A 140 gallon tank initially contains 5 lbs salt dissolved in 40 gallons of water. Brine containing 1 lb salt per gallon begins to flow into the tank at the rate of 3 gal/min and the well-mixed solution is drawn off at the rate of 1 gal/min. How much salt is in the tank when it is about to overflow? (Round your answer to the nearest integer.)

96.46

Step-by-step explanation:

Volume of the Gallon =140 gallons

At time t=0, V(0)=40 gallons

V(t)=2t+k, Where K is a constant.

Since V(0)=40

V(0)=2(0)+k=40

k=40

V(t)=40+2t

The Change in Salt Concentration

Rearranging

Using Integrating Factor:

At t=0, C(0)=0.125, k_0=5

At V(t)=140

V(t)=40+2t=140

t=50

Just  the tank  overflows, C(t)=96.46

answer: plz put a pic in so i can answer it

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