Agumball machine is in the shape of a sphere with a radius of 6 inches. a store manager wants to fill up the machine with miniature gumballs, which have a radius of 1/3in. how many gumballs will fit in the machine?

To know how many gumballs will fit in the machine, the volume of the minature and the machine should be calculated. Volume of sphere:

V = (4/3) pi* r^3

Volume of the machine r = 6 in

V = (4/3) pi* 6^3 = 904.77 in3

Volume of the miniature gumballs

V = (4/3) pi* (1/3)^3 = 0.1551 in3

Divide the two volume to get the number of gumballs that can fill the machine

904.77 in3/ 0.1551 in3 = 5832

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497

s

step-by-step explanation: