Lenny’s favorite radio station has this schedule: news: 13 min. commercials: 2 min. music: 45 min. if lenny chooses a time of day at random to turn on the radio to his favorite station, what is the probability that the news will be on?

The probability that the news will be on  = 0.217

Step-by-step explanation:

Given: The number of minutes given by radio station to News = 13

The total time given by radio station =

If Lenny chooses a time of day at random to turn on the radio to his favorite station, then the probability that the news will be on will be given by :-

The probability that the news will be on  = 0.217

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}