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Man, these are hard! I can't figure any of them out...

You mentioned that a_k can also be 0, but thats not true (unless n_k=1, but that leads to the answer P=3)

why? because then the prime you chose will be divisible by 3.

(3n₁)²+(3n₂)³+(3n₃)²+2*3*n₁*a₁+2*3*n₂*a₂+2*3*n3*a₃+a₁²+a2₂²+a₃²=

[((3n₁)²+(3n₂)³+(3n₃)²+(3n₃)2+2*3*n₁*a₁+2*3*n₂*a₂+2*3*n3*a₃)]+a₁²+a2₂²+a₃²=

3*(3*n₁²+3*n₂²⁺3*n₃²+a_3*n₃*2+a_1*n₁*2+a₂*n₂*2)+a₁²+a2₂²+a₃².

remember, a_k (k=1,2,3)=1 or 2.

there are 4 combinations for the values of the a's (3 1's, 2 1's, 1 1, or 3 2's).

all of the combinations are divisible by 3.

meaning, there is only one option- P=3.

g'(5) = 6

This means the slope of the tangent line we're after is 6.

g(5) = -3

This means the tangent line passes through the point (5,-3).

So now all we need to do is simply find the equation for a line with a slope of 6 that passes through the point (5,-3).

y = mx + b

Plug in what we know and solve for what we don't (in this case, b).

-3 = 6(5) + b

-3 = 30 + b

-33 = b

Now use the slope and y intercept to make the equation.

y = 6x - 33

"I assume prime triplets are any 3 consecutively prime numbers ....    Is that correct?    For now I will assume so."

"3 consecutive prime numbers" is a necessary, but not sufficient condition, Melody.  For example: 31, 37 and 41 are consecutive primes, but they don't have the form (p, p+2, p+6) or (p, p+4, p+6) that define prime triplets (as GingerAle pointed out above).

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Thanks Guest,

Ok lets look at this.   I am redoing your working in the hope that all becomes clear to me.  

First a definition:

Prime triplet . 

set of three prime numbers Which form of arithmetic sequence with common difference two is called a triplet prime .

\(\frac38=\frac{x}{100}\)

Now just solve for x.

\(\frac{3(100)}{8}=x \\~\\ \frac{300}{8}=x\)

37.5 %

PPMCC:  Pearson Product Moment Correlation Coefficient?

Don 't know of a simple way by hand other than slogging through the formula!

However, you could use the online calculator at: http://www.socscistatistics.com/tests/pearson/Default2.aspx 

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Yes it is.

It depends upon what we know about the triangle......

If we know two sides and an included angle between these sides, then Erlich's approach is correct.

If we only know the three sides, we can use someting known as "Heron's Formula"  which is

Area  = sqrt [ s * (s - a) * (s - b) * (s - c) ]

Where a, b, c are the sides and "s"  is the semi-perimeter given by

[ a + b + c ] / 2

This is a special type of question:

f(x)

what you have to in those questions is subtract f(x) from both sides and see when 0

you probably dont know what im talking about by now, so ill give you an example (The example you wrote here):

-8(11*x+6)+6(8+5x)=g(x)

2*x+x=3*x=f(x)

g(x)-f(x)=-8(11*x+6)+6(8+5x)-3*x=-88*x-48+48+30x-3*x=27*x-88*x=-61*x>0 add 61*x to both sides and get....

0>61*x divide both sides by 61

0>x

and thats the answer

heres another way to think about it:

if x multiplied by a negative number is bigger than 0 then it means x is a negative number.

why? because if 0 is multiplied by a negative number we get 0 (and 0 is not bigger than 0). if we multiply a positive number by a negative number we get a negative number (and no negative number is bigger than 0)

if we multiply a negative number by a negative number we get a positive number. positive numbers are bigger than 0 and thats what we need.

You cant find x and y if you know only one sides length and 1 angle. you cant solve it. you can express y using x tho.

You dont find it with the law of cosine....

you use the law of cosine to find the length of the triangle's edge. if you want to find the triangle's area you need to use the law:

sin(A)*AB*AC/2=area.

if 7x-12=3x then we can subtract 3x and add 12

4x=12 we can divide by 4

x=3

and thats the answer

a+(-b)=a-b

-a-b=0-a-b

What does M have to do with it? is "M

if thats right, then according to the law of cosines 

(AB)²=(CB)²+(CA)²-2(CB)*(CA)*(cos(M 2+13 ²-2*29*13*cos(41)=440.948976511858

(AB)²=440.948976511858

AB=(440.948976511858)^1/2=20.9987851199029607

therefore AB=20.9987851199029607

You forgot one ')', please correct it and ill try to explain ( there are 4 ('s and three )'s)

thank you for the answer. now i understand! thx

Mr. Banker, I was playing monopoly with my dog and cat again, just waiting for you chime in.

