CPhill

For the second one

A... P (2 , 3  without replacement)  = (2/13) * ( 1/12)  =  2 / 156

B.....P ( 2, 5 without replacement)  = (2/13) * (2/12)  = 4 / 156

C...P( 3, 2 with replacement)  = ( 1/13)  * (2/13)  =  2 / 169

D....P ( 5, 2 with replacement )  =  (2/13) * ( 2/13)  =  4 / 169

So......your answer is correct....!!!

I believe the first one is  A  and B

A  =  { 3 }    B  = { 2, 4, 6, 8 }

So   A and B  =  A ∩ B   =   {     }        (empty set )

Q3......both x, y are negative in this quadrant  and r is always positive

So   

sin  (theta) =  y / r  ⇒  negative

cos (theta) =  x / r ⇒  negative

-pi/6  is a 30°  reference angle in the 4th quadrant

A 30°  in the fist quadrant  has the coordinates  (  √3/2, 1/2)

But...in the 4th quadrant, the y coordinate is negative....so..

(  √3/2,  -1/2)

7pi / 4  is a 45°  reference angle in the 4th quadrant

A 45°  angle in the first quadrant has the coordinates  (√2 / 2, √2 / 2)

But...in the 4th quadrant, the y coordinate is negative....so

(√2 / 2,  - √2 / 2)

I don't know if this helps, or not....but Rom answered something like this  here :

https://web2.0calc.com/questions/real-life-situation_1

And  here :

https://web2.0calc.com/questions/last-part-of-real-life-situation

OK..thanks, Melody.....I see that  !!!

8 : 5   means that we have 13 equal parts

So.....

Number of red is 8 of these parts  =  (8/13) * 351   =  216

Number of white is 5 of these parts  =  (5/13) * 351  =  135

Ah, yes....that makes sense  !!!!

So....in that case...we have

4 colors on the top

3 colors in the middle

3 colors on the bottom

4 x 3 x 3  =   36

And you are correct.....!!!!

Here's my best attempt

We have 4 ways to choose the "top" color

Then, 3 ways to choose the next color

Then, 2 ways to choose the "bottom" color

So......the total possible flags  are   4 x 3 x 2   =   24

Another way to see this is all the possible sets  we can make by permuting  any 3 colors from a set of 4 colors....ordering the colors in the sets from left to right [ corresponding to top to bottom ], we have

4P3   =  24