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yea GM You have posted alot of word questions lately! 

*****

Nice,heureka  !!!!

1/1300  =  1/13 *  ( 1/100)  =  .00076923

The part in red is the repeating part with a period of 6

So

When  n  = 16

2 + 6 (16)  =  2 + 96  = 98 digits  to the right of the decimal point

So....the 100th digit will be the second digit in the period  =  7

Using  the square of the  distance  formula  we  have that

( 2a  -3)^2  + ( a -4  - (- 1) )^2  =  26      simplify

(2a - 3)^2  + ( a - 3)^2   =  26

4a^2 - 12a + 9  + a^2 - 6a + 9  = 26

5a^2  - 18a  - 8   = 0      factor

(5a  + 2)  (a - 4)  =  0

Set  each factor to 0  and solve for a

5a + 2  = 0                       a  - 4   =   0

5a   = -2                          a   = 4

a = -2/5 

And  the product  is    (4) ( -2/5)  =   -8/5

please help me! take your time if you'd like :)

a)  P ( VS  given   F  )   =   37 / ( 37 + 192)  = 37/ 229 

b)   P ( VS  and F)   =  37/700

c)  P ( VS or F)  = P(VS)  + P (F)  -  P (VS   ∩ F)  =  

                            (37 + 22 + 11)  /700  + (37 + 192)/700    - 37/700   =

                                [ 70  + 229  - 37 ] / 700  =  

                                               262/700   =   131 / 350

d) P ( F)  =  (37 + 192)  / 700  =   229 / 700

e)  P (VS)    =  (37 + 22 + 11)  /700  =   70 /700  = 1/10

f)  P ( F given VS ) =   37  / 70  

g)   Apparently.....those with military veteran status    have a more favorable view  of capital punishment  than those without  veteran military status

Those with  military status    have  a  probability  of  37/70   = about 53% of favoring capital punishment

Thos without  military veteran status  have  a probability of   192 / (192 + 204 + 234)  = 192/630 = only  about 30%  of favoring capital punishment

 7% of $600.00 = 40$

Another way

C (7,1)  * C(6,1)               42               7

_____________  =     _______  =   ___ 

   C ( 13,2)                       78              13

-6x^2  + 30x - 216      factor out the  -6

-6  (x^2  - 5x  +  36)     complete the square on x

Take 1/2 of 5  = 5/2......square it  = 25/4     add and subtract this within the parentheses

-6 ( x^2  - 5x  +  25/4 +  36  - 25/4)        factor  the first three terms....simplify the rest

-6 [ (x - 5/2)^2  + 119/4 ]      distribute the  -6  acroos the terms in the  brackets

-6 (x  -5/2)^2  -357/2

a  =  -6     b  =  -5/2      c  =  -357/2

a  +  b  +  c    =   -  (12/2  + 5/2  + 357/2)   = - (374/2)  = -187

x^2  +  8x  +  c

This is  a parabola  that turns upward

The x coordinate of the  vertex  is    -8/2  = -4

So  we need to solve this

(-4)^2  + 8(-4)  + c  = -2

16  -32 +c  = -2

-16 + c  =-2

c =  14

See the graph here : https://www.desmos.com/calculator/bk8d4d0o0t

Thanks, jugoslav.....here's another approach

Note that CF  = 1     and  if we let A =(0,0).....then E  =(1/2, 1/2)

Since CF  and CD  are tangents drawn from an exterior point, the are equal

If we let the equation of the semi-circle be a circle with a radius of 1/2  centered at (1/2,0)

And let us  construct a circle centered at C =  (1,1) with a radius of 1

These two circles will intersect at F which will let us solve this easily

Equation of  semi-circle  is    (x-1/2)^2  + y^2  = (1/2)^2   ⇒   x^2 - x + 1/4 + y^2  = 1/4 ⇒

x^2 - x + y^2    = 0     (1)

Equation of the  circle  centered at C is    (x -1)^2  + (y - 1)^2  = 1^2  ⇒ x^2 - 2x + 1 + y^2 - 2y + 1   =  1 ⇒

x^2 - 2x + y^2  -2y  + 1    =  0     (2)

Subtract  (2) from (1)  and we have that

x + 2y -1   =  0

x  = 1 - 2y       (3)

Sub this into (1) to find the  y  coordinate  of F

(1 -2y)^2  - (1 -2y)  + y^2   =  0

4y^2  - 4y  + 1  - 1 + 2y + y^2   = 0

5y^2 -2y  =  0 

y ( 5y - 2)    = 0 

We  seek to solve this

5y  - 2    =  0

5y  =2

y = 2/5

And  using (3)    x   =1 - 2 (2/5)   =   1/5

So  the coordinates of F  are  (1/5, 2/5)

We can  now find the  three sides of triangle DEF

DE  =  sqrt [  (1/2 -1)^2  + (1/2 - 0)^2 ]  =  sqrt  [ 1/4 + 1/4] =  sqrt (1/2)  =  1/sqrt (2) 

EF = sqrt [ (1/5 - 1/2)^2 + ( 2/5 - 1/2)^2 ]  = sqrt [ (3/10)^2  + (1/10)^2 ]  = 1/sqrt (10)

DF =  sqrt [ ( 1 - 1/5)^2  +  ( 2/5 - 0)^2 ] =  sqrt  [ (4/5)^2 + (4/5)^2 ]  = 2/sqrt (5)

Using the Law of Cosines

FE^2  = DE^2  + DF^2  - 2 ( DE * DF)cos (EDF)

1/10 = 1/2  + 4/5  - 2 ( (1/sqrt (2)  * 2/sqrt (5) ) *cos (EDF)

(1/10 - 1/2 -4/5)

_____________    = cos EDF  =  3/sqrt (10) 

  4/sqrt (10)

And sin  EDF  =  sqrt (1 - (3/10)^2 )  =    sqrt  ( 1 - 9/10)  = sqrt (1/10)

So  area of DEF  =   (1/2)DE * DF sin (EDF)  = ((1/2) (1/sqrt (2) * 2/sqrt (5)) ( 1 /sqrt (10)  = 

(1/sqrt (10) )^2   =   1/10

idk but this is from aops alcumus 

Nevermind, I solved it.

My solution:

The odds that the first student you pick is a girl is 7/13. The oddd that the secound student you pick is a boy is 6/12=1/2. So the you have to multiple 7/13 x 1/2 = 7/26. After that you have to multiple everything by 2! because the order doesn't matter and you get 7/26 x 2! =7/13.

Because exact answers are left for the asker.

The question has already been answered several times. 

Why have you asked this same question twice in two days you little  ##@%##$%#@@#  ?

You have 9 answers on one thread and 5 on the other.

You are totally out to waste everybody's time! 

And jugoslav, why have you fully answered on both threads without even commenting?  

What is 7% of $600.00?

7%  x  $600 =

7/100  x  $600 =

0.07  x  $600 =$42 dollars

t(g(16)) = 3-(16^2)^2

If u add 600+7%=642

If u subtract 600-7%=558

ITS AS SIMPLE AS THAT ....... UM I HOPE THIS HELPED YOU

Probability that no dice show a 6:  p1 = (5/6)^5

Probability that exactly one die shows a six:  p2 = 5*(1/6)*(5/6)^4

Probability that at least two dice show a six: p = 1 - p1 - p2 ≈ 0.196