The number of boys is a random variable that is binomial distributed. Recall that mean and standard deviation for a binomial distribution are
and
, respectively, where n = number of trials and p = probability of success.
In this case, n = 51. Since the gender selection method has no effect of boys and girls, the probability for a boy to be born is .5. So p = .5. Then the mean is
and the standard deviation is
Using a differential equation, it is found that the bacteria's population will triple in 4.75 hours.
<h3>What is the differential equation used in this problem?</h3>
- The bacteria in certain culture increase at a rate proportional to the number present, which means that the population is described by the following differential equation:
- In which k is the growth rate.
Applying <em>separation of variables</em>, the solution is:
The number of bacteria doubles in three hours, hence P(3) = 2P(0), which is used to find k.
Hence:
It triples when P(t) = 3P(0), hence:
The bacteria's population will triple in 4.75 hours.
A similar problem, also involving a differential equation, is given at brainly.com/question/14423176
15 = ½ (7x-6)
distribute ½ into parentheses
15 = ½(7x) - ½(6)
15 = ⁷/₂x - 3
multiply by 2
30 = 7x -6
subtract +6 to both side
30 + 6 = 7x
36 = 7x
devide 7 to both side
36
------ = x
7
I think it is..................