<u>650 cannonballs
</u>
Explanation step by step:
upper layer = 1 ^ 2
second layer = 2 ^ 2
third layer = 3 ^ 2
layer 12 is 12 ^ 2
<u>The formula is:
</u>
<u>n * (n + 1) * (2n + 1) / 6
</u>
<u>n = 12
</u>
<u>12 (12 + 1) (2 * 12 + 1) / 6
</u>
<u>12 * 13 * 25/6 =
</u>
<u>650
</u>
<u>
</u>
There are 650 cannonballs in this pyramid.
as you already know, the slope of the tangent line is simply the derivative of the function, so
![r=2cos(3\theta )\implies \cfrac{dr}{d\theta }=2\stackrel{chain~rule}{\left[ -sin(3\theta )\cdot 3 \right]} \\\\\\ \left. \cfrac{dr}{d\theta }=-6sin(3\theta ) \right|_{\theta =\frac{\pi }{6}}\implies -6sin\left( 3\cdot \frac{\pi }{6} \right)\implies -6sin\left( \frac{\pi }{2} \right)\implies -6](https://tex.z-dn.net/?f=r%3D2cos%283%5Ctheta%20%29%5Cimplies%20%5Ccfrac%7Bdr%7D%7Bd%5Ctheta%20%7D%3D2%5Cstackrel%7Bchain~rule%7D%7B%5Cleft%5B%20-sin%283%5Ctheta%20%29%5Ccdot%203%20%5Cright%5D%7D%20%5C%5C%5C%5C%5C%5C%20%5Cleft.%20%5Ccfrac%7Bdr%7D%7Bd%5Ctheta%20%7D%3D-6sin%283%5Ctheta%20%29%20%5Cright%7C_%7B%5Ctheta%20%3D%5Cfrac%7B%5Cpi%20%7D%7B6%7D%7D%5Cimplies%20-6sin%5Cleft%28%203%5Ccdot%20%5Cfrac%7B%5Cpi%20%7D%7B6%7D%20%5Cright%29%5Cimplies%20-6sin%5Cleft%28%20%5Cfrac%7B%5Cpi%20%7D%7B2%7D%20%5Cright%29%5Cimplies%20-6)
8
Because 16 ounces is a pound half of 16 is 8, 8 ounces is half a pound. :)
Answer:
(a) 
The expected number in the sample that treats hazardous waste on-site is 0.383.
(b) 
There is a 0.000169 probability that 4 of the 10 selected facilities treat hazardous waste on-site.
Step-by-step explanation:
Professional Geographer (Feb. 2000) reported the hazardous waste generation and disposal characteristics of 209 facilities.
N = 209
Only eight of these facilities treated hazardous waste on-site.
r = 8
a. In a random sample of 10 of the 209 facilities, what is the expected number in the sample that treats hazardous waste on-site?
n = 10
The expected number in the sample that treats hazardous waste on-site is given by




Therefore, the expected number in the sample that treats hazardous waste on-site is 0.383.
b. Find the probability that 4 of the 10 selected facilities treat hazardous waste on-site
The probability is given by
For the given case, we have
N = 209
n = 10
r = 8
x = 4




Therefore, there is a 0.000169 probability that 4 of the 10 selected facilities treat hazardous waste on-site.