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3 years ago

What is the vertex of the graph of the function f(x) = x2 + 3x - 2?

Mathematics

1 answer:

UkoKoshka [18]3 years ago

6 0

Answer:

see below

Step-by-step explanation:

We need to write it on vertex form (f(x) = a(x - c)² + d where (c, d) is the vertex) and to do that we will complete the square.

f(x) = x² + 3x - 2

= (x² + 3x + 9/4) - 9/4 - 2

= (x + 1.5)² - 4.25

The vertex is (-1.5, -4.25).

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The number of failures of a testing instrument from contamination particles on the product is a Poisson random variable with a m

Mazyrski [523]

Answer:

The probability that the instrument does not fail in an 8-hour shift is $P(X=0) \approx 0.8659$

The probability of at least 1 failure in a 24-hour day is $P(X\geq 1 )\approx 0.3508$

Step-by-step explanation:

The probability distribution of a Poisson random variable X representing the number of successes occurring in a given time interval or a specified region of space is given by the formula:

$P(X)=\frac{e^{-\mu}\mu^x}{x!}$

Let X be the number of failures of a testing instrument.

We know that the mean $\mu = 0.018$ failures per hour.

(a) To find the probability that the instrument does not fail in an 8-hour shift, you need to:

For an 8-hour shift, the mean is $\mu=8\cdot 0.018=0.144$

$P(X=0)=\frac{e^{-0.144}0.144^0}{0!}\\\\P(X=0) \approx 0.8659$

(b) To find the probability of at least 1 failure in a 24-hour day, you need to:

For a 24-hour day, the mean is $\mu=24\cdot 0.018=0.432$

$P(X\geq 1 )=1-P(X=0)\\\\P(X\geq 1 )=1-\frac{e^{-0.432}0.432^0}{0!}\\\\P(X\geq 1 )\approx 0.3508$

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KATRIN_1 [288]

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Step-by-step explanation:

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4 years ago

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<u>Solution:</u>

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Hope this helps! If so, lmk! Thanks and good luck!

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2 years ago

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Answer:

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Step-by-step explanation:

The solution is the area in which both areas intersect. In other words, the dark grey area.

-hope it helps

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2 years ago

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