1. For the first one, we have this many possibile outcomes :

C(20,3) * 10  = 11,400   ...so....the probability of winning on one ticket is  1 /11,400  = 0.0000877192982456 = about .0088%

Well I never !!!!!       ROF LOL

I like your treble cleffs Badinage.  Are you a musician?

No...I didn't like your answer.....because I don't.....LOL!!!!

100 because she had them

3155328000000

Didn't you like my answer Chris.    LOL

LOL, Melody!!!

Look at the general form of a parabola

y =a(x - h)^2 + k

Asymptotes occur where things are either undefined or where they reach some limit.....but, here......there are no bounds on x.  "y" is "bounded" .....in a sense......by whether the parabola is upward turning or downward turning.......but there are no "asymptotes"

yes i though that was right 

No... That's impossible, you can't have 71pi when donuts cost 2$ each. The first 5 numbers of pi are 31415 which is obviously the ZIP code of Savannah GA. Savannah is obviously the birthplace of Julliette Gordan Low, the founder of the Girl Scouts. What are the Girl Scouts known for? Cookies. America is known both for it's GS cookies and for all of the wonderful donuts we all eat. Sooooo... The units should obviously be in Diabetes!

>> what if it was d/dx( 2 + sin (30x))

= 30.cos(30x)  (Answer) 

$$\frac{d}{dx}\;[2+(sin30)x]=sin30 = 0.5$$

what if it was 2 + sin 30x 

Notice that sin 30 = 1/2......so  differentiating both things will result in "0"

Well if you have a kuko (to eat?) then you are probably not a kuko because that would make you a cannibal.

And, if you are not a kuko to start with then it would not make any sense to ask it you will stay a kuko. 

However, if you ask if you are a kuko under these conditions then you really must be a kuko.

I think this is an enigma.   

I got 72pi because there is a sale on donuts at krispy Kreme and there was a weather delay during Miguelito's trip.

@@ End of Day Wrap   Fri 10/4/15    Sydney, Australia    Time 10:25pm    ♪ ♫

Good evening :)

Great answers today from Mellie, Natthada, Civonamzuk, JaceXXmace, Garmoon, Geno3141, Alan, Badinage, Zoezelin, MathsGod1, CPhill and AmandaXo.  Thanks all. 

Interest posts:

FTJ means "For the Juniors"

Sat  11/4/15

FTJ means "For the Juniors"

Very nice anon - are you the same anon?

0!=1

I could just say that it is define that way which is certainly true.

or I could say that 0! is the number of ways that 0 items can be odered - that would be just one way.

Now

5C1 is the number of ways that 1 item can be  chosen from 5 it equals      $$^5C_1=\frac{5!}{1!(5-1)!}=\frac{5!}{1*4!}=5\\\\$$

5C0 is the number of ways that 0 item can be  chosen from 5 it equals  [the answer has to be 1 there is only one way of chosing nothing]

    $$\\^5C_0=\frac{5!}{0!(5-0)!}=\frac{5!}{0!*5!}=\frac{1}{0!}\\\\
$ the only way this can work is if 0!=1$\\\\
so\\\\
0!=1$$

Here's an  informal "proof"....

3! =  4! / 4

2! =  3! / 3

1!  = 2!/ 2

So, by extension

0!   = 1! / 1    = 1

S = Number of students

$300 per student + single grant = Funding

300S + 4000 = 124 900

300S = 120 900

S = 120 900/300 = 403

Therefore the number of students is equal to 403

I would tend to use a formula if the equation were more complex.

Nice answer MG,

Another answer:

you could just say     $${\frac{{\mathtt{170}}}{{\mathtt{16}}}} = {\frac{{\mathtt{85}}}{{\mathtt{8}}}} = {\mathtt{10.625}}$$

So he can work 10 full hours OR any number of hours just short of 10.625 hours  :)

Yes that is what they mean MG :)

sec[tan^-1(5/6)]

you should draw a right angled triangle to help 'see' what I say, let $$\theta$$ be one of the acute angles.

Let       $$\theta = tan^{-1}(5/6)$$

$$tan\theta=\frac{opp}{adj}=\frac{5}{6}$$

If the opp is 5 and the adj is 6 then hypotenuse is    $$\sqrt{25+36}=\sqrt{61}$$

$$\\sec\theta = \frac{hyp}{adj}=\frac{\sqrt{61}}{6}\\\\
$therefore$\\\\
sec[tan^{-1}(5/6)]=\frac{\sqrt{61}}{6}\\\\$$