(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:
25%
Step-by-step explanation:
Her profit is $20,000 on her cost of $80,000, so is ...
20,000/80,000 × 100% = 25%
Y = mx + b
b: y-intercept (when x equals zero)
m: slope ((y₂ - y₁) ÷ (x₂ - x₁))
Y - Intercept:
To find the y-intercept, just look at the table. The y-intercept is whatever y equals when x equals zero. In this case it is -8.
Slope:
(y₂ - y₁) ÷ (x₂ - x₁)
Pick two points and substitute them into this equation. Let's use (-3, 1) and (-2, -2).
(-2 - 1) ÷ (-2 + 3)
-3 ÷ 1
-3
Now substitute these values back into the equation.
y = mx + b
y = -3x - 8
The answer is a.