Answer:
Inverse Laplace of
will be 
Step-by-step explanation:
We have to find the inverse Laplace transform of 
We know that of
is 
As in H(s) there is square of 
So i inverse Laplace there will be multiplication of t
So the inverse Laplace of
will be 

Answer:

Step-by-step explanation:
Sample size 52 card
Pay for J or Q 
Pay for King or Ace 
Pay for others 
Therefore
Probability of drawing J or Q

Probability or drawing King or Ace

Probability or drawing Other cards

Therefore
Expected Gain is mathematically given as



Well this depends on the the the size of the cover
Answer:
height is 15
Y = L = Length
therefore 15y = (-x^2) +(300/20)
Step-by-step explanation:
15 = -x^2 +(300/20)
is the same as;
15 = (300/20) - (x^2)
we just add y to 15 and that can represent a division for x
y = L
Where area cm^2 can be shown as 300 as 15 x 20 = 300
when we divide by length we get the height as asked in the question.
Answer:

Step-by-step explanation:
The base of the pyramid we need to study is a hexagon.
Let's look at the attached image of an hexagon to understand how we are going to find the area of this figure.
Notice that an hexagon is the combination of 6 exactly equal equilateral triangles in our case of size "2x" (notice that the "radius" of the hexagon is given as "2x")
Therefore the area of the hexagon is going to be 6 times the area of one of those equilateral triangles.
We know the area of a triangle is the product of its base times its height, divided by 2: 
We notice that the triangle's height is exactly what is called the "apothem" of the hexagon (depicted in green in our figure) which measures
, so replacing this value in the formula above for the area of one of the triangles:

Then we multiply this area times 6 to get the total area of the hexagon (6 of these triangles):
Area of hexagon = 
which is the last option given in the list.