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I'm used to some different terminology, but I believe the "retail merchant margin" is the same thing as the percent "mark-up" on the price.' This is given by.....

(Sales Price - Cost) / (Sales Price)  = (34 - 26)/34 = about 23.6%

And the margin on the cost is - I believe -  the same thing as the percent "mark-up" on the cost...this is given by....

(Sales Price - Cost) / (Cost) = (34 - 26)/26 = about 30.8%

Here is a copy of an urgent telegram message I sent to Chimp Darwin:

This was sent via telegram because Chimp Darwin is in a very primitive place.

To Chimp Darwin

I may have discovered another candidate for our missing link species study stop

This one seems lower on the evolutionary scale than the other one we tried to recruit stop

This one will not even make a good bartender stop The other one could at least remember his password (which is actually too bad) stop

Several aspects make this one interesting stop

He has a marine cnidarian of the family Physaliidae as an avatar stop but doesn’t comprehend underwater distances from the surface stop

His eyes brain stomach and every other organ seems to be their own animal stop

The tentacles sting and this is worse than throwing p**p stop

We will need plankton because he probably won’t eat bananas stop

I have Fishin’ Chimp but bring fish and chips I’m hungry stop

Unique opportunity stop Don’t monkey around stop reply ASAP stop

Lancelot_Link (A.P.E.)

PS bring Decoder Ring stop

                                                       Fishin’ Chimp

Don't be upset with CPhill. He is a really nice guy. He thought you were abusing me and he just came to my defense.  I think that is really sweet.  :))

Thanks Chris :)

Oh, the decoder ring was a joke. :)

I mightn't do it like that 

I'd do it like this

$$\\tan x = -1\qquad $ Tan is neg it the 2st and 4th quad$\\
\frac{sinx}{cosx}=-1\\\\
$just think about first quad equiv for a moment$\\
tanx=1\qquad x=45 degrees\\\\
\\$And 180-45=135 degrees in the 2nd quad$\\
\\$And 360-45=315 degrees in the 4rd quad$\\
$therefore$\\
$135 degrees and 315 degrees are the answers$\\$$

Thank you Britishrain.  :)

Ah, thanks for the correction!!!!!!    I'll do an edit.....!!!

Just use the on-site calculator....hit the "2nd" button and then "atan" and key in "-1"...then, hit "="

Note that if we're in the interval [0, 360] degrees.....the arctangent = -1 at 135 degrees and at 315 degrees...!!!

Phil, you multiplied 2* (-x) and got -4x.  Should be -2x and that makes the answer -2/5.

I can't get 3.1 out of that.....it looks like you're taking the square root of a negative...also, there are an unequal number of parentheses......????

(-2)⁶ / 4³  =   64 / 64  = 1

Convert the % to a decimal and multiply

For instance, 60% of 120 =

.60 x 120 = 72

1 nanosecond= .000000001seconds x 1hr/3600seconds x 1 day/24 hrs x 1yr/365days =

0.0000000000000000317 yrs

Excuse me?

3(x+2)=2(2-x)  simplify

3x + 6 = 4 - 4x       add 4x to both sides and subtract 6 from both sides

7x = -2                  divide by 7 on each side

x = -2/7

--------------------------------------------------------------------------------------------------------------

Edited answer....

3x + 6 = 4 - 2x       add 2x to both sides and subtract 6 from both sides

5x = -2                  divide by 5 on each side

x = -2/5

I hope not....if you had any more to say....I'd have to pull out my "secret decoder ring"

i am perfectly calm im not mad at all it was a question i was wondering if she was trying to be mean becuase i didn't want to get at mad at her for something so wasnt trying to do and im not mad becuase she said that she wasn't trying to be mean so would you like to end the conversation here i dont feel like there's anything more to say

Excuse me, britishrain (maththis???)....I believe Melody gave you a compliment....she was just trying to help you out with your answer........geesh !!!!........let's calm down.......!!!!!

i have another account on this website becuase if i dont write my username and password down i forget and on my account mathis i didn't write them down so i forgot my password so this is my other account

other account??  Why are you useing 2 accounts  (especially on the same question)

Now I really am confused LOL.  :)

I am trying to be nice!

I certainly do not think that you are stupid!

Most of these questions get answered by the same few people.  

It is great when other people like yourself also offer some answers.

btw [by the way] this is my other account

are you trying to be nice? or do you think im stupid!

Using cos^(x/2) = [1 + cos(x)] / 2

Then

2 * [1 + cos(x)] / 2 = cos(2x)  →

1 + cos(x) = cos(2x)  →

And using  cos(2x) = 2cos^2(x) - 1

1 + cosx = 2cos^2(x) - 1    →

2cos^2(x) - cosx - 2 = 0

let x = cosx

2x^2 -x - 2 = 0     .....using the on-site solver......

$${\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{17}}}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{{\mathtt{4}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{17}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}{{\mathtt{4}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{0.780\: \!776\: \!406\: \!404\: \!415\: \!1}}\\
{\mathtt{x}} = {\mathtt{1.280\: \!776\: \!406\: \!404\: \!415\: \!1}}\\
\end{array} \right\}$$

So, using the cosine inverse, and ignoring the second answer, we have.....

cos^-1 [(1 - √17)/4] = x ......  so x = 141.331°  and x = 218.668°

After simplifying all the multiplications and divisions, you get:

Numerator:  ln(20) * log(5) * log(e) * log(2) * log(100)

Denominator:  log(20) * log(25) * log (16)

The change of base formula says that ln(20) = log(20) / log(e)

         so log(e) / log(20)  =  1 / ln(20)

         so ln(20) * [log(e) / log(20)]  becomes ln(20) * [1 / ln(20) ]  =  1

Now, the numerator that we have left is:   log(5) *  log(2) * log(100)

the denominator is:                                 log(25) * log(16)

Now, log(100)  =  2   and    log(25)  =  log(5^2)  =  2log(5)    and    log(16)  =  log(2^4)  =  4log(2)

Making these substitutions, we have:

Numerator:  log(5) * log(2) * 2

Denominator:  2 * log(5) * 4 * log(2)

Cancelling, we end with:  1/4

$$\\2(2)^2+3(-3)^2\\
=2*4+3*9\\
=8+27\\
=35$$