Yana and amber play a word game using tile letters. each person takes 7 tiles from a set of tiles. points are earned by using the chosen letter tiles to make a word. points are lost when tiles are returned to the set and new tiles are chosen. the table shows the points earned or lost by each girl in their first six turns of the game.

A Yana's average number of points is 0.5 points greater than Amber's

Step-by-step explanation:

i added up all of Yana's points = 15

I added up all of Amber's points = 12

then i divided them both by 6 because there is 6 numbers total so then i got

Yana = 2.5 Amber = 2

2.5 - 2 = 0.5 so Yana's average number of points is 0.5 points greater than Amber's

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geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}