(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:
.....
Step-by-step explanation:
Selling price of app per user = $10 per month
Total no. of user in first month = 10
To tal no. of user added per month = 7
We have to find how much money is earned in one year
So the formula is n/2 * (2a +(n-1)d)
Here we have n = 12 which is total no. of months
a = 100 , which is money earned in one month
d = 70 , which is increase in money earned per month
So money earned in a year comes out to be 5820
25 is the greatest common factor of 75 and 25. 3 x 25 = 75.
Answer:
10 ft to nearest foot.
Step-by-step explanation:
We use the Pythagoras theorem:
12^2 = 6^2 + h^2 where h is the height on the barn
h^2 = 12^2 - 6^2
h^2 = 144 - 36 = 102
h= √108 = 10.39
