Solve the given initial value problem using the method of Laplace transforms. 26, 0≤t≤6, y" + 2y' +26y=g(t), y(0) = -2, y'(0) = 0, where g(t) = 52, 6

Q: f ​P(E)=0.60​, ​P(E or ​F)=0.65​, and​ P(E and ​F)=0.10​, find​ P(F).

A: Let E and F are two events. The known probabilities are, ​P(E)=0.60​, ​P(E or ​F)=0.65​, P(E and…

Q: If P(A) = 0.3, P(B) = 0.3, and P(A and B) = = P(A or B) = X 0.2, find P(A or B).

A: we have probability of P(A)= 0.3 and P(B)=0.3 and P(A and B)=0.2

Q: P(A U B) = 0.9, P(B) = 0.8, P(A n B) = 0.5. Find P(A). %D

A: We have given that,  P(A∪B) = 0.9, P(B) = 0.8 and P(A∩ B) = 0.5 Then,  We will find P(A) = ?

Q: If w 5x2 + 2y2, x = -3s+t, and y = s – 4t, find in terms of s and t. Provide your answer below:

A: Given:   w = 5x2 + 2y2     x = -3s + t      y = 3 - 4t

Q: Find (a) u × v, (b) v × u, and (c) v × v.…

A: Given : u =0,2,1v = 1,-3,4(a) u x v = ijk0211-34u x v =i 21-34    -j0114  +k021-3          = i(8+3)…

Q: Q5 1 Find proj; (w) where w= and v = 2 -2 3

A: Solution:Given     w=10-2     and     v=123To find:projvwFormula:projvw=P wwhere P=v vTvT v

Q: o(E)=3:2, find p(E)

A: Odds of E (3/2) And we have to find p(E) =?

Q: determine f ∗g. Q. f(t)=6t2, g(t)=5t3

A:

Q: Let wr₁ (t) = and r₂(t) =. Find (r₁(t)- r₂(t)). O 04t² +6t³ 0312 +8+4 0

A:

Q: If ​P(E)=0.55​, ​P(E or ​F)=0.70​, and​ P(E and ​F)=0.20​, find​ P(F).

A: Given that P(E)=0.55​, ​P(E or ​F)=0.70​, P(E and ​F)=0.20​ The formula of addition of two events…

Q: If P (A) = 0.6, P(B)=0.1, and A and B are mutually exclusive, find P (A or B). P(4 or B) = |

A:

Q: Let r(t) = (a) Find 7 (t). (b) Find Ñ (t). (c) Find K (t)

A:

Q: 7k +5)dx t

A:

Q: Complete the table. h(t) |t + 4| t -5 -4 -3 -2 -1 h(t)

A: The given function is: h(t)=12t+4 which is a modulus funtion.

Q: for b find y...

A: