(a) If <em>f(x)</em> is to be a proper density function, then its integral over the given support must evaulate to 1:

For the integral, substitute <em>u</em> = <em>x</em> ² and d<em>u</em> = 2<em>x</em> d<em>x</em>. Then as <em>x</em> → 0, <em>u</em> → 0; as <em>x</em> → ∞, <em>u</em> → ∞:

which reduces to
<em>c</em> / 2 (0 + 1) = 1 → <em>c</em> = 2
(b) Find the probability P(1 < <em>X </em>< 3) by integrating the density function over [1, 3] (I'll omit the steps because it's the same process as in (a)):

Its A. 10,000 divided by 250 is 40. Then multiply 40 by 2 and you get 80
10,000 / 250 = 40
40 * 2 = 80
80= A.
Answer:
c. 6
Step-by-step explanation:
The degree of a vertex is the number of arc ends that intercept it. (The other end of the arc is irrelevant.)
Vertex A is connected to B (1), D (2), F (1), and itself (2). There are a total of 6 arc ends that meet vertex A. Its degree is 6.
Surface area =
=
x 3.14 x 3 x 3 x 3 = 3.14 x 4 x 3 x 3 = 113.04 yd^2 = approx. 113.1 yd^2