All Answers 358150 Answers

I asume the total number of tickets is 10⁵

The chance that none of your 5 is drawn is approximately (1-5/10⁵)¹⁰⁰ = 0.99995¹⁰⁰

("approximately" because I've ignored the fact that a drawn ticket will not be replaced; but with such a large number of tickets the impact of this will be small).

Therefore the chance of you winning is p = 1 - 0.99995¹⁰⁰

$${\mathtt{p}} = {\mathtt{1}}{\mathtt{\,-\,}}{{\mathtt{0.999\: \!95}}}^{{\mathtt{100}}} \Rightarrow {\mathtt{p}} = {\mathtt{0.004\: \!987\: \!645\: \!188\: \!015\: \!9}}$$

or p ≈ 0.005

Yes, all 3 of you are very clever  

Great answer from Anonymous !!

Here's another possibility:

5 + 5 + 5 ≠ 550     (and that makes the equation "correct" ....well, at least in a "perverse" way!!!)

Draw a line on the first plus sign. This turns it into a 4! 

So then its 545 + 5 = 550

Thanks Rosala :)

I love all these pictures!

According to your predictions I must be the funniest 

Was hoping to also be the sexiest though

I liked that expression too Alan.  It may also make its way into my vocabulary !

I think that "There is more than one way to skin a cat.", must be a common phrase in many counties.  

Here's another.  "He is as crooked as a dog's hind leg"   Crooked means dishonest.

I think the "skin a cat" expression probably has more to do with the "cat-o-nine-tails" (a whip used to keep recalcitrant sailors in order in days of yore) than cute furry animals!

I must be mad, but I really like the expression "I can do this with two fingers up my nose".  From now on I shall use it whenever I can!!

Sorrry that is will and thx 4 the answ

Ai, that sounds awefully unpleasant.

Please don't skin the cat!

Several of our expressions sound very strange when you literally translate them such as;

it is a truth as a cow!

or

I can do this with two finger up my nose

or

That's as correct as a bus

So given 'all craziness on a stick' are there more english expressions that are funny or strange?

@@ End of Day Wrap:     Tues 16/9/14     Sydney, Australia      Time 7:20pm        ♬

Good evening all,
Lots of fantastic answers from DragonSlayer554, Alan, CPhill, Rosala, NinjaDevo, WinterGhost17, Reinout-g and lots form me.  Thanks everyone.

Here are some of the more interesting posts:

1) Rosala's Laughs.    (Thanks Rosala)

Wed 17/9/14

1) Reinout's Lunchbox unwrap.  Thank you  

In English the phrase is "All roads lead to Rome".  

There is another (rather unpleasant) phrase: "There is more than one way to skin a cat"

In NSW, Australia schools.  

If you are doing physics you have to use the physics formulas.

If you are doing mathematics you have to use calculus.

I think that our expression is "All roads lead to Rome".  

Aaah that explains a lot. All right, so we know the profit is the amount the watch sells for minus the amount the watch was bought for. From the initial $500 profit we know that the watch was bought for $2000-$500 = $1500. Given that the watch would now sell for $1800 we know there is a profit left of only $1800-$1500 = $300. The percentage of the profit with respect to the total selling price would be $300/$1800*100 = 16.67%

Reinout 

I'm not sure whether this is an English expression, but in Dutch we have the expression;

'there are several ways that lead to Rome'.

I think that it pretty much sums up these answers.

I didn't know the equation Alan used.

Melody's approach is one I hadn't directly thought of, but I think I like it better than sticking your nose into physics formulas 

I think that wipp is a typo for 'will'   LOL

I'm lost in the translation of your question. Might be because I don't know the abbreviation wipp...

Could you be more specific please :)

Note that the kinematics equations arise very simply from calculus:

dv/dt = a    

If a is constant then v = at + u (where u is v(0))

ds/dt = v so ds/dt = at + u so s = at²/2 +ut + s(0), and we usually set s(0) = 0, or redefine s as s-s(0), so

s = at²/2 + ut

We also have v² = (at + u)² = a²t² + 2atu + u² = 2a(at²/2 + ut) + u² = 2as + u²

For the last part, we again have

$$v = at$$

where v is the change in velocity.

