(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)):

Answer:
31.5 square feet of counter top
Step-by-step explanation:
x represents the number of square feet
40x + 750 = 2010 subtract 750 from both sides
40x = 1260 divide both sides by 40
x = 31.5
Answer:
0.034
Step-by-step explanation:
thirty-four thousandths
or
zero point zero three four
Answer:
30
Step-by-step explanation:
All of these have no x-intercepts, since x-intercepts require y to be 0. Their y-intercepts are:
(0, 4)
(0, -18)
(0, 16)
(0, -7)
respectively.