Answer:
a. P(X ≤ 5) = 0.999
b. P(X > λ+λ) = P(X > 2) = 0.080
Step-by-step explanation:
We model this randome variable with a Poisson distribution, with parameter λ=1.
We have to calculate, using this distribution, P(X ≤ 5).
The probability of k pipeline failures can be calculated with the following equation:
Then, we can calculate P(X ≤ 5) as:
The standard deviation of the Poisson deistribution is equal to its parameter λ=1, so the probability that X exceeds its mean value by more than one standard deviation (X>1+1=2) can be calculated as:
Solution -
drawing a perpendicular from AQ to TS, we get a right angle triangle AQT
Using Pythagoras Theorem,
AT² = AQ² + QT²
⇒26² = 24² + QT² (∵ Due to symmetry AQ = RS)
⇒QT² = 676-576 = 100
⇒QT = 10
As TS = QT + QS = 12 + 10 = 22 ( ∵ Due to symmetry AR = QS )
∴ TS = 22 (ans)
Sin²t +cos²t =1
<span> x=2+3 sin t
sin t=(x-2)/3
</span><span>y=1-1/2cos t
y-1= - (cos t)/2
cos t =-(y-1)/(1/2)
</span>(x-2)²/3² + (y-1)²/(1/2)² = 1
Ellipse
Answer:
Starting on a platform 2 feet above sea level, dive down to a location that is 18 feet below sea level, and then rise 8 feet.
Step-by-step explanation:
Using the 2 + (-20) + 8 to describe movement relative to sea level ;
2 can be taken as the starting point, positive values represents elevation above sea level ;
2 can be taken as 2 feet platform above sea level ;
- 20 represents distance dived from platform, negative signifies elevation below sea level ; the distance dived relative to sea level is (-20 + platform height)
(-20 + 2) = - 18
8 feets means a final elevation of 8 above sea level (positive value).
Volume of cylinder A = π(12^2/4) x (40/2) = 2,262 cubic feet which will be hauled by locomotive BR73.
Volume of cylinder B = π(8^2/4) x 24 = 1,206 cubic feet which will be hauled by locomotive CG35.
Volume of cylinder C = π(16^2/4) x 16 = 3,217 cubic feet which will be hauled by locomotive YH61.
Volume of cylinder D = π(6^2/4) x 12 = 339 cubic feet which will be hauled by locomotive A450.
