If I had 20 dollars every other week for a year how much would I have

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.

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

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

6 0

3 years ago

Expand the bracket with distributive law <br>4(3x-4)

USPshnik [31]

B cause vid off the things

7 0

2 years ago

Which of the following is a negative aspect of wind power?

harina [27]

Answer:

C is the answer, as wind turbines are more expensive

8 0

2 years ago

Derive the equation of the parabola with the focus <br> is (-7,5) and the directrix of y=-11

Volgvan

So, notice, the focus point is at -7, 5, and the directrix is at y = -11.

keep in mind that the vertex is half-way between those two fellows, and the distance from the vertex to either one of them is "p" units, check the picture below.

with that focus point and that directrix, the half-way over the axis of symmetry will be -7, -3, that's where the vertex is at, and notice the distance "p", is 8 units.

since the parabola is opening upwards, "p" is positive 8.

$\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
4p(x- h)=(y- k)^2
\\\\
\boxed{4p(y- k)=(x- h)^2}
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ( h, k)\\\\
 p=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\
-------------------------------\\\\
\begin{cases}
h=-7\\
k=-3\\
p=8
\end{cases}\implies 4(8)[y-(-3)]=[x-(-7)]^2
\\\\\\
32(y+3)=(x+7)^2\implies y+3=\cfrac{1}{32}(x+7)^2
\\\\\\
y=\cfrac{1}{32}(x+7)^2-3$

8 0

3 years ago

What is the solution to the system of equations g(x)=-2x-3 f(x)=x+1-4

Ainat [17]

Answer: Not positive that this is right but here is what I got.

Step-by-step explanation:

Set up the composite result function.

g ( f )( x )

Evaluate g(f)(x) by substituting in the value f into g

(2x - 3) + 1

Add -3 and 1

g ( 2 x − 3 ) = 2 x − 2

4 0

3 years ago