(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:
Benchmark can be defined as the standard or reference point against which something can be measured, compared, or assessed.
Step-by-step explanation:
Answer: the fourth one
Step-by-step explanation:
Turn the fraction into a improper fraction.
4 5/6 -> 29/6
Divide both numbers.
29 / 6 = 4.833...
Best of Luck!
3,000 in.
(4 x 10) + (7.5 x 10) = 3000
The dimensions on the sketch are 10 times less than the actual rug.
40 in., 7.5 in.
The drawing lengths are ten times more, so you just multiply the dimensions by 10, and then multiply the product you find out to find the actual area of the rug.
