Answer:
1) 275
2)60
Step-by-step explanation:
1) 55 x 5 =275
2) 12 x 5 = 60
<em><u>Hope it helps!</u></em>
Answer with Step-by-step explanation:
In case of Bernoulli trails
The probability that a random variable occurs 'r' times in 'n' trails is given by
![P(E)=\binom{n}{r}p^r(1-p)^{n-r}](https://tex.z-dn.net/?f=P%28E%29%3D%5Cbinom%7Bn%7D%7Br%7Dp%5Er%281-p%29%5E%7Bn-r%7D)
where
'p' is the probability of success of the event
Part a)
probability that no contamination occurs can be found by putting r = 0
Thus we get
![P(E_1)=\binom{5}{0}0.1^0(1-0.1)^{5}=0.5905](https://tex.z-dn.net/?f=P%28E_1%29%3D%5Cbinom%7B5%7D%7B0%7D0.1%5E0%281-0.1%29%5E%7B5%7D%3D0.5905)
part b)
The probability that at least 1 contamination occurs is given by
![P(E)=1-(1-p)^{n}](https://tex.z-dn.net/?f=P%28E%29%3D1-%281-p%29%5E%7Bn%7D)
Applying values we get
![P(E_2)=1-(1-0.1)^{5}=0.4096](https://tex.z-dn.net/?f=P%28E_2%29%3D1-%281-0.1%29%5E%7B5%7D%3D0.4096)
Answer:
3) 16.2
Step-by-step explanation:
The supplement to the 115° angle on the right is 65°, the same as the angle at upper left. The vertical angles at C are the same measure, so this tells you that the two triangles FCB and ACD are similar by the AA similarity postulate. That being the case, corresponding sides are proportional:
CB/CD = CF/CA
CB = CD·CF/CA = 7.2·21.6/9.6
CB = 16.2
_____
When given two "point-to-point" triangles like this, quite often there is some sort of similarity relationship involved. First, you need to figure out what it is; then you need to make use of it as needed to answer the question being asked.
Answer:
The union of two sets is guaranteed to result in an equal or larger set than if they were intersected.
This only makes sense because intersecting sets is exceptional, only values that already exist in both sets are in the result. Whereas a union of two sets gives you all of the content of both.
The only time when an intersection is even equal to a union is when the two sets are identical. If they aren't then the intersection will be smaller.