Y is the midpoint of AB, The coordinates are A(-3,-7) and B(-1,1) What is the coordinate Y?

Mathematics

1 answer:

NISA [10]3 years ago

5 0

The formla of a midpoint of AB:

$M\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)$

We have A(-3, -7) and B(-1, 1). Substitute:

$x_M=\dfrac{-3+(-1)}{2}=\dfrac{-4}{2}=-2\\\\y_M=\dfrac{-7+1}{2}=\dfrac{-6}{2}=-3$

<h3>Answer: M(-2, -3)</h3>

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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:

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

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(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.

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