Answer:
0.36427
Step-by-step explanation:
Mean = λ = 18 messages per hour
P(X = x) = (e^-λ)(λ⁻ˣ)/x!
P(X ≤ x) = Σ (e^-λ)(λ⁻ˣ)/x! (Summation From 0 to x)
But the probability required is that the messages thay come in an hour is between 15 and 20, that is, P(15 < X < 20)
P(15 < X < 20) = P(X < 20) - P(X ≤ 15)
These probabilities will be evaluated using a cumulative frequency calculator.
P(X < 20) = 0.65092
P(X ≤ 15) = poissoncdf(18, 15) = 0.28665
P(15 < X < 20) = P(X < 20) - P(X ≤ 15) = 0.65092 - 0.28665 = 0.36427.
You can use the Poisson distribution calculator here
https://stattrek.com/online-calculator/poisson.aspx

Answer:
1.01 × 10⁴ - scientific notation
10,100 - decimal notation
Answer:
none
Step-by-step explanation:
We are given a triangle ABC with ∠A = 30°, sides a = 4 and b = 10.
According to the 'Law of Sines- Ambiguous Case', we have,
If a < b×sinA, then no triangle is possible.
If a = b×sinA, only one triangle is possible
If a > b×sinA, two triangles are possible.
So, we have,
b×sinA = 10 × sin30 = 10 × 0.5 = 5.
Now, as
4 = a < bsinA = 5.
We get, according to the rule, no triangle is possible.
Answer:
p(t) = 0 for t = 1
p(t) = 1 for t = 1/8 = 8^-1
Step-by-step explanation:
the graph you will have to do yourself.
just go there and type in

well, don't type "log" in letters.
you start by typing the "-" sign, and then you need to look up the functions by clicking on the "funcs" button and look for the log functions .
pick the

option. and then simply enter 8 as the first parameter in the {} brackets and x as the second in the () brackets.
and then you see.
any logarithm is 0 for x (or t) = 1.
because any a⁰ = 1.
and the logarithm gives you that exponent of the base number that leads to the given x value.
in other words : a logarithm is the inverse function of an exponential function.
the exponential function is
y = a^x
and the logarithm then determines

that is all.
and

means that the logarithm itself delivered -1.
and 8^-1 = 1/8
so, p(t) = 1 for t = 1/8