Faith has some coins in two different pockets. The shaded areas in the diagrams below represent the value of the coins in each pocket. What is the total value, in dollars, of the coins that Faith has in both pockets?​

$3.05

Step-by-step explanation:

Each box is $0.05

The shades boxes represent the value of coin in each pocket :

Number of shaded boxes on the left = 24

Value of coins in left pocket = 24 * $0.05 = $1.2

Number of shaded boxes on the right = 37

Value of coins in right pocket = 37 * $0.05 = $1.85

Tital value if coins :

$1.85 + $1.2

= $3.05

step-by-step explanation:

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}