1/2 * 1/2 = 1/4 there is a 25% chance that they will both occur
Answer:
A + B + C = π ...... (1)
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L.H.S.
= ( cos A + cos B ) + cos C
= { 2 · cos[ ( A+B) / 2 ] · cos [ ( A-B) / 2 ] } + cos C
= { 2 · cos [ (π/2) - (C/2) ] · cos [ (A-B) / 2 ] } + cos C
= { 2 · sin( C/2 ) · cos [ (A-B) / 2 ] } + { 1 - 2 · sin² ( C/2 ) }
= 1 + 2 sin ( C/2 )· { cos [ (A -B) / 2 ] - sin ( C/2 ) }
= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - sin [ (π/2) - ( (A+B)/2 ) ] }
= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - cos [ (A+B)/ 2 ] }
= 1 + 2 sin ( C/2 )· 2 sin ( A/2 )· sin( B/2 ) ... ... ... (2)
= 1 + 4 sin(A/2) sin(B/2) sin(C/2)
= R.H.S. ............................. Q.E.D.
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In step (2), we used the Factorization formula
cos x - cos y = 2 sin [ (x+y)/2 ] · sin [ (y-x)/2 ]
Step-by-step explanation:
Answer:
Step-by-step explanation:
The scale factor described denotes a reduction operation. The missing dimension is given by simple rule of three:
38 < 4x + 3 +7 - 3x (original equation)
38 < 4x - 3x + 3 + 7 (combine like terms)
38 < x + 10 (simplify)
38 - 10 < x + 10 - 10 (subtract 10 from both sides to get (x) alone)
28 < x (simplify)
x > 28 (switch to get x on the left (its proper equation writing >.<) )
Answer:
22.5%
Step-by-step explanation:
let the standard deviation for market portfolio = σₙ
Also let the standard deviation for fully diversified portfolio = σₓ
<u>To calculate fully diversified portfolio</u>
fully diversified portfolio has <em>σₓ = βσₙ</em>
From the given question beta (β) = 1.25
Also standard deviation for market portfolio (σₙ) = 18% = 0.18
<em>From the equation above, σₓ = βσₙ </em>= 1.25×0.18 = 0.225
= 22.5% (converting to percentage)
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