Step-by-step explanation:
this is the anwser it is inverse trigonometry
The perimeter is 16 inches
4.5+5.5+6=16
(1) Looks like the joint density is

In order for this to be a proper density function, integrating it over its support should evaluate to 1. The support is a triangle with vertices at (0, 0), (4, 0), and (4, 4) (see attached shaded region), so the integral is


(2) The region in which <em>X</em> > 2 and <em>Y</em> < 1 corresponds to a 2x1 rectangle (see second attached shaded region), so the desired probability is

(3) Are you supposed to find the marginal density of <em>X</em>, or the conditional density of <em>X</em> given <em>Y</em>?
In the first case, you simply integrate the joint density with respect to <em>y</em>:

In the second case, we instead first find the marginal density of <em>Y</em>:

Then use the marginal density to compute the conditional density of <em>X</em> given <em>Y</em>:

Step-by-step explanation:
angle A and Angle D are congruent. as are Angle C and Angle F.
because you have two pairs of congruent angles this proves the triangles are similar using AA Theorem.
I couldn't read the 3rd question. if you post as a comment I can look at it better.