All Answers 358108 Answers

If the probability that an object is acceptable is 0.70, and it is assumed that the probability of whether or not an object is acceptable or defective is independent from whether or not other objects are wither acceptable or defiectime(that is, whether or not an object is defective does not influence whether or not any other objects are defective), I believe that the best answer is:

0.70 x 0.70 x 0.70  =  0.343  34.3%

If there were only 100 objects to choose from and 70 are know to be accepable, then 70/100 x 69/99 x 68/98 would be the correct way to proceed; however, if this is a production line that may create thousands every hour, then 0.70³ is a better estimate.

Everything is easy when you know how and you have the right tools :))

Thank you for that update Heather.  

The Queen always need to be kept informed of all Camelot's proceedings.

Yours truely

Queen Melody I    (I was Queen Guinevere but now I have yet another identity)   I like it!  

$$\\\\\\$Ok let's take this slow...$\\\\\\
$So if 23 beats for every 15 second we need to find out per minute$\\\\
$15\times\mathbf{4}=60$\\\\
$So\;then\;we\;do\;23\times\mathbf{4}=92$\\\\
$\;92\;beats\;per\;minute,\;so\;92\times60\;for\;an\;hour$\\\\
5520 beats per hour\\\\
5520\times24 = for\;a\;day = 132480\\\\
132480\times365=3179520\\\\\\
3179520\;beats\;per\;year\;is\;your\;answer\\\\$$

Let the number she sold be X

She made 2 more than she sold so she made X+2

She sold X at $7 each so that is a total of 7X dollars

She made X+2 at $3 each so that is  3(X+2)  dollars

So her profit was 7X-3(X+2) and that was equal to 74

7X-3(X+2) =74

7X-3X-6=74

can you finish it from here  ?          

Wow you made that look a lot easier...

Slope is (Y2-Y1)/(X2-X1)  that is (4 +2)/(6-3)=6/3=2. Note that you can do these gradient calculations  the other way around and obtain the same answer. That is (-2-4)/(3-6)= -6/-3=2,as before.

6.454552e+24

correction, prob is 70/100 x 69/99 x 68/98. Approx 33.85%.

sorry xerxes,answer is simply     1metre/2pi.

Here's the solution; let Earth's circumference be 2pi R. New circumference then is 2pi (R + delta R) where delta R is the height we want to find.

so 2pi R + 1 metre= 2pi(R+ deltaR),the 2pi R 's cancel out,giving 2pi delta R = 1 metre,so delta R,the height,is 1 metre /2pi. We did not need to know the Earth's circumference in order to solve the problem.

@@ End of Day Wrap   Mon 11/5/15   Sydney,   Australia Time    12:40am (Really Tues) ♪ ♫

Hi all,

The 11th May is a great day because exactly one year ago today CPhill became a moderator of this site.  I was going to put up balloons but Chris likes marbles a whole lot more.  So here is a gift, from all the members, for you Chris.  

It has been a wonderful year.  Thankyou Chris for helping me shape this forum into its present form.  It is a place that you, I, Alan and all the members can be very proud of.  

Today our wonderful answerers were DarkBlaze347, Alan, MrGenius, CPhill, Rayhan, Awesomeee, TitaniumRome, xerxes, Badinage and Mathcad.  Thank you all :)

If h is the height it can be lifted, then we have:

Original circumference = pi*d  where d is diameter of the earth.

New circumference = pi*(d+2h)  since the new diameter is d+2h.

New - Old circumference:  pi*(d + 2h) - pi*d = 1m so that pi*2h = 1m  or h = 1/(2pi) m or h ≈ 0.159m

(xerxes, your next to last line should say "We have ∼0.3197 meters more).

.

Mathcad, you might want to note that 31! = 0 mod(31)  not 30 mod(31)  (i.e. it is exactly divisible by 31).

Wilson's theorem says that 30! = 30 mod(31).

.

I know, I realised that. Another thing I leant today - however, I am pretty sure they taught me that you can't get a root if the radicant is negative.

it would just work with odd denominators, wouldn't it? 

Tues 12/5/15

If you would like to comment on other site issues please do so on the Lantern Thread.  Thank you.    

FTJ means 'For the juniors' 

Interest Posts:

d = 12 472km

r = 6 236km

p = d * pi = $${\mathtt{12\,472}}{\mathtt{\,\times\,}}{\mathtt{\pi}} = {\mathtt{39\,181.943\: \!575\: \!571\: \!901\: \!270\: \!1}}$$

Let's add a meter:

(1m = 1/1000km)

$${\mathtt{39\,181.943\: \!58}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{1\,000}}}} = {\mathtt{39\,181.944\: \!58}}$$

And back to the diameter:

$${\frac{{\mathtt{39\,181.944\: \!58}}}{{\mathtt{\pi}}}} = {\mathtt{12\,472.000\: \!319\: \!719\: \!393\: \!786\: \!5}}$$

We have ~3.197 Meter more.

We can lift it now by 1.5985 Meter on each side. 

What I did was perfectly valid Xerxes,  even Alan got the same real answer as I did.  

I never managed to work out paint at all and it has been on my computers for ever!

Or you could just writie it as xy

Either way there is an invisable * sign  

Mathcad is right but there is really more than 1 slant height.  

And, what kind of Pyramid is it anyway.  

Just use Pythagoras.The slant height is the hypotenuse of the triangle where the other 2 sides are the vertical height of the pyramid,and half the length of the base.

Mathcad, what makes you think that there were 70 to start with?