The second line
least to greatest: -3, -2.4, -21/4, -1.5, -11/8
Kilo = 1,000
Hecto = 100
Deca = 10
Base (unit) = 1
Deci = 0.1
Centi = 0.01
Milli = 0.001
The vertex of this graph is the maximum
Answer:
(a) ![E(X) = 0.383](https://tex.z-dn.net/?f=E%28X%29%20%3D%20%200.383)
The expected number in the sample that treats hazardous waste on-site is 0.383.
(b) ![P(x = 4) = 0.000169](https://tex.z-dn.net/?f=P%28x%20%3D%204%29%20%3D%200.000169)
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
![$ E(X) = \frac{n \times r}{N} $](https://tex.z-dn.net/?f=%24%20E%28X%29%20%3D%20%20%5Cfrac%7Bn%20%5Ctimes%20r%7D%7BN%7D%20%24)
![$ E(X) = \frac{10 \times 8}{209} $](https://tex.z-dn.net/?f=%24%20E%28X%29%20%3D%20%20%5Cfrac%7B10%20%5Ctimes%208%7D%7B209%7D%20%24)
![$ E(X) = \frac{80}{209} $](https://tex.z-dn.net/?f=%24%20E%28X%29%20%3D%20%20%5Cfrac%7B80%7D%7B209%7D%20%24)
![E(X) = 0.383](https://tex.z-dn.net/?f=E%28X%29%20%3D%20%200.383)
Therefore, the expected number in the sample that treats hazardous waste on-site is 0.383.
b. Find the probability that 4 of the 10 selected facilities treat hazardous waste on-site
The probability is given by
For the given case, we have
N = 209
n = 10
r = 8
x = 4
![$ P(x = 4) = \frac{\binom{8}{4} \binom{209 - 8}{10 - 4}}{\binom{209}{10}} $](https://tex.z-dn.net/?f=%24%20P%28x%20%3D%204%29%20%3D%20%20%5Cfrac%7B%5Cbinom%7B8%7D%7B4%7D%20%5Cbinom%7B209%20-%208%7D%7B10%20-%204%7D%7D%7B%5Cbinom%7B209%7D%7B10%7D%7D%20%24)
![$ P(x = 4) = \frac{\binom{8}{4} \binom{201}{6}}{\binom{209}{10}} $](https://tex.z-dn.net/?f=%24%20P%28x%20%3D%204%29%20%3D%20%20%5Cfrac%7B%5Cbinom%7B8%7D%7B4%7D%20%5Cbinom%7B201%7D%7B6%7D%7D%7B%5Cbinom%7B209%7D%7B10%7D%7D%20%24)
![$ P(x = 4) = \frac{70 \times 84944276340}{35216131179263320}](https://tex.z-dn.net/?f=%24%20P%28x%20%3D%204%29%20%3D%20%20%5Cfrac%7B70%20%5Ctimes%2084944276340%7D%7B35216131179263320%7D)
![P(x = 4) = 0.000169](https://tex.z-dn.net/?f=P%28x%20%3D%204%29%20%3D%200.000169)
Therefore, there is a 0.000169 probability that 4 of the 10 selected facilities treat hazardous waste on-site.
As we already have the model that describes the change of the population in Italy in terms of the years that have elapsed, we only have to replace the conditions that are requested in that equation.
Therefore to find the population of Italy in the year 2000 (t = 10 years) substitute t = 10 in the equation and have:
![p = 56.8e^{0.0015*10}\\](https://tex.z-dn.net/?f=p%20%3D%2056.8e%5E%7B0.0015%2A10%7D%5C%5C)
million people
To find the population of Italy in 2008 (t = 18 years)
substitute t = 18 in the equation and have:
![p=56.8e ^{0.0015*18}\\](https://tex.z-dn.net/?f=p%3D56.8e%20%5E%7B0.0015%2A18%7D%5C%5C)
million people
To predict the population in Italy for 2015 and 2020 with this model, we substitute in the equation t = 25 and t = 30
t = 25
million people
t = 30
million people