Aswimming pool whose volume is 10,000 gal contains water that is 0.01% chlorine. starting at t = 0, city water containing0.001% chlorine is pumped into the pool at a rate of 5 gal/min. the pool water flows out at the same rate. what is thepercentage of chlorine in the pool after 1 h? when will the pool water be 0.002% chlorine?

a) The percentage of chlorine after 1 hour is 0.00973%.

b) The pool water will habe a concentration of 0.002% chlorine at 4394 minutes (or 73.24 hours).

Step-by-step explanation:

We can define as X(t) the amount of chlorine that is in the pool at time t.

Then, the rate of change of X can be written as

being Ci the concentration of chlorine of the inflow (0.001%), f_in the inflow (5 gal/min) and f_out the outflow (the same as the inflow, 5 gal/min).

When t=0, the concentration is 0.01%, so the amount of chlorine X is

Replacing in the equation, we have

The amount of chlorine for any time t is then

a) At one hour (t=60 min), the amount of chlorine is

This amount means a concentration of

b) A concentration of 0.002% of chlorine means an amount of chlorine of

Then we can calculate

answer: a. 13/44

step-by-step explanation: judging by the information given to us, we are looking for experimental probability. we can see that 13 males have chosen chocolate ice cream. there are 44 ice creams in total (remember that the total is always the denominator). so our answer is 13/44.

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