All Answers 358149 Answers

Lots and lots

or maybe just 1 - It is in the middle more or less. 

Thanks heureka, it worked a treat although the progam did advise me to enter another line as well - then all errors were gone.

I am not sure what you mean.

A translation is a slide.  The 2-dimensional shape can be slid in any direction but it can not be rotated or reflected.

So, for instance, it you added 2 in the x direction and 6 in the y direction you would have to do the same for all the points.

does that help?

I don't understand the question I am sorry.

It could have been worse for the donkey I guess.

https://www.youtube.com/watch?v=KCrROBbIPnY

The vectors are in the third quadrant and their angles with respect to the horizontal axis are obtained from tan(angle)=y_value/x_value, so the angle between them is given by:

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{\left(-{\mathtt{4}}\right)}{\left(-{\mathtt{5}}\right)}}\right)}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{\left(-{\mathtt{3}}\right)}{\left(-{\mathtt{4}}\right)}}\right)} = {\mathtt{1.789\: \!910\: \!608\: \!246}}$$ degrees

or 1.8° to the nearest tenth of a degree.

@@ End of Day Wrap - Friday 16/5/14   Sydney, Australia Time 22:15

Hi everybody,

I almost forgot to do the wrap!  That doesn't happen often.

Lots of great answers today from reinout-g, heureka, zegroes, CPhill, Alan, winnie and SpawnofAngel.  Thank you so much.  I'd especially like to thank Chris (CPhill).  Chris has been answering questions all day long. He does this regularly without complaint and I really appreciate it.  There is not any appreciation expressed my most of the question askers, that is true, but there are a few who express their gratitude and they make a big difference to the moral of the answerers.  Today 3 of these people were AngelAmy, zegroes and chilledz3non.  We thank you very much.

Reinout-g has been looking after our brain teasers and puzzles.  Notification of new ones are posted on the forum but they can always be found in with the sticky topics in the bottom right corner of the screen.  There are  some great puzzles in there - take a look. Thank you reinout for looking after the puzzles they are an important aspect of the forum!   If other people would like to post puzzles you are free to do so. If they are good I will give them a green puzzle icon and reference them in one of the puzzle threads.

Reinout also worked out how the individual post are referenced.  I might keep this till another time, there are a few more specifics that I want to work out.  Again, thank you reinout.

Once again heureka has presented some great answers with very impressive LaTex.  Thank you heureka!

I have been copying some of the Latex and some of the reference addresses over onto the LaTex thread which is located in the Sticky Topics. (Near the puzzles)

Lets see what posts we had today.

Difficult one

I just want to think about this some more.

The number of combinations of 3 from 16 is  16C3 = 560

We want 1 particular combination so the probability will be  $${\frac{{\mathtt{1}}}{{\mathtt{560}}}}$$

Different method of attack.  Same answer.

I think I'm onto something here!  

First, what is a nonstop?

for the first scenario you can have BBR, BRB, RBB

 $$\mbox{P(2 blacks and a red)=}3\times \frac{7}{16}\times \frac{6}{15} \times \frac{5}{14}=\frac{3}{16}$$

Now I am not sure what the second part of your question is.

Do you want B1, B2, and R1  where all the reds and all the blacks have different numbers?

In this case it would  be 

$$\mbox{P(B1, B2 and R1)= }6\times \frac{1}{16}\times \frac{1}{15} \times \frac{1}{14}=\frac{6}{3360}=\frac{1}{560}$$

I am not particularly good at probability but I think that is correct.

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

16! is the number of different ways the 16 nonstops can be ordered.  Assuming that they are all different from each other.  We don't care about that, we are only concerned with 3 of them.

Cardinal numbers are counting numbers 1,2,3,4,  etc

If I wanted the set of cardinal numbers between 8.6 and 15.19 then the answer would be

{9, 10, 11, 12, 13, 14, 15}

So that is an example of a cardinal set.

However 

The cardinal number OF the above set is 7 because there are seven elements in the set.

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

I would like another mathematician to comment on this answer.  I have done very little work with set notation etc.

a television company charges $36 per month and increases it by 15% what is the rate now?

You need to know this     $$15\% =\frac{15}{100}=0.15$$ 

Now there are 2 ways.

15% of 36 = 0.15*36 = $5.40   This is the increase.

New rate  = $36+$5.40 = $41.40

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

The other way is for you to recognise that the original cost is 100% if it is increased by 15% then the new percentage will be 115% = 1.15

115% of $36 = 1.15*36 = $41.40

The second way is quicker but some people find it harder to understand.

you do this

Hallo Melody,

use

\usepackage{pgfplots}

Bye

heureka

Thanks anonymous and Heureka!

Hi Chris, 

Thanks for providing us with this challenge.

I would however like you to move it onto a new post in the body of the forum and put the green puzzle icon next to it.    It can then be referred in one of the puzzle threads.

An alternative would be to just put it straight into a puzzle thread in the first place.  I think that is what reinout-g has been doing.  

You may like to talk to reinout about how he would like it done.  He is in charge of the puzzles.

Thanks, Melody.

P.S. I use this thread just to 'jot' down ideas and posts that I am likely to use in the 'End of Day Wrap'

It is just a bits and pieces thread.