For the ball going down, the change in velocity is given by.

$$v = 9.8*0.964 \approx 9.45 m/s$$

Since for the ball going upwards a = -9.8 and t = 0.964

the change in velocity for the ball going upwards is given by

$$v \approx -9.45m/s$$

For the ball going downwards, the speed has increased from 13.1 to 22.55m/s

This means that the current kinetic energy is given by

$$E_k = \frac{1}{2}mv^2 = \frac{1}{2}m(22.55)^2$$

Given question a, we knew the ball started with a total energy of

270.045 * m

Therefore the rest of the energy must be left as potential energy, or

$$\begin{array}{lcl}
E_p = 270.045* m - \frac{(22.55)^2}{2}*m = mgh\\
270.045-\frac{22.55^2}{2} = 9.8h\\
h = \frac{270.045-\frac{22.5^2}{2}}{9.8} \approx 1.73 \mbox{ meters}\\
\end{array}$$

For the ball going upwards we know the speed decreased from 13.1 to 13.1-9.45 = 3.65

The kinetic energy at a speed of 3.65m/s is given by

$$E_k = \frac{1}{2}mv^2 = \frac{m3.65^2}{2}$$

This means the rest has become potential energy.

Since we know $$E_t = 270.045$$

$$E_p = E_t-E_k = 270.045*m - \frac{m3.65^2}{2} = m*(9.8)*h$$

Therefore $$h = \frac{270.045-\frac{3.65^2}{2}}{9.8} \approx 26.88 \mbox{ meters}$$

The difference in height is therefore given by

26.88 - 1.73 = 25.15 meters

Reinout 

I think I'd just use v² = u² + 2as where v = final velocity (= 0), a = gravitational acceleration (-9.8m/s²), s = distance (= 6.5m)

0 = u² - 2*9.8*6.5

$${\mathtt{u}} = {\sqrt{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{9.8}}{\mathtt{\,\times\,}}{\mathtt{6.5}}}} \Rightarrow {\mathtt{u}} = {\mathtt{11.287\: \!160\: \!847\: \!617\: \!969\: \!5}}$$

initial velocity ≈ 11.3 m/s

Do you need it done by calculus?

Ok I might do it by calculus

$$\\\ddot y=-9.8\\
\dot y=-9.8t+v\\
y=-4.9t^2+vt\\
\mbox{max height when }\doty=0\qquad(y=6.5m)\\
-9.8t+v=0\\
v=9.8t\\\\
y=-4.9t^2+vt\\
6.5=-4.9t^2+9.8t^2\\
4.9t^2-6.5=0\\
t=\sqrt{\frac{6.5}{4.9}}\\\\
\mbox{Initial Velocity}=9.8\times\sqrt{\frac{6.5}{4.9}}=11.287\;\;m/s\\\\$$

Assume he gets heads h times; then he must get tails 20-h times. So

5*h - 3*(20-h) = 4

5h - 60 +3h = 4

8h - 60 = 4

8h = 64

h = 8

He threw heads 8 times.

The useful formulae here are the constant acceleration kinematics formulae, namely:

1.  v = u + at

2.  v² = u² + 2as

3.  s = ut + (1/2)at²

u is initial velocity, v is final velocity, a is acceleration, t is time, s is distance. 

So, we can use equation 2. to find the final velocity of the ball thrown vertically down (assuming no resistance due to air drag):

v² = 13.1² + 2*9.8*18.8

$${\mathtt{v}} = {\sqrt{{{\mathtt{13.1}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{9.8}}{\mathtt{\,\times\,}}{\mathtt{18.8}}}} \Rightarrow {\mathtt{v}} = {\mathtt{23.239\: \!836\: \!488\: \!237\: \!175\: \!2}}$$

So, velocity of first ball hitting ground is approximately 23.24m/s.

For the second ball the velocity as it hits the ground will be the same as it will lose speed as it rises and then regain the same speed by the time it gets back to the balcony, from where it will behave like the first ball to the ground!

To find the times use equation 3. for the first ball. and, for the second ball, equation 1. (setting v = 0) for the upward part of the flight and 3. for the downward part.