My cat was the banker this time and he hadn’t embezzled any money yet.  I asked him why and he said he was too excited about reading your newest post. For some reason my cat likes you. There is no accounting for his taste though; he likes mice and rats–especially rats. 

Anyway, to the point: while the formula you present here is correct, there isn’t any explicit time involved in this question. Nope, just orders (or invoices, if you prefer). It might be a day, a week, a month, or years between the orders.  Your presentation would only be correct if the owner generated one sales invoice per year.  If that’s the case, he should fire himself. Probably, he just needs to fire his banker.

 I understand that in banker theory, time equals money, but really, it’s what one does in time that counts.   The asker can probably figure that out though, he posted a reasonably articulated question, so he probably knows to substitute the order number for the time in this equation—which is impressive considering a banker didn’t.

You know, there’s a human who works for Lancelot Link’s A.P.E Company; he’s one of the very few humans in his employ. He’s the company’s principal investment banker.  Now, I would have thought that a genetically enhanced chimp would fill such an important position. I asked Lancelot why. He explained that while a genetically enhanced chimp would be vastly superior to a human, it would also be difficult to detect the sophisticated embezzlement schemes he would capitalize on. It’s much, much easier to catch humans. 

Chimp Loki discovered a genetic marker that is very common in human bankers and extremely common in investment bankers. I asked chimp Loki to explain. What he said was quite funny, but shocking–so shocking, I’m sure one or more of the moderators will delete it, after reading it –maybe while laughing.  Because of the deletion risk, I will include it in a separate post. 

The answer is 3

Proof:

P=3*n₁+a₁

Q=3*n₂+a₂

R=3*n₃+a₃

a1,a2,a3=1 OR 2

P²+Q²+R²=(3*n₁+a₁)²+(3*n₂+a₂)²+(3*n₃+a₃)²=(3n₁)²+(3n₂)²+(3n₃)²+2*3*n₁*a₁+2*3*n₂*a₂₊2*3*n₃*a₃+a₁²+a₂²​+a₃²​

If a₁=a₂=a₃=1 OR 2 the formula is divisible by 3.

same applies if one of them is 1 and if 2 of them are 1.

meaning it will always be divisible. but something here doesnt make sense right? thats right, if one if them is 3 it works. meaning one of them has to be 3. we already know none of them can be 2, and 1 is not a prime, so P=3 (always).

3 kilometers / 30 minutes = 0.1 kilometers / minute

0.1 kilometers per minute (or 6 kilometers per hour)

oh i'm sorry for the inconvience Melody. thank you for caring. and also for answering my question. it's just that i am a little too weak in math and somehow i'm not able to comprehend things a lot,forgive me. but thank you very much for your patience and i do know i was'nt very polite. and yes i'll put the link to the original thread next time. Thank you.

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Yes     \(\sqrt{-32}=-2\)

And that I think is the only answer BUT

if

\(x^5=-32\\ then\\ x=2cis(\pi+\frac{2\pi n}{5})\qquad n \in Z\\ x=2cis(\frac{5\pi}{5}+\frac{2\pi n}{5})\qquad n \in Z\\ x=2cis(\frac{\pi}{5}),\quad x=2cis(\frac{3\pi}{5}),\quad x=2cis(\frac{5\pi}{5}),\quad x=2cis(\frac{7\pi}{5}),\quad x=2cis(\frac{9\pi}{5})\\ x=2cis(\frac{\pi}{5}),\quad x=2cis(\frac{3\pi}{5}),\quad x=-2,\quad x=2cis(\frac{7\pi}{5}),\quad x=2cis(\frac{9\pi}{5})\\ \)

Sara I just answered this (on an earlier post) and now I see that CPhill has answered it too.

It is ok to make a new post requestingonce again that your question get answered, it is ok to say that you are not happy with your original answer/s,  but please include a link to the original question.

You do not need 2 moderators to answer your question, not both at the same time anyway!