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Thanks guest and asinus, it is a fascinating cake and a great message but it is not my birthday  ......

Maybe I can have 2 birthdays this year      Cool!   

12*nCr(18,7)*(1/12)^7*(11/12)^11 = 0.0040925417608967

That is the probability of getting 7 in the same month but it includes the probability of getting 7 in 2 different months as well.  I mean it includes it twice.

So you would have to subtract

18C7 * (1/12)^7 * (11/12)^11    *    11C7 * (1/12)^7 * (11/12)^4 *  12C2 

nCr(18,7)*(1/12)^7*(11/12)^11*nCr(11,7)*(1/12)^7*(11/12)^4*nCr(12,2)=0.0000001463682172

I'm reasonably confident on the first part but have less confidence on the secontd part (the part to be subrtracted)

0.0040925417608967-0.0000001463682172 = 0.0040923953926795

Cringe

Congratulations to you Melody! Thank you for everything you do for us.

  !

What is the total length of the lines that Pat draws on the second piece of paper?

Hello Guest!

\(l=\dfrac{18}{2(3-1)}\cdot 2(16-1)=\color{blue}135\)

 The total length of the lines that Pat draws on the second piece of paper is 135.

  !

The functions are A, D, F

Do you understand what EP is telling you ?

Yes, yu wre right the first time.  c=0

so now you have    

\(f(x)=ax^2+bx\\ now \;what? \)

sub in the other 2 and you will get two equations that you can solve simultaneously to get a and b.

Give it a go and get back to us with what you have tried  

y = k x^1/4  

3 sqrt 2 = k (81)^1/4

   ^{k = sqrt 2}

y = sqrt 2 ( 4)^1/4  =   sqrt 2 (2²)^1/4  = sqrt 2   ( 2^1/2 ) =   sqrt2  sqrt 2  = 2

Don't give an answer just explain how I'm supposed to solve it.

The equation is... \({2 \over 3 } \times {3 \over 4 } \times { 4 \over 5} \times \space ... = {1 \over 500} \)

Notice that the 3s and 4s cancel out. The only number that will not get canceled is the denominator of the last fraction and the numerator of the first fraction (2).

This means: \({2 \over x} ={ 1 \over 500}\) and \(x = 1000\). 

Using the infor given, the final fraction must be \(999 \over 1,000\), meaning the sum is \(999 + 1000 =\color{brown}\boxed{1,999}\)

But remember....when f(0)    x = 0    so you get    a(0)^2 + 0 * x  + c       and this equals 'c'

                                                                                   AND you are told  f(0) = 0                        NOW what can you say about 'c' ?

https://web2.0calc.com/questions/geometry_85849

arctan (142/246) =  29.995 ~~ 30 degrees

Height is \(\sin(34) = {x \over 18}\)

Width is \(\cos(34) = {x \over 18}\)

is height and length the same also ty for teh answer :)

Using the equation:

 \(\sin(34) = {x \over 18}\)

\(18 \times \sin(34) = x\)

Evaluating this, we find the height is \(\color{brown} \boxed{10.06547226}\)

Now, doing the same thing, but with \(\cos(34)\) instead, we find the width is \(\color{brown}\boxed{14.92267631}\)

Ask me if you have any questions!

Maybe c=0 or ax^2+bx=-c?

Thanks EP

Hi Guest, it is really good that you are interacting with EP

Why don't you get an account and get known to us.  

In general, you will get a get a much better deal that way and it is really nice for us, (existing members) to have polite and keen students as a part of our community here.  

f(0)=0  what can you get from that?

Start with not using   478

   then you have  2 x 2 x 2 x 2 x 2 = 32   combos

then you can have  ONE  8      or  ONE 7     or  ONE  4      each in one of the 5 positions = 15     the other 4 positions 2 x 2 x 2 x 2   possible

                                 15  x 16 = 240

then you can have TWO of the 4 7 8       47    74    78   87   48   84             5 C 2   x 6 = 60

     the other three positions  would be   2 x 2 x 2 = 8 

           60 x 8 = 480 

you can have all of 4 7 8    in 6 orders   x   5 C3 = 60    the other two positions filled by 2 x 2

                                       4 x 60 = 240

Summing the reds =      992  possible numbers         ( same answer guest found !)

In cases such as this one, it is often a lot easier to compute the combinations first, then convert them into permutations as follows:

(22222, 22223, 22224, 22227, 22228, 22233, 22234, 22237, 22238, 22247, 22248, 22278, 22333, 22334, 22337, 22338, 22347, 22348, 22378, 22478, 23333, 23334, 23337, 23338, 23347, 23348, 23378, 23478, 33333, 33334, 33337, 33338, 33347, 33348, 33378, 33478) >>Total = 36 combinations.

These 36 combinations break down as follows:

2 Ccombinations  x   1 Permutation each == 2P

8 C x 5P ==40P    

2 C x 10P ==20P  

12 C x 20P ==240P     

3 C x 30P ==90P  

8 C x 60P ==480P  

1 C x 120P==120P  

Total combinations ==  36

Total permutations == 992

Thanks Alan  

Here is a better place to start:

On the 'Home' page ....go to the 'About'  then  'Imprint'   tab for contact info......

Both stations have rising prices, but B is rising more slowly and is now  likely less than A ....so go to B .

FALSE     perpindicular lines cross at 90 degree angles