Melody

It is more confusing becasue some of what is written is WRONG.  

There are 20 ways that this can happen

and there are  6*6*6 = 216 different possible rolls     

              6 choices for the 1st roll, 6 for the second, 6 for the third = 6*6*6 different outcomes  (order definitely counts)

P(that it WILL happen ) =    \(\frac{20}{216}\)

P( that it  DOES NOT happen ) =   \(1-\frac{20}{216}\)

P( that it WILL NOT happen twice in a row  ) =  \((1-\frac{20}{216})^2\)

Does that make more sense? 

I do not think there is any solution

How many values of r are there such that floor(4r) + r = 15.5?

Let  r = K+t       where  K is a positive integer   and   0<=t<1      (t for tiny)

\(\lfloor 4r\rfloor + r = 15.5\\ \lfloor 4(K+t)\rfloor + K+t = 15.5\\ \lfloor 4K+4t\rfloor + K+t = 15.5\\ \text{t is the only non integer so t=0.5}\\ \lfloor 4K+2\rfloor + K= 15\\ 4K+2+ K= 15\\ 5K= 13\\ K=2.6\\ \text{But K has to be an integer}\\ \text{That is a contradiction}\\ \text{Therefore there are no solution.}\)

I thought you probably did that.

I am sure there must be a way to nut it out logically with minimal trial and error attempts.

But i expect using C++ is fun and effective :)

Let there be d ducks and c cows.

you know that  d+c=24

It is reasonable to assume ever duck has 2 legs so that is 2d   duck leges

Also there would be 4c   cow legs

Total legs = 2d+4c = 66

so

d+c=24         (1)

2d+4c = 66   (2)

solve simultaneously.

2*4 is 8  and   2*2=4

half means divide by 2 and the opposite of divide is multiply.

You are not meant to use a calculator at all.

You are meant to understand how to do it.

The number out the front is an approximation of a surd (since it is a surd it cannot be expressed as a rational number.)

hint 

\(cos(3 \pi)+isin(3\pi)=e^{3\pi i}\)

Thanks  

Did you have a logical method or was it just trial and error?

Maybe you just had a computer check all the combinations for you?

Let the entire distance be 3x

Normally that takes 180 minutes

speed would be  (3x)/180  =  x/60   miles per minute

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

Storm day

It would take 60 minutes to go the first distance of x

then

276-60 = 216 minutes to go the next leg of 2x

speed is   \(\frac{x}{60}-\frac{20}{60}=\frac{x-20}{60}\;miles\; per \;minute\)

speed = distance /time

\(\frac{x-20}{60}=\frac{2x}{216}\\ \frac{x-20}{60}=\frac{2x}{27*8}\\ \frac{x-20}{10}=\frac{x}{18}\\ 18x-360=10x\\ 8x=360\\ x=45 miles\\ Total \;\;distance = 3*45 = 135miles.\)

Can anyone see an easy way to do this?

You have asked 22 questions and you have not even once responded to an answer.

Why should people help you?