Answer:
Step-by-step explanation:
The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"
Let X the random variable that measures the number os trials until the first success, we know that X follows this distribution:
In order to find the expected value E(1/X) we need to find this sum:

Lets consider the following series:
And let's assume that this series is a power series with b a number between (0,1). If we apply integration of this series we have this:
(a)
On the last step we assume that
and
, then the integral on the left part of equation (a) would be 1. And we have:

And for the next step we have:

And with this we have the requiered proof.
And since
we have that:
Ok, 6×25=150, since there are 6 sides, the answer is 150cm.
Answer:
3. 2x + y = −1
Step-by-step explanation:
To find the equation of the line, we write it first in the slope-intercept form:

where
m is the slope
q is the y-intercept
From the graph, we see that the line crosses the y-axis at y = -1, so the y-intercept is -1:

Now we have to find the slope, by calculating the rate of change of the line through 2 points:

Taking the two points at (-2,3) and (1,-3), we find:

So the equation of the line is

Now we have to re-arrange it in the standard form, so in the form

where a, b and c are integer numbers.
To do that, we simply add +2x on both sides of the equation of the line in the slope-intercept form, and we get:

So, option 3).
The light's coverage area is given mathematically as i.e. Area=
Given that a lighthouse casts a revolving beam of light as far as they peir and asked the area is covered.
The revolving beam of light covers the whole space i.e entirely 360°
I.e. it forms a circle-like region
Area of circle =
{ where r is the radius of circle}
Let's assume the distance traveled by light as "d"
as it forms a circular region, it forms a circle of radius "d"
Mathematical connection i.e. area of the region
⇒area of circular region=
{where d is the radius of region}
Learn more about area here:
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Answer:
5
Step-by-step explanation:
First figure out the equation:
We know this is a linear equation because it appears to have a constant slope
Its y-intercept is where it passes in the y-axis, so it's -8
Furthermore, you should also figure out the slope. Notice that the y value increments by 3 every 1 x-value. Rise/Run is 3/1 = 3. Thus, the slope is 3
So your equation is g(x) = 3x - 8
Now we find our inverse function, which is just swapping the x-y values.
Thus, inverse of g(x) ==> y = 3x - 8 ==> x = 3y - 8 ==> x+8 = 3y ==> 
Plug in 7 for x and you get 5