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Over [174]
3 years ago
13

Functions f(x) and g(x) are shown below:

Mathematics
1 answer:
kondor19780726 [428]3 years ago
4 0
We look for the minimum of each function.
 For f (x) = 3x2 + 12x + 16:
 We derive the function:
 f '(x) = 6x + 12
 We match zero:
 6x + 12 = 0
 We clear the value of x:
 x = -12/6
 x = -2
 We substitute the value of x in the equation:
 f (-2) = 3 * (- 2) ^ 2 + 12 * (- 2) + 16
 f (-2) = 4
 For g (x) = 2sin(x-pi):
 From the graph we observe that the minimum value of the function is:
 y = -2
 Answer:
 
A function that has the smallest minimum y-value is:
 
y = -2
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See steps below

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The probability that the bulb fails the first year is

\bf P(X\leq 12)=1-e^{-12/24}=1-e^{-0.5}=0.39347

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Let A and B be the events,

A = “The bulb will last at least 24 months”

B = “The bulb will last at least 18 months”

We want to find P(A | B).

By definition P(A | B) = P(A∩B)P(B)

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Now the probability that exactly k bulbs need replacement is

\bf \binom{6}{k}(0.39347)^k(1-0.39347)^{6-k}

<em>Probability that at least one of them needs replacement at the first inspection = 1- probability that none of them needs replacement at the first inspection. </em>

This means that,

<em>Probability that at least one of them needs replacement at the first inspection =  </em>

\bf 1-\binom{6}{0}(0.39347)^0(1-0.39347)^{6}=1-(0.60653)^6=0.95021

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