What is $0.1369 rounded to the nearest cent
2 answers:
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Answer:
a. 0.1536
b. 0.9728
Step-by-step explanation:
The probability that a component fails, P(Y) = 0.2
The number of components in the system = 4
The number of components required for the subsystem to operate = 2
a. By binomial theorem, we have;
The probability that exactly 2 last longer than 1,000 hours, P(Y = 2) is given as follows;
P(Y = 2) = × 0.2² × 0.8² = 0.1536
The probability that exactly 2 last longer than 1,000 hours, P(Y = 2) = 0.1536
b. The probability that the system last longer than 1,000 hours, P(O) = The probability that no component fails + The probability that only one component fails + The probability that two component fails leaving two working
Therefore, we have;
P(O) = P(Y = 0) + P(Y = 1) + P(Y = 2)
P(Y = 0) = × 0.2⁰ × 0.8⁴ = 0.4096
P(Y = 1) = × 0.2¹ × 0.8³ = 0.4096
P(Y = 2) = × 0.2² × 0.8² = 0.1536
∴ P(O) = 0.4096 + 0.4096 + 0.1536 = 0.9728
The probability that the subsystem operates longer than 1,000 hours = 0.9728
The range of the function f(x) is the set of all values that function f takes.
The domain of the function f(x) is the set of all possible values for x.
From the given graph you can see that the domain is all real numbers,
The maximal y-value that f takes is 3 at x=-1. For all another x from the domain, y is less than 3.
Thus, the range of the given function is
Answer: