Slope = opposite / adjacent
<span>
<span>
</span></span>arc tangent (slope) = 1.8 / 4.5
arc tangent (slope) = 2/5
arc tangent (slope) = 21.801 Degrees
Since the standard deviation is not given, we assume the process is a Poisson process, with mean 12000 miles.
From Poisson distribution tables, we see that with a value of lambda(mean)=12000, the lower tail probability for x=12140 miles is 0.9000105, which means that the 90 percentile is 12140 miles.
The lower-tail probability of 9000 miles is 6.2*10^(-181) which is essentially zero.
NOTE: if the problem were modelled with a normal distribution, the probabilities would be completely different.
Answer:
Assumption
Let A be the event that the person stops at first signal.
Let B be the event that the person stops at second signal.
Given
Probabilities:
P(A)=0.40
P(B)=0.50
P(A∪B)=0.50
(a) Stops at both signals
The probability that person stops at both signals is intersection of events A and B
P(A∩B) = P(A)+P(B)−P(A∪B)
= 0.4+0.5−0.6=0.9−0.6
=0.3
(b) Stops at first but not at second
The given case is intersection of event A wth compliment of B
P(A∩¯B) = P(A)−P(A∩B)
=0.40−0.30
=0.10
(c) Stops at exactly one signal
The given case is sum of events that when a person stops either only first signal or at only second signal.
P = [P(A)−P(A∩B)]+[P(B)−P(A∩B)]
= [0.4−0.3]+[0.5−0.3]
= [0.1]+[0.2]
= 0.10+0.20
=0.30
Answer:
16 runs.
Step-by-step explanation:
We have been given that on the first day of baseball tournament Jessie scored 2 runs. On the second day, 4 runs. On the third day, 6 runs.
We can see that runs scored by Jessie form an arithmetic sequence, where each successive term is 2 more than the previous term.
Since we know that formula for nth term of an arithmetic sequence is:
, where,
,
,
,
.
Since on the first day Jessie scored 2 runs, so
and difference between two consecutive terms is 2 (4-2=2), so d will be 2.
Upon substituting our values in arithmetic sequence formula we will get,
![a_n=2+(n-1)*2](https://tex.z-dn.net/?f=a_n%3D2%2B%28n-1%29%2A2)
![a_n=2+2n-2](https://tex.z-dn.net/?f=a_n%3D2%2B2n-2)
![a_n=2n](https://tex.z-dn.net/?f=a_n%3D2n)
Therefore, formula for nth term of sequence representing number scored by Jessie on the baseball tournament is
.
Let us find the 8th term of sequence by substituting n=8 in our sequence formula.
![a_8=2*8](https://tex.z-dn.net/?f=a_8%3D2%2A8)
![a_8=16](https://tex.z-dn.net/?f=a_8%3D16)
Therefore, Jessie should score 16 runs on the eighth day of baseball tournament.
How to solve it:
•1. multiply 7 x 1= 7
•2. multiply 7 x 4k= 28k
so the answer is: 7+28k
i hope i have been helpful :)