Answer:
Case(a): ![p[b]=\frac{1}{3}p[a]](https://tex.z-dn.net/?f=p%5Bb%5D%3D%5Cfrac%7B1%7D%7B3%7Dp%5Ba%5D)
Case(b): ![p[b]=0](https://tex.z-dn.net/?f=p%5Bb%5D%3D0)
Case(c): ![p[b]=\frac{1}{2}p[a\cap b]](https://tex.z-dn.net/?f=p%5Bb%5D%3D%5Cfrac%7B1%7D%7B2%7Dp%5Ba%5Ccap%20b%5D)
Step-by-step explanation:
Given
(a) events a and b are a partition and p[a] = 3p[b].
(b) for events a and b, p[a ∪ b] = p[a] and p[a ∩ b] = 0.
(c) for events a and b, p[a ∪ b] = p[a]− p[b].
we have to find the p[b] in each case:
Case (a): events a and b are a partition and p[a] = 3p[b].
gives ![p[b]=\frac{1}{3}p[a]](https://tex.z-dn.net/?f=p%5Bb%5D%3D%5Cfrac%7B1%7D%7B3%7Dp%5Ba%5D)
Case (b): for events a and b, p[a ∪ b] = p[a] and p[a ∩ b] = 0.
⇒
⇒
∵ p[a ∩ b] = 0.
Case(3): for events a and b, p[a ∪ b] = p[a]− p[b].
p[a ∪ b] = p[a]− p[b]
⇒ ![p[a]+p[b]-p[a\cap b]=p[a]-p[b]](https://tex.z-dn.net/?f=p%5Ba%5D%2Bp%5Bb%5D-p%5Ba%5Ccap%20b%5D%3Dp%5Ba%5D-p%5Bb%5D)
⇒ ![2p[b]=p[a\cap b]](https://tex.z-dn.net/?f=2p%5Bb%5D%3Dp%5Ba%5Ccap%20b%5D)
⇒ ![p[b]=\frac{1}{2}p[a\cap b]](https://tex.z-dn.net/?f=p%5Bb%5D%3D%5Cfrac%7B1%7D%7B2%7Dp%5Ba%5Ccap%20b%5D)
908÷40=22.70
22.70÷2=11.35
11.35+22.70=34.05
34.05*10=340.50
908+340.50=1,248.50
1,248.50 for 50 hours
Let
x------> the number of multiple choice question
y------> the number of free response question
we know that
-----> equation A
-----> equation B
Substitute equation B in equation A
Find the value of x
therefore
the answer is
the number of multiple choice question are
the number of free response question are
Answer:
57
Step-by-step explanation:
Given that :
Standard deviation (σ) = 5 minutes = (5 *60) = 300 seconds
Margin of Error, E = 78
Assume a confidence interval of 95%;
Using the relation :
((Zα/2 * σ) / E)²
(1 - α)/2 = (1 - 0.95)/2 = 0.05 /2 = 0.025
Z0.025 = 1.96
Sample size = ((1.96 * 300) / 78)²
Sample size = (588 / 78)^2
Sample size = 7.5384615^2
Sample size = 56.828
= 57 samples
Answer:
yxu and tux are the alternate interior angles
Step-by-step explanation:
you just go across and then the other side
so pretty much mirroring it twice