In post-apocalyptic neverland, clean water is sold in "2-liter" bottles off the back of a truck that arrives every day. the arrival time is normally distributed with mean 2: 54 pm and standard deviation 24 minutes. the time it takes for the water to sell out is also normally distributed with mean 33 minutes and standard deviation 7 minutes. the price of a "2-liter" bottle fluctuates from day to day according to a normal distribution with mean 128 rubles and standard deviation 4 rubles. the amount of water in a "2-liter" bottle varies from bottle to bottle according to a normal distribution with mean 63.5 ounces and standard deviation 1 ounce. assume that all days, all times, and all bottles are independent.

on april 3, 2020, you buy four "2-liter" bottles of clean water. what is the probability that it costs you more than 500 rubles? give your answer to 4 decimal places.

0.7734

Step-by-step explanation:

The average in this problem is 128 and the standard deviation is 4.

We buy 4 bottles.  We want the probability that the cost is more than 500 rubles; this means the average of each bottle would be

500/4 = 125 rubles.  This is our X value.

Using the z score formula, we have

Using a z table, the area under the curve less than this is 0.2266.  We want the probability that the cost is more than this, which would be to the right; we subtract from 1:

1-0.2266 = 0.7734

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.