(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)):

8 / 200 = 4 / 100 = 0.04 ;
Answer:
W=2.73
Step-by-step explanation:
Is means equals and of means multiply
W = 7% of 39
Change to decimal form
W = .07 * 39
W=2.73
Answer/Step-by-step explanation:
✔️Slope of the first graph:
Using two points on the line, (0, 1) and (3, 2),

Slope = ⅓
✔️Slope of the second graph:
Using two points on the line, (0, 0) and (1, 1),

Slope = 1
✔️Slope of the third graph:
Using two points on the line, (0, 1) and (2, 2),

Slope = ½