Acompany that manufactures and bottles apple juice uses a machine that automatically fills 16–ounce bottles. there is some variation in the amounts of liquid dispensed into the bottles. the amount dispensed is approximately normally distributed with mean 16 ounces and standard deviation 1 ounce. what proportion of bottles will have more than 17 ounces?

 0.1587

Step-by-step explanation:

Given : The amount dispensed is approximately normally distributed with Mean :

Standard deviation :

The formula to calculate the z-score :-

For x= 17

The p-value =

The proportion of bottles will have more than 17 ounces = 0.1587

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}