A triangle ABC has sides AB=50 and AC=10. D is mid-point of AB
and E is mid-point of AC. Angle bisector AG from vertex A meets
side BC at G and divides it in 5:1 ratio. So BG=5 times GC. AG cuts
ED at F. Find the ratio of the areas of the trapeziods FDBG to
FGCE.
(A) Let a,b,c∈Z. Prove that if gcd(a,b)=1 and a∣bc, then
a∣c.
(B) Let p ≥ 2. Prove that if 2p−1 is prime, then p
must also be prime.
(Abstract Algebra)
Suppose A*B*A′ holds(B is between A and A') and D ∈
Int(∠ABC). Prove that C ∈ Int(∠A′BD).
(a) Prove that C ∈ H(D,line A′B).
(b) Prove that C ∈ H (A′, line←→BD). Use point A.
(c) Deduce that C∈Int (∠A′BD).
Let A and B be events with P(A) = 0.5, P(Bc ) = 0.4, P(Ac ∩ Bc )
= 0.3.
(a) Calculate P(A ∪ B), P(A ∩ B), P(B|(A ∪ B)), and P(Ac
|B).
b) Are A and B independent? Explain why.
Use boolean algebra to prove that:
(A^- *B*C^-) + (A^- *B*C) + (A* B^- *C) + (A*B* C^-) + (A*B*C)=
(A+B)*(B+C)
A^- is same as "not A"
please show steps to getting the left side to equal the right
side, use boolean algebra properties such as distributive,
absorption,etc