Find the area of the circle to the nearest whole number, if necessary!

Mathematics

1 answer:

astra-53 [7]2 years ago

5 0

Answer:

The circle has an area of about 1385 square mm.

Step-by-step explanation:

Let's recall that circles have an area that can be found with the following formula:

$A=\pi r^{2}$

where r is the radius of the circle.

Now, focus your eyes on the circle. We are shown that the diameter of this circle is 42 mm, but we only want the radius. Since the radius is half the diameter, the radius is 21 mm. Now, we can solve for the area of the circle.

$A=\pi (21)^2\\A=441\pi \\A=1385.44236...$

So, to the nearest whole number, the area of the circle is 1385 square mm.

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Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with mean 1/0.41/0

lbvjy [14]

Answer:

a) P(t>3)=0.30

b) P(t>10|t>9)=0.67

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:

$P(t>k)=e^{-\lambda t }=e^{-0.4t}$

(a) the probability that a repair time exceeds 3 hours?

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

(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.

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