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_{. . . the only number that can evenly divide the them all is one. That's what I see, what did I miss?}

You didn’t miss anything. One is common to all of these numbers. See god is number one and he’s omnipresent; this is proof of his omnipresence.  

_{I'm not a mathematician. I'm a muslim.}

No kidding?  I’m not a mathematician yet, but I’m a pastafarian. Anyway, there is no reason you cannot be both. 

Pastafarians and the FSM and are very tolerant of other’s religious beliefs, including mathematical religious beliefs.  For example, I still make oblations to the god of my ancestors, The Banana Goddess, when I make banana daiquiris.  I make a special one, with 432 imperial minims of gold rum, and offer it to her. She usually doesn’t drink it, so I oblige as a high priestess pro tempore, and drink it for her.  Sometimes I offer it to a worthy soul.  It’s a great honor.

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_{I'm saying this about 19 because of the mention of the number 19 by God in The Holy Qur'aan as a number of significance. (74 : 30-31).}

Ok. What does significant mean in this context?   In statistics, “significant” means the calculated event occurred more often than chance. The higher the event counts are above the expected value the more significant the statistic, and the statistician has more confidence that it didn’t happen by chance. This means there is a greater confidence that it happens for reasons other than chance. It doesn’t mean it didn’t happen by chance.  

Let’s say (hypothetically) after several statistical analyses that 19 occurs 30 times more than chance and 20 times more than any other comparable text.  What does this mean? Does it mean a deity inspired the words?  Maybe, but someone could argue the deity is evil. Here’s how:

The verses you use from the Qur’an (74:30-31) and the verses following, explains that 19 is the exact number of angels (or demons) guarding Hellfire.  Hellfire is where Allah sends unbelievers and other evil people. Allah used 19 angles because 19 is used to represent evil and when you see 19, you should know it represents evil.  Allah tricked the writer of the Qur’an to use words that would cause 19 to occur 30 times more than chance, so that the future readers would be enlightened and know the text is really a cryptic presentation of satanic verses.  Statistical analyses support this theory.  (I don’t need statistical analyses to know this hypothetical more than probably pịsses you off, along with every follower of Islam. This sometimes happens when science meets religion. The two are often in conflict.)  

_{What is the chance, that the number that Qur'aan says is of significance, has so many relations between the sentence with which virtually all chapters of Qur'aan begins (In the Name of Allaah, The Most Beneficent, The Most Merciful)?}

The chance depends on how the relationships are analyzed, what values are assigned to what letters, how often the letters are used, how often the letters are used in relation to other letters, and how often words are used in relation to other words, etc.  Any of these will bias the results towards or away from common divisors.

_{The chance of a random number being dividable by 19 with no remainder is small.}

It’s only small if 5.2631% is small.  

_{Also regardless of wether we just line up the values of the letters individually, suggesting that even swapping two random letters in the sequence, would make the sentence less compatible with the number 19.}

Swapping letters shouldn’t make a difference if you are summing the values.  Here is a numerical equivalent using ASCII decimal codes, Here, GOD = 71, 79, 68. Adding these numbers gives 218. In this context, GOD equals DOG because both equal 218. Cats are usually annoyed by this; they think GOD should equal CAT.  Dogs, of course, do not have a problem with this.

Here’s is one of my favorite numerical analysis using (appropriately enough) the ASCII code. 

The founder of Microsoft is Bill Gates III. Here’s a proof he’s in league with the devil!

By converting the letters of his current name to the ASCII values and adding his III (proof this it is not just any Bill Gates), you get the following:

B        I        L       L          G        A      T         E         S        III

66 +  73 +  76 + 76  +   71  +  65 +  84  +  69  +  83 +  3  =  666

This is the beginning of humanity’s ultimate and total enslavement.

Here’s more proof

M S  - D O S   6 . 2 1

77+83+45+68+79+83+32+54+46+50+49 = 666

W I N D O W S 95

87+73+78+68+79+87+83+57+53+1 = 666

You have to add 1 to this because it only equals 665 if you don’t. 665 is an evil number anyway, but 666 is more recognized.

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_{It sure doesn't look to me like someone was sitting and looking at a list of numbers dividable by (up to 62 digits) and hoping to find something that would match. Rather I think, if someone would get more creative, they would find even more astonishing "lottery wins".}

Actually, someone was. That someone was moi. As explained above, I did it so you would notice that one is common to all of these numbers.  You are right about more wins if you are more creative. The look on my father’s face, when he saw the bible code results, was a big win.  That wasn’t a big of a win compared to faking a pregnancy when I was 16. That was second in drama only to my faking a suicide when I was 13. Creativity does give more astonishing lottery wins, for sure. 

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_{The refering of all these things to chance is completely fine by me, if one is one hundred percent sure, that his world view is unshakeable. The matter of the fact is, that most people's arent.}

I don’t know anyone who is one hundred percent sure of his or her worldview. I do know a few who act as if they are – at least when expressing certain opinions.  I change my opinion about ideas and concepts all the time. New information comes in to view every day. My perception changes over time. Thinking is a dynamic process; at least it is supposed to be.  My perception of the world is very different compared to when I was a child and it’s different from just a few months ago.  

