fact you cant multiply infinity, but another thing-

You think the wrole "combinations" thing applies to infinity as well. But it doesnt. And even if it did, you made some serious mistakes.

Here's an example: you said the number of "combinations" of numbers with all the decimal places up to the n^th place is infinity*10ⁿ. But by that you just proved that the "infinity" you defined in your post, multiplied by any number, is infinity! why? what you said is, there are infinity combinations for the integer part of the numbers and 10 combinations for every decimal place, making infinity*10*10*10......(n times)*10=infinity*10ⁿ combinations. Here's another way to aproach this: Every number with n decimal places can be written as x/(10ⁿ) when x is an integer. in addition, every number that can be written as x/(10ⁿ) is a number that can be written with n decimal places. That means the number of combinations is the number of combinations for the x in my formula=infinity. Therefore infinity=infinity*10ⁿ. 

Then your broken logic somehow concluded that 10*10*10.....=infinity. I know it looks "obvious", but you cant just say it without defining it, although the only way you defined infinity was "The number of combinations for an integer". You cant just say that. You have to prove it.

Another problem with your post is YOU DIDNT DEFINE INFINITY*INFINITY. Ok, So, somehow infinity*10*10*10.... is infinity squared (Suppose you actually proved it). What the h**l does it mean? what the h**l does "infinity squared" combinations mean? is it an infinite number of squares? is it the proof god exists? is it a banana?

I appreciate your interest in mathematics, i really do. But you have to understand that mathematics is a precise subject. You have to prove things strictly, and make sure you define EVERYTHING.

(12*9)/2

108/2=54

what a strange question.

4(sin^4 30^o+cos^4 60a^o)-2(cos^2 45^o-sin2 60^o)  -    [4(sin^4 30^o+cos^4 60a^o)-2(cos^2 45^o-sin2 60^o)] =0

perhaps you want to know what the value is ...

\(4(sin^4 30^o+cos^4 60a^o)-2(cos^2 45^o-sin2 60^o)\\ =4(\frac{1}{2^4}+cos^4 60a^o)-2(\frac{1}{2}-sin2 60^o)\\ \text {interpretation of meaning (possible errors)}\\ =4(\frac{1}{2^4}+cos^4 60^o)-2(\frac{1}{2}-sin^2 60^o)\\ =4(\frac{1}{2^4}+\frac{1}{2^4})-2(\frac{1}{2}-\frac{3}{4})\\ =4(\frac{2}{2^4})-2(\frac{-1}{4})\\ =\frac{1}{2}+\frac{1}{2}\\ =1 \)

so

4(sin^4 30^o+cos^4 60^o)-2(cos^2 45^o-sin^2 60^o) -1 =0

This is definetly the right answer!!