How many gallons of a 25% acid solution should be added to 10 gallons of a 12% acid solution to obtain a 20% acid solution?

16 Gallons

Step-by-step explanation:

x = 25% gallon amount

.25 x   +  .12 (10)   =     .20 (10+x)

.05x = .8

x = 16 gal of 25%

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