At a cement plant, sand is stored in a container called a hopper. the shape of the container is an inverted cone. the height is 18 feet and the radius is 12 feet. if the hopper is full and sand is emptied at the rate of 4 ft3/min, how fast is the level of sand dropping when the sand level is 6 feet high? v = 1/3r2h

Step-by-step explanation:

There is a relation with the initial and final dimensions of the hopper according to the sand level when its high is 6 feet as follows:

Where the calculated is given with the 6 feet hgh.

Then we have the sand flow formula which is:

Where A represents the area of the transversal section and v  the velocity that we need to know, the area is:

And finally the sand is dropping when the level is 6 feet high with the velocity (v) :

you can not drow on this

step-by-step explanation:

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560