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saveliy_v [14]
3 years ago
11

The volume of a box(V) varies directly with its length(l). Using k for the constant of proportionality, express the relationship

between V and l if V varies directly with l.
Mathematics
1 answer:
pochemuha3 years ago
8 0

Answer: V = L (k)

Step-by-step explanation:

Hi, to answer this question we have to write an equation with the information given:

  • <em>Volume of a box = V </em>
  • <em>Length = l </em>
  • <em>Constant of proportionality = k</em>

We know that the volume of the box (V) varies directly with its length (l).

So, the expression for the volume is:

V = L (k)

Feel free to ask for more if needed or if you did not understand something

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Answer:

a) P(t>3)=0.30

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Step-by-step explanation:

We have a repair time modeled as an exponentially random variable, with mean 1/0.4=2.5 hours.

The parameter λ of the exponential distribution is the inverse of the mean, so its λ=0.4 h^-1.

The probabity that a repair time exceeds k hours can be written as:

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P(t>3)=e^{-0.4*3}=e^{-1.2}= 0.30

(b) the conditional probability that a repair takes at least 10 hours, given that it takes more than 9 hours?

The exponential distribution has a memoryless property, in which the probabilities of future events are not dependant of past events.

In this case, the conditional probability that a repair takes at least 10 hours, given that it takes more than 9 hours is equal to the probability that a repair takes at least (10-9)=1 hour.

P(t>10|t>9)=P(t>1)

P(k>1)=e^{-0.4*1}=0.67

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