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The common ratio  is   -3   

So....the sum of the 1st 5 terms  is

(1/18) [ 1 - (-3)^5 ] / [ 1 -  (- 3 ) ]  =

(1/18) [ 244 ] / 4  =

244 / 72  =

61 / 18

Here's a problem using the same idea : https://web2.0calc.com/questions/help-please_46127

x  =  3√2 cos ( 3pi/4)  =  3√2  ( -1/√2)   =   -3

y  =  3√2 sin (3pi/4)  =  3√2  (1/√2)  =  3

So

(-3, 3 )

P (Queen  given a Face Card)

We have  12 Face Cards....4 are Queens....so

4 / 12  =

1 / 3   ≈   .33

Thank you!! 

r  =  2

And θ  is 30°= pi/6 past  pi/2   =  pi/2 + pi6  =  3pi/6 + pi/6 = 4pi/6  = 2pi/3

So

(r,  θ)  = ( 2, 2pi/3 )

And Chris is only a few days behind her!!!

Given that M( 1, -6) is the midpoint of {AB} and A(-2, 1) is one endpoint, what is the sum of the coordinates of point B?

x coordinate  = [ x - 2 ] / 2  =   1     multiply both sides by 2

x - 2  =  2      add 2 to both sides

x = 4

y coordinate  =     [ 1 + y ]  / 2  =   -6      multiply both sides by 2

1 +y  =  - 12      subtract 1 from both sides

y  =  -13

So   B  =  ( 4, -13)

Amazing.....!!!!

[ I can never seem to catch her....LOL!!!  ]

Use midpoint formula 

So it is 2, -5

Then 2 + (-5) = -3

Here :

https://web2.0calc.com/questions/a-square-defg-varies-inside-equilateral-triangle

P( Red or Face)  = P(Red) + P(Face) - P(Red and Face)   =  26/52 + 12/52  - 6/52  =  32/52

The center will be directly in between these points on the diameter

2,-5         2-5 = -3

P(Boy or Blue)  = P(Boy) + P(Blue) - P(Boy and Blue)  =  26/61  +  21/61 -15/61  =  32 / 61

BUT 6 of them are counted in the 26 red cards

for any suit there are 3 face cards (J, Q, K) 
there are 4 suits 
so 3*4 = 12 face cards total

Ooops .....sorry

26 red cards + 6 add'l face cards    32/52

9 face cards?

26 red cards + add'd 6 face cards (the black ones)      out of 52 cards   =  32/52

P ( A or B)  = P(A) + P(B)  - P(A and B)  =  3/12  +  4/12   -  1/12    =  6 / 12

D. Share elements

P (A or B)  = P(A u B)   =  union of A and B

P ( green drawn given that the first marble was white)

We have 14 marbles left  and 2 are green...so...

2 / 14

Using the distance formula....we can find the radius

√ [ (-2 - 10)^2  + ( -2 - 3)^2 ]   =  √ [(-12)^5 + (-5)^2]  = √169 =  13

So....the circumference =   2 pi * r   =  2 pi (13)  =  26 pi