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This kind of experiments are ruled by Bernoulli's formula. If you have probability p of "success", and you want k successes in n trials, the probability is
It's easier to compute the first probability by difference: instead of computing the probability of the event "at least one of the surveyed eats breakfast", let's compute the probability of its contrary: none of them eats breakfast. So, we want 0 successes in 4 trials, with probability of success 0.34. The formula yields
Since the contrary has probability 17%, our event "at least one of the surveyed eats breakfast" has probability 83%.
As for the second question, the event "at least three of the surveyed eats breakfast" is the union of the events "exactly three of the surveyed eats breakfast" and "exactly four of the surveyed eats breakfast". So, we just need to sum their probabilities:
Answer:
a)
b)
c) the steady state mass of the drug is 2000 mg
d) t ≅ 153.51 minutes
Step-by-step explanation:
From the given information;
At time t= 0
an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500
The inflow rate is 0.06 L/min.
Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant.
The objective of the question is to calculate the following :
a) Write an initial value problem that models the mass of the drug in the blood for t ≥ 0.
From above information given :
Therefore;
with respect to x(0) = 0
b) Solve the initial value problem and graph both the mass of the drug and the concentration of the drug.
By Using Integration Method:
However; if x(0) = 0 ;
Then
C = -2000
Therefore
c) What is the steady-state mass of the drug in the blood?
the steady-state mass of the drug in the blood when t = infinity
x = 2000 - 0
x = 2000
Thus; the steady state mass of the drug is 2000 mg
d) After how many minutes does the drug mass reach 90% of its stead-state level?
After 90% of its steady state level; the mas of the drug is 90% × 2000
= 0.9 × 2000
= 1800
Hence;
t = 153.5056729
t ≅ 153.51 minutes