(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)):
To find the inverse, switch the x and y, and then solve for y (f(x) is the same as y)
So we get:
x=1.50y-30 (add 30 to both sides)
x+30=1.50y (divide both sides by 1.5)
x/1.5+30/1.5=y
y=x/1.5+20
Hope this helps
Answer:
32%
Step-by-step explanation:
Given
Cost of Crockpot = $125
Coupon = $40
Coupon applies on items greater than $100
Required
Percent saved if coupon is applied.
If she applies coupon on the Crockpot, then she'll be saving $40.
Percent Savings = Amount Saved / Total Amount
Percent Savings = $40/$125
Percent Savings = 0.32
Convert to Percentage
Percent Savings = 0.32 * 100%
Percent Savings = 32%.
Hence, she'd save 32% if she applies the coupon of $40 on the Crockpot
Answer:
11 17/21
Step-by-step explanation:
Answer:For the first one 26.73 would turn into 27 and 89.42 would stay 89
Step-by-step explanation: Any number that is 5 or greater can be used to round any number.