_{There are plenty of flaws in the idea, that we are advanced chimps.}

For the record, I never said that.  I have said that I am a genetically enhanced chimp. We are different from humans. For one thing, we have opposable big toes. This comes in very handy when playing a piano piece written for four hands. In this case, one chimp equals two humans.  You should see us type!

_{When we say, that we have 98% in common with chimps DNA-wise, that is based on a flawed understanding of DNA. Back when this was discovered, the general idea among scientists was, that only that 1,5% of the DNA was significant. Since then we have found many tasks being governed by the other 98,5% of the DNA-string, and therefor now when we compare the DNA of a chimp and a human, we should make a comparison of the whole DNA-string, leading to a significant drop in similarity compared to only comparing that 1,5% that actually almost matches.}

That discovery was more than 35 years ago, and the range is 95% to 98% common DNA.  It seems reasonable the humans who discovered this would also figure out the details of how the assemblies function as well as the lengths of sequences. They did.  The mitochondrial DNA (mtDNA) )—originally thought to be “junk” DNA, controls this assembly more than the other nuclear DNA.  Even at the low end of the DNA spectrum, chimps are more closely related to humans than they are to any other animal, including gorillas.   

_{I could go on with the rest of the flaws in the theory of evolution, but I'm here for the math, and particularly the chance of such a sentence having meaning.}

I’m sure you could go on about the flaws, there are many. The germ theory has many flaws too. Girolamo Fracastoro proposed the germ theory in 1546 and it’s well older than the Darwinian theory of evolution (1858). If we fully understood it, we wouldn’t have germ-based diseases anymore. Even with these flaws, we still know there are germs, and we still know how to control them enough to prevent and cure many diseases.  

The DNA theory is a separate branch of science, and it well more corroborates rather than contradicts the veracity of Darwinian evolution theory.  To my knowledge, when there are conflicts, the Darwinian evolution theory is updated to reflect the DNA theory. 

_{Thanks for a comprehensive answer, though. I still hope, that a master of statistics would tell me how to calculate it.}

You’re welcome. I hope you find what you are looking for. 

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Maybe this will help:

sum of tetrahedron edges = red line + orange line + yellow line + green line + blue line + purple line

red line = \(\sqrt{3^2+2^2}=\sqrt{13}\)

orange line = \(\sqrt{3^2+4^2}=\sqrt{25}=5\)

yellow line = \(\sqrt{2^2+4^2}=\sqrt{20}=2\sqrt5\)

sum of tetrahedron edges = \(\sqrt{13}+5+2\sqrt5+3+2+4=14+\sqrt{13}+2\sqrt{5} \approx 22.078\)

The compact disc format has been declining in popularity, and one music executive has predicted that CD sales will decrease by 15% per year. If the executive's company sold 29,000,000 CDs this year, how many will the company sell 7 years from now?

\(FV=29000000(1-0.15)^7\)

29000000*(1-0.15)^7 = $9 296 736 in the year

Hmmmmm..I think that yours is a much better approach than mine..

Mine does assume that you can cut a piece and glue it on. Why not cut off a bunch of pieces and use them all to make a box..instead of throwing paper away. And on mine, for the four littler prisms, you could use some of the old paper that you cut off from other prisms to make the bases.

\(\frac14\div\frac58=\frac14\times\frac85=\frac{1\times8}{4\times5}=\frac8{20}=\frac25\)

I can try to explain my answer more thoroughly 

Here I have shaded in the middle triangle and labeled points A, B, and C.

The yellow section is half of the area of the circle MINUS the area of the gray triangle.

area of the circle = π * radius²

area of the circle = π * (4)²

area of the circle = 16π   sq. cm.

area of the gray triangle = (1/2) * base * height

the base = 8 and the height = AO

Point O cuts line CB in half..OB = (1/2) * CB

Point A cuts line OB in half..AO = (1/2) * OB

We know line CB = 8....so OB = (1/2) * 8 = 4... and.. AO = (1/2) * 4 = 2

So, the height = 2,  and the base = 8.

area of the gray triangle = (1/2) * 8 * 2

area of the gray triangle = 8   sq. cm.

The yellow section is half of 16π MINUS 8 sq. cm.

yellow section = (1/2) * 16π - 8

yellow section = 8π - 8   sq. cm.

Solve the equation for x, and then set the denominator = 0. Whatever y value makes the denominator = 0 is not attainable.

y = \(\frac{1-x}{2x+3}\)               Multiply both sides by (2x + 3)

y(2x + 3) = 1 - x     Distribute
2xy + 3y = 1 - x     Add x to both sides.
2xy + 3y + x = 1    Subtract 3y from both sides.

