(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)):
-circumference is equal to pi×diameter, area is equal to pi×radius^2
-28.26÷3.14=9, 9÷2=4.5, 4.5×4.5=20.25, and 20.25×3.14=63.585
-rounded to the nearest hundredth, the answer is 63.59
Answer:
A, the first option
Step-by-step explanation:
Morgan should first take the 40% off then apply the $15 coupon
Lets say her total was $150.
If you take the 40% off first, you get $90
150 * .6 = 90 (since you are taking off 40% you are still paying the rest of the 60% so you can just save extra steps by multiplying by .6 and not .4)
Now you subtract 15 from that value.
90 - 15 = 75 If Morgan takes the 40% off first and then applies the $15 dollar coupon, she has to pay $75.
If she applies the $15 coupon first, her total before the 40% is $135
150 - 15 = 135
The total will come out to be $81
$135 * .6 = 81
If Morgan takes the discount first before applying the coupon she has to pay less and saves the most money.
