Step-by-step explanation:
1. hundred thousand
2.hundred thousand
Given differential equation, (D4 - 5D3 + 5D2 + 5D - 6)y = 0
=> For general solution of equation,
Solve D4 - 5D3 + 5D2 + 5D - 6 = 0
=> D4 - 5D3 + 6D2 - D2 + 5D - 6 = 0
=> D2 (D2 - 5D + 6) - (D2 - 5D + 6) = 0
=> (D2 - 5D + 6)(D2 - 1) = 0 ................................(1)
Now
D2 - 1 = (D - 1)(D + 1) and
Factors of D2 - 5D + 6
D2 - 5D + 6 = D2 - 2D - 3D + 6
= D(D - 2) - 3(D - 2)
= (D - 3)(D - 2)
Therefore, equation (1) implies
(D2 - 5D + 6)(D2 - 1) = (D - 3)(D - 2)(D - 1)(D + 1) = 0
=> D = 3, 2, 1, -1 or D = -1, 1,, 2, 3
=> General solution of differential equation is,<span>
=><span> y = C1 e-x + C2 ex + C3 e2x + C4 e3x</span> .
Hope it helps
</span>
Answer:
The least possible number of coins that Pirate Jack has is 77.
Step-by-step explanation:
i) let the number of coins in the piles for the parrots be x.
ii) therefore we can say that the total number of coins be 7x + 4
iii) let the number of coins in the piles for for the pirates be y.
iv) therefore we can say that the total number of coins be 11y + 4
v) therefore we can say that 7x + 4 = 11y + 4
vi) therefore 7x = 11y
vii) therefore the least possible number of coins that Pirate Jack has is equal to the LCM of 11 and 7 which is 77.
viii) x = 11 and y = 7
7 men= 5 women
380 men= x women
=> 7x = 5 . 380
7x = 1900
x= 1900/7
x= 271,4
wich means 271 women
HOPE IT HELPS
Answer:
Step-by-step explanation:
a. #We notice this is a Poisson probability function expressed as:
x-number of occurrences in a given interval.
-mean occurrences of the event
-The mean is calculated as:
#the probability of no accidents in a 15-minute period is :
Hence, the probability of no accident in a 15-min period is 
b. The the probability of at least one accident in a 15-minute period. is calculated as:
Hence, the probability of at least one accident in a 15-minute period is 
c. The probability of four or more accidents in a 15-minute period is calculated as:
![P(X\geq 4)=1-P(X\leq 3)=1-[P(X=0)+P(X1)+P(X=2)+P(X=3)]\\\\=1-[5.574\times10^{-7}+a. \ 8.026\times10^{-6}+\frac{14.4^2e^{-14.4}}{2!}+\frac{14.4^3e^{-14.4}}{3!}]\\\\=1-[8.584\times 10^{-6}+5.779\times10^{-5}+2.774\times10^{-4}]\\\\=0.9997](https://tex.z-dn.net/?f=P%28X%5Cgeq%204%29%3D1-P%28X%5Cleq%203%29%3D1-%5BP%28X%3D0%29%2BP%28X1%29%2BP%28X%3D2%29%2BP%28X%3D3%29%5D%5C%5C%5C%5C%3D1-%5B5.574%5Ctimes10%5E%7B-7%7D%2Ba.%20%5C%208.026%5Ctimes10%5E%7B-6%7D%2B%5Cfrac%7B14.4%5E2e%5E%7B-14.4%7D%7D%7B2%21%7D%2B%5Cfrac%7B14.4%5E3e%5E%7B-14.4%7D%7D%7B3%21%7D%5D%5C%5C%5C%5C%3D1-%5B8.584%5Ctimes%2010%5E%7B-6%7D%2B5.779%5Ctimes10%5E%7B-5%7D%2B2.774%5Ctimes10%5E%7B-4%7D%5D%5C%5C%5C%5C%3D0.9997)
Hence,the probability of four or more accidents in a 15-minute period. is 0.9997
