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nope.

Omg I'm so sorry your my idol in this website btw so I try to be more like you

so sorry 

9/12 of 120 = losers = 90 losers

3/12            = winners = 30 winners

revenue from 120 entries = 120 x 20 = 2400

                  30 winners x 30 = 900 paid out

2400-900 = net 'winnigs' = 1500                       (you had it correct)

HECK!!!

LuckyDucky stole my thunder....LOL!!!!!

Just  "anchor" April and May in any two seats  with one seat in between

Note that  they can be seated in two ways

The other people can be seated in   6!  ways

So.....the total arrangements   =    2 * 6!   =   2 * 720  =  1440

We seat April first. She has 8 choices. We seat May next. She has 2 choices: two spots to the left of April or two spots to the right of April. Then, the remaining six members can sit in ways. This appears to give a total of 8*2*6!  seatings. However, because two seatings are considered the same if one is a rotation of the other, each distinct seating is counted 8 times in this product, once for each possible location of April. So, we must divide by 8 to give a total of 2*6! = 2*720 = 1440 seatings.

We might have instead started by noting that it doesn't matter where April sits. She starts by sitting anywhere, and we count the number of ways the members sit relative to April. May still has 2 choices: two spots to the left of April or two to the right of April. The remaining six participants then can be seated in 6! ways, for a total of 2*6! = 1440 seatings, as before.

Yeah, its undefined.

The probability is:
4!/(2!.2!.2^4) + 4!/(3!.2^4) =3/8 + 1/4 = 5 / 8

confused on b

When the equation is in this form ( where the coefficient of  y  is  1 ),

we can pick off the slope of the line as the coefficient of  x .

Here, the coefficient of  x  is  \(\frac32\)   so

slope of line  m   =   \(\frac32\)

And...

slope of line perpendicular to  m  =  the negative reciprocal of  \(\frac32\)

slope of line perpendicular to  m  =  \(-\frac23\)

The equations that have  \(-\frac23\)  (or something equaivalent to  \(-\frac23\) ) as the coefficient of  x  represent lines perpendicular to  m

The slope of the given line = m = 3/2    perpindicular  is  - 1/m  = -2/3

   which answer(s) have slope = -2/3 ????

First part is pretty simple:

B.  3 out of 12 is a 7     9/12 is NOT a 7        9/12 (of 120 people) will lose    3/12 will win

        can you doit from this partial solution?

Agreed, but is there a more efficient way? o _ O

Last one

Let  the universal set U  = {1,2,3,4}

Let X  = {1,2}

So X '  =  all the elements not in X  = { 3, 4}

Let Y  = {2,3}

So Y '  = allthe elements not in Y  =  { 1,4}

So

X ' ∩ Y '   =   { 3,4}  ∩ {1,4}  =    {4}

Graph B is correct

I agree the only way I know how to do it is brute force, similarly I think CPhill answered this question with the same techqnie as you...

By the way everything below this is 100% CPhill's work even though I used the same methord

16 possible outcomes

P         N           D           Q                     Value  of Heads

H        H           H           H                        .41

T        H           H           H                        .40

T        T           H            H                        .35

T        T           T            H                        .25

T        T           T           T                            0

H       T            T           T                         .01

H       H           T            T                        .06

H      H            H            T                        .16

T       H           T            T                         .05

T      T            H            T                         .10

H      T            T            H                         .26

T      H           H             T                         .15

T      H           T             H                         .30

H     T            H            T                          .11

H     T            H            H                          .36

H     H           T             H                          .31

P ( 15 cents or more of heads)  = 10/16 =  5/8

I'm guessing...

A followed by any other letter is a valid possibility. B followed by any letter except A or B is a valid possibility.

With A there are 25 possibilities, with B there are 24 possibilities, with C there are 23, etc.

25 + 24 + 23 + 22 + 21 + . . . + 3 + 2 + 1   =   (1/2)(25)(25 + 1)   =   325  

Second one

Let the universal set U  = { 1, 2, 3 , 4 }

Let X  = { 1,2}

Let Y = { 2,3)

Y ' = { 1, 4 }

So

X U Y '   =   ( 1,2) U (1,4}  =   (1, 2, 4 }

Graph D is correct

As Hec solves above. remember slope = rise / run    'rise' would be the y direction ' run'  would be the x direction

    then use the formula in Hecticar's answer   and    note    it does not matter which point you call  x₁  y_{1    or}  x₂  y₂  

We can also note that to form a sequence with two different letters in alphabetical order, we need first pick the letters we'll use, then put them in order. We can choose two letters to use in \($\binom{26}{2} = 325$\) ways, and there's only 1 way to put each pair in order.

Hence, there are 325 sequences that fit the problem.

First one

X'    =  all the elements that are NOT contained in X

This is represented by  graph   "C"

slope of line passing through the points  (x₁, y₁)  and  (x₂, y₂)   =   \(\dfrac{y_2-y_1}{x_2-x_1}\)

slope of line passing through the points  (6, 7)  and  (4, 2)   =   \(\dfrac{2-7}{4-6}\)   =   ?

I solved this question in one of my posts :D

Here, check it out: https://web2.0calc.com/questions/plz-help-cents-lord

Wow, that reasoning blows my mind (JK) its very well said!

Now I have logic to back up my answer.

:D

Here's proof of LuckyDucky's answer  of 0 choose 0

C(0,0)  =

      0!                    1                1

__________  =   _____   =  _____   =  1

(0 - 0)! * 0!           0! * 0!        1  * 1

But....think about this...we have no objects and we want to choose none of them

There's only one way to do this.....forget about it   !!!!

so undefinded?