More Latex by Heureka:    

$$\\\left(
\frac
{
1\;glass\
}
{
\frac{1}{8}\;\textcolor[rgb]{1,0,0}{\not}l
}
\right)*
\left( \frac{2.5\;
\textcolor[rgb]{1,0,0}{\not}{l}
}
{1\;bottle} \right)=2.5*8\;\frac{glass}{bottle}=20\;\frac{glass}{bottle}\\\\
\Rightarrow 20\;\mbox{glass per one bottle}$$

\\\left(
\frac
{
1\;glass\
}
{
\frac{1}{8}\;\textcolor[rgb]{1,0,0}{\not}l
}
\right)*
\left( \frac{2.5\;
\textcolor[rgb]{1,0,0}{\not}{l} 
}
{1\;bottle} \right)=2.5*8\;\frac{glass}{bottle}=20\;\frac{glass}{bottle}\\\\
\Rightarrow  20\;\mbox{glass per one bottle}

By Heureka

$$\\\left(
\frac
{
150
\;\textcolor[rgb]{1,0,0}{\not}c\textcolor[rgb]{1,0,0}{\not}m
}
{
1\;rod
}
\right)*
\left( \frac{1\;piece
}
{1\frac{1}{4}\;\textcolor[rgb]{1,0,0}{\not}c\textcolor[rgb]{1,0,0}{\not}m} \right)=
\frac{150}{\frac{5}{4}}\;\frac{piece}{rod}=\frac{150*4}{5}\;\frac{piece}{rod}=
30*4\;\frac{piece}{rod}=120\;\frac{piece}{rod}
\\\\
\Rightarrow 120\;\mbox{pieces per one rod}$$

\\\left(
\frac
{
150
\;\textcolor[rgb]{1,0,0}{\not}c\textcolor[rgb]{1,0,0}{\not}m
}
{
1\;rod
}
\right)*
\left( \frac{1\;piece
}
{1\frac{1}{4}\;\textcolor[rgb]{1,0,0}{\not}c\textcolor[rgb]{1,0,0}{\not}m} \right)=
\frac{150}{\frac{5}{4}}\;\frac{piece}{rod}=\frac{150*4}{5}\;\frac{piece}{rod}=
30*4\;\frac{piece}{rod}=120\;\frac{piece}{rod}
\\\\
\Rightarrow  120\;\mbox{pieces per one rod}

This is what I get in Texmaker.  I did add the dollar signs but I don't think anything else is different.

Can you see what the prob/s are?    Thanks Heureka.

$$\\\left(
\frac
{
1\;glass\
}
{
\frac{1}{8}\;\textcolor[rgb]{1,0,0}{\not}l
}
\right)*
\left( \frac{2.5\;
\textcolor[rgb]{1,0,0}{\not}{l}
}
{1\;bottle} \right)=2.5*8\;\frac{glass}{bottle}=20\;\frac{glass}{bottle}\\\\
\Rightarrow 20\;\mbox{glass per one bottle}$$

\\\left(
\frac
{
1\;glass\
}
{
\frac{1}{8}\;\textcolor[rgb]{1,0,0}{\not}l
}
\right)*
\left( \frac{2.5\;
\textcolor[rgb]{1,0,0}{\not}{l}
}
{1\;bottle} \right)=2.5*8\;\frac{glass}{bottle}=20\;\frac{glass}{bottle}\\\\
\Rightarrow  20\;\mbox{glass per one bottle}

More great Latex from Heureka.  Thanks.

$$\\\left(0.084\;\frac{kg}{
\textcolor[rgb]{1,0,0}{\not}{w}\textcolor[rgb]{1,0,0}{\not}{e}\textcolor[rgb]{1,0,0}{\not}{e}\textcolor[rgb]{1,0,0}{\not}{k}
}\right)* \left( \frac{1\;
\textcolor[rgb]{1,0,0}{\not}{w}\textcolor[rgb]{1,0,0}{\not}{e}\textcolor[rgb]{1,0,0}{\not}{e}\textcolor[rgb]{1,0,0}{\not}{k}
}{7\;days} \right)=\frac{0.084}{7}\frac{kg}{days}=0.012\;\frac{kg}{days}\\\\
\Rightarrow 0.012\;\mbox{kg per day}$$

\\\left(0.084\;\frac{kg}{
\textcolor[rgb]{1,0,0}{\not}{w}\textcolor[rgb]{1,0,0}{\not}{e}\textcolor[rgb]{1,0,0}{\not}{e}\textcolor[rgb]{1,0,0}{\not}{k}
}\right)* \left( \frac{1\;
\textcolor[rgb]{1,0,0}{\not}{w}\textcolor[rgb]{1,0,0}{\not}{e}\textcolor[rgb]{1,0,0}{\not}{e}\textcolor[rgb]{1,0,0}{\not}{k}
}{7\;days} \right)=\frac{0.084}{7}\frac{kg}{days}=0.012\;\frac{kg}{days}\\\\
\Rightarrow  0.012\;\mbox{kg per day}

Thanks Heureka - More great LaTex too!

I've never used \not before.  I've use the cancel package but I don't think that works in here.

Have you ever used the Texmaker program.  I prefer to practice in there but I couldn't get your code to work in there.  I think i sent you a message.  Do you have any idea what the problem may be?

Thanks

Melody.

$${\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{9}} = {\mathtt{324}}$$

Thank you Francis and Company.  

I liked this unit of measurement!!

Mickey