How do you do this question?
2 answers:
Each little tickmark is a slope value telling you which direction to go. If you place yourself at the origin (0,0) then the tick mark here tells us to go roughly in the northeast direction. As you step forward to the northeast just a tiny bit, the slope value changes to aim more toward the east (rather than north). For more information, check out Euler's method. Specifically it's Euler's method dealing with slope fields.
The diagram below shows what could be each step of this process. Each red dot is a stepping stone, so to speak, going from (0,0) to (50,0). This is an approximation. Without the actual function F(t, S), it's hard to say where exactly S(50) is located. But S(50) = 0 is a fairly good guess I think. MathPhys has a great diagram showing what could be the solution for S(t) given the initial condition S(0) = 0. Note how they drew a curve through all of the red points I've marked.
Answer:
S(50) = 0
Step-by-step explanation:
The initial condition is S(0) = 0, so start at the origin. The slope there is approximately 1. So as t increases by a small amount, S increases by the same amount. Continuing this logic, we end up tracing the vector field until we get to t=50, where S is approximately 0.
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Answer:
a) 0.1720
b) 0.8298
c) 19
Step-by-step explanation:
For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
In this problem we have that:
(a) If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).
This is when
.
So
(b) If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).
This is when
So
So
(c) If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.
The expected value of the binomial distribution is:
In this question, we have
So
The nearest integer to 18.7 is 19.