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2 years ago

The time to failure (in hours) of fans in a personal computer can be modeled by an exponential distribution with l=0.0003

Mathematics

1 answer:

Dvinal [7]2 years ago

3 0

Answer: 0.0497870 ; 0.87754

Step-by-step explanation:

Given that :

λ = 0.0003

Defining a continuous distribution function :

F(x) = 1 - e^-λx = 1 - e^-0.0003x ; x ≥ 0

a. What proportion of the fans will last at least 10,000 hours?

P(x ≥ 10000) = e^-0.0003(10000) = 0.0497870

b. What proportion of the fans will last at most 7000 hours?

P(x ≥ 7000) = 1 - p(x ≤ 7000) = 1 - e^-0.0003(7000)

1 - 0.12245642825 = 0.87754

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3 years ago

16 plus 5 times a number is more than the number minus 8. Write an inequality and solve it

Radda [10]

n > -6 is the inequality for 16 plus 5 times a number is more than the number minus 8

Solution:

Given statement is:

16 plus 5 times a number is more than the number minus 8

We have to write a inequality

From given statement,

16 plus 5 times a number is more than the number minus 8

Let the number be "n"

Therefore,

16 plus 5 times "n" is more than "n" minus 8

Here, "plus" means addition and "minus" means subtraction and "times" means multiplication

Thus the statement is translated into inequality as:

$16 + 5n >n-8$

Simplify the inequality

$16 + 5n >n-8\\\\\mathrm{Subtract\:}16\mathrm{\:from\:both\:sides}\\\\16 + 5n -16 > n - 8 -16\\\\5n >n-24\\\\\mathrm{Subtract\:}n\mathrm{\:from\:both\:sides}\\\\5n-n>n-24-n\\\\\mathrm{Simplify}\\\\4n>-24\\\\\mathrm{Divide\:both\:sides\:by\:}4\\\\\frac{4n}{4}>\frac{-24}{4}\\\\n>-6$

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3 years ago

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Naddik [55]

Answer:

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2 5

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3 6

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