Identify the sample space in the following tree diagram A.) H, T
B.) TTT, TTH, THT, THH, HTT, HTH, HHT, HHH
C.) HHH, THH, TTH, TTT
D.) HT, TH, TT, HT

There are 2 sides per coin, and 3 flips, so 2^3 = 8 total items in the sample space

Tracing each branch from left to right will help form the 8 different outcomes. For instance, if you go along the upper most path of the upper tree, then you'll get HHH meaning you got 3 heads in a row. The next branch down would be HHT, and so on.

Correct question is;

Find the surface area of that part of the plane 10x + 7y + z = 4 that lies inside the elliptic cylinder x²/25 + y²/9 = 1

A(S) = 15π√150

Step-by-step explanation:

We are given;

10x + 7y + z = 4

Making z the subject, we have;

z = 4 - 10x - 7y

Now, area of the surface as part of z = f(x, y) is;

A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA

From z = 4 - 10x - 7y,

∂f/∂x = -10

∂f/∂y = -7

Thus;

A(S) = ∫∫√[(-10)² + (-7)² + 1]dA

A(S) = √150 ∫∫dA

Where ∫∫dA is the elliptical cylinder

From the general form of an area enclosed by an ellipse with the formula;

x²/a² + y²/b² = 1 and comparing with

x²/25 + y²/9 = 1, we have;

a = 5 and b = 3

So, area of elliptical cylinder = πab

Thus;

A(S) = √150 × π(5 × 3)

A(S) = 15π√150