Answer:a
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
your welcome!!
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.
4 goes into 26 6 times with a remainder of 2.
26 ÷ 4 = 6 2/4
6 2/4 = 6 1/2
Your answer is 6 1/2
Answer:
The measure of arc a is 86°
Step-by-step explanation:
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
so
86°=(1/2)[arc c+arc a]
see the attached figure with letters to better understand the problem
In this problem
Triangles ABO and CDO are congruent by SSS postulate theorem
∠AOB=∠COD
∠AOB=arc a -----> by central angle
∠COD=arc c -----> by central angle
therefore
The measure of arc a is congruent with the measure of arc c
arc a=arc c
so
86°=(1/2)[2arc a]
86°=[arc a]
arc a=86°