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Call the people  A, B, C, D

Possible sets

(A B) (C) (D)

(A C)  (B) (D)

(A D) (B) (C)

(B C) (A)(D)

(B D) (A) (C)

(C D) (A) (B)

Another way to see this....just  pick any  2 of 4 people for the first set =  C (4,2)  =  6 sets

2x  - y  =   -2

x - 2y  = 14

system determinant  =     2   -1    =     2(-2)  - (1) (-1)  =  -4 + 1   = -3

                                         1   -2

x determinant  =      -2    -1  =      (-2)(-2) - (-1)(14)  =   18

                                14   -2

y determinant  =      2   -2   =    (2)(14) - (-2)(1)  = 30

                                1   14 

Value of  x  =   18/-3  =   -6

Value of y =  30 / -3   = -10

So  (x, y)  = (-6,-10) 

Identifiable arrangements  =

Number of Letters  !

_________________

Repeated Letters !

So  we have

 8!              40320            40320

____ =    ________  =   ______  =   3360  idetifiable arrangements

2! 3!           2 * 6                12

Second one

Let the side of the pentagon  = x

Let the side of the hexagon  = y

So

3x  = 2y    ⇒     3x - 2y  = 0      (1)

x + y  = 10  ⇒  2x + 2y = 20    (2)

Add (1) and (2)  and we have that

5x  = 20

x  = 4

And   x + y  =10....so y  = 6

So

4BC + 5PQ  =

4x + 5y  =

4(4) + 5(6)  =

46

5³ x 75 = 9375 cm^3

The vertex angles  of a regular hexagon  each measure 120°

Therefore,

3m + 40  = 120               2n - 30 = 120      

3m  = 80                         2n =  150

So                                    

6m  = 160

So 

6m + 2n  =

160  + 150  =

310°

8^2 x 5/8 = 320/8 = 40 ft²

8 C 4   is the number of ways to choose 4 children for one of the teams....the reamining 4 would wind up on the other team

8 C 4 =70 ways

The coefficient signs run + + - - -, just one change, so Descartes' rule of signs says that there is precisely one positive root.

Replace x by - x to get

 \(\displaystyle f (-x)=x^{4}-2x^{3}-11x^{2}+5x-6,\)

and you see three sign changes, indicating three or one negative roots. 

"Dilated" means enlarge 

Thus, if a cube with V=75 and enlarged by a factor of 5 then the volume after dilation (Dilated cube) is 5V=5(75)=375

\(\frac{4^x}{3}=\frac{1}{12}\) Multiply both sides by 3

\(4^x=\frac{1}{4}\) Take log using the law: \(a^b=c\) = \(log_ac=b\)

\(log_4\frac{1}{4}=x\) Evaluate by indices laws  or by calculator. Indeed we know that 4^-1=1/4 so,

\(log_4\frac{1}{4}\)= -1 

Therefore, 

x= -1 

Melissa read 126 pages in a book.
This represents 30% of the total numbers of pages.
How many pages are in her book?

\(\begin{array}{|rcll|} \hline x*30\ \% &=& 126 \\ x*0.3 &=& 126 \\ x &=& \dfrac{126}{0.3} \\ \mathbf{x} &=& \mathbf{420} \\ \hline \end{array}\)

In her book are 420 pages.

The graph should help:

The terminal side of θ passes through the point (7, −1) .

What is the exact value of sinθ in simplified form?

If I understand the question properly, none of those are the answer

The point is in the forth quad so sin is negative

opposite is 1

adjacent is 7

\(hypotenuse\;\; is\;\; \sqrt{50}=5\sqrt2\\ sin \theta = \frac{-1}{5\sqrt2}  = \frac{-\sqrt2 }{ 10}\)

Here are the images for the problem.

10 / 8 = 1.25

1.25 * 7 = 8.75

Ratio:    10 : 8 = 8.75 : 7

If/when you know the answers please share them with the forum :)

(b) I also bought 7 different postcards. How many ways can I send the postcards to my 3 friends, so that each friend gets at least one postcard?

This is much harder.

Maybe

(3*7*6)+(6*7*6*5)+2*(3*7*6*5*4)  = 6426

It is most likely incorrect.

(a) While travelling abroad, I bought 7 identical bags of candy for 3 friends. How many ways can I distribute the candy to my 3 friends, so that each friend gets at least one bag of candy?

a)  Give each of the friends on bag.

There are 4 bags left to be shared between the 3 friends

   * |* *| *

Using stars and bars I think there are  6C2 = 15 ways

(b) I also bought 7 different postcards. How many ways can I send the postcards to my 3 friends, so that each friend gets at least one postcard?

This is much harder.

I'm not sure.

I'm not sure of the answer but here is my explanation.

Let's count the total number of marbles in the bag, which is 20. 

If you pick the first red marble the chances are 2/20. If you pick the second red marble (it has to be two red marbles in a row) the probability is 1/19.

So the answer is just 2/20 * 1/19, or 1/190. 

~~GF

Never mind, hectictar posted a solution to another guy's post. Sorry!

There are 34 possibilties.

The answer is 26/99.

1,0000,0000 = 2^7 * 5^7

7 + 7 = 14