2xy + x = 1 - 3y     Factor out an x on the left side.
x(2y + 1) = 1 - 3y   Divide both sides by 2y + 1

x = \(\frac{1-3y}{2y+1}\)

Now set the denominator = 0 and solve for y.

2y + 1 = 0

2y = -1

y = \( -\frac12 \)

Therefore, the value of y that is not attainable is \( -\frac12 \)

How can I factorize it using imaginary numbers?

There is only one correct way to interpret a math problem. You probably just made a careless mistake somewhere. For this, just remember to work on the inntermost brackets each step, and multiplication/division comes before addition/subtraction. 

-11 + 2(-5 - 6(-1 - 3(2 - 7) ) )

-11 + 2(-5 - 6(-1 - 3(-5) ) )

-11 + 2(-5 - 6(-1 - 3(-5) ) )

-11 + 2(-5 - 6(-1 - -15) )

-11 + 2(-5 - 6(14) )

-11 + 2(-5 - 6(14) )

-11 + 2(-5 - 84)

-11 + 2(-89)

-11 + 2(-89)

-11 - 178

-189

Ah something is slightly off..the diagonal must be longer than the length of the sides...!

I think you forgot a one zero at the end...it should be

\(c=\sqrt{28800}=120\sqrt2 \approx 169.706\)      (meters)    

They interpreted your PEMDAS in a different way, just like in the way:

1 + 6(7 + 3). The calculator and you might have different answers: 70, and 61.

The two sides of the triangle are 120 "meaters" long.

Pythagorean theorem is as follows:

\(c^2=a^2+b^2\)

"a" and "b" are the sides. "c" is the diagonal.

So substitute the length in:

\(c^2=120^2+120^2\)

And simplify

\(14400+14400=c^2\)

\(28800=c^2\)

\(c=\sqrt{2880}\)

\(c=24\sqrt{5}≈53.7\)

Answer:

\(24\sqrt{5}\)    or    \(53.7\)

what is 4 to the 3power divided by 78 times 56 and divided by 925=?

\(\frac{4^3}{78}\times \frac{56}{925}\\ \frac{4^3}{39}\times \frac{28}{925}\\ \text{can't simplify any more}\)

What is the problem....  is every calc that ever was at you disposal broken?

Max, your use of the term "how can you not know" is condescending.

Since you want people to interact with you it is not a sensible choice of words.

Anyway,  I hope you get what you want from your chat site :)

A die is rolled 12 times Find the probability of rolling no more than 4 twos

Each roll is an independent event. So this is binomial probability.

You have to work out the prob of 

0 rolls of 2

1 rolls of 2

2rolls of 2

3 rolls of 2

4 rolls of 2

add then all together and subtract the answer from 1.

P(0 rolls of 2)=  \((\frac{5}{6})^{12}\)

P(1 rolls of 2)=  \( \binom{12}{1}(\frac{1}{6})^1(\frac{5}{6})^{11}\)

P(2rolls of 2)=  etc

P(3 rolls of 2)=

P(4 rolls of 2)=

etc

Factorize (x2 -0.7x+0.49) into two terms such that:  (x- something) (x- something)

I can see straight off that there are no real solutions to this.

There are imaginary solutions but you might not know about imaginary numbers yet.

look at the discriminant

\(\triangle=b^2-4ac=0.49-4*0.49<0\)

Hence there is no real roots so this cannot be factorised without using imaginary number :)

\left| x - \left| x-1 \right| \right| = \lfloor x \rfloor

\(\left| x - \left| x-1 \right| \right| = \lfloor x \rfloor \)

firstly

\(\left| x - \left| x-1 \right| \right| \ge 0\qquad \text{because it is an absolute value}\\ so \;\;\;\lfloor x \rfloor \ge0\\ \therefore\quad x\ge0 \)

so

\(\left| x - ( x-1 ) \right| = \lfloor x \rfloor\\ \left| x - x+1 \right| = \lfloor x \rfloor\\ 1 = \lfloor x \rfloor\\ 1\le x<2\)

A 4" by 6" by 8" rectangular solid is cut by slicing through the midpoint of three adjacent edges. What is the number of inches in the sum of the lengths of the edges of the tetrahedron that is cut? 

\(Sum \ of \ the \ lengths\\=\sqrt{3^2+2^2}+\sqrt{3^2+4^2}+\sqrt{2^2+4^2}\\=\sqrt{13}+\sqrt{25}+\sqrt{20}\\=\sqrt{12}+5+2\cdot \sqrt{5}\)

\(Sum \ of \ the \ lengths=12.936\)

  !

sum 1 to 10.   

Or 

10

1+9=10

2+8=10

3+7=10

4+6=10

+5

=55

I tried doing the math, isn't is 55? because 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9  + 10 = 1 + 10 ( 2 + 9) (3 + 8) (4 + 7) (5 + 6) ( 6 + 5) (7 + 4) ( 8 + 3) (9 + 2) (10 + 1) = 11 + 11 + 11 + 11  + 11 = 11*5 = 55