A committee has four members ( P 1 , P 2 , P 3 , and P 4 ) . In this committee P 1 has twice as many votes as P 2 ; P 2 has twice as many votes as P 3 ; P 3 and P 4 have the same number of votes. The quota is q = 49 . For each of the given definitions of the quota , describe the committee using the notation [ q : w 1 , w 2 , w 3 , w 4 ] . ( Hint : Write the weighted voting system as [ 49 : 4 x , 2 x , x , x ] , and then solve for x .) a. The quota is defined as a simple majority of the votes. b. The quota is defined as more than two-thirds of the votes. c. The quota is defined as more than three-fourths of the votes.
A committee has four members ( P 1 , P 2 , P 3 , and P 4 ) . In this committee P 1 has twice as many votes as P 2 ; P 2 has twice as many votes as P 3 ; P 3 and P 4 have the same number of votes. The quota is q = 49 . For each of the given definitions of the quota , describe the committee using the notation [ q : w 1 , w 2 , w 3 , w 4 ] . ( Hint : Write the weighted voting system as [ 49 : 4 x , 2 x , x , x ] , and then solve for x .) a. The quota is defined as a simple majority of the votes. b. The quota is defined as more than two-thirds of the votes. c. The quota is defined as more than three-fourths of the votes.
Solution Summary: The author explains the weighted voting system if quota q is defined as a simple majority of the votes.
A committee has four members
(
P
1
,
P
2
,
P
3
,
and
P
4
)
. In this committee
P
1
has twice as many votes as
P
2
;
P
2
has twice as many votes as
P
3
;
P
3
and
P
4
have the same number of votes. The quota is
q
=
49
. For each of the given definitions of the quota, describe the committee using the notation
[
q
:
w
1
,
w
2
,
w
3
,
w
4
]
. (Hint: Write the weighted voting system as
[
49
:
4
x
,
2
x
,
x
,
x
]
, and then solve for
x
.)
a. The quota is defined as a simple majority of the votes.
b. The quota is defined as more than two-thirds of the votes.
c. The quota is defined as more than three-fourths of the votes.
Find the exact values of sin(2u), cos(2u), and tan(2u) given
2
COS u
where д < u < π.
2
(1) Let R be a field of real numbers and X=R³, X is a vector space over R, let
M={(a,b,c)/ a,b,cE R,a+b=3-c}, show that whether M is a hyperplane of X
or not (not by definition).
متکاری
Xn-XKE
11Xn-
Xmit
(2) Show that every converge sequence in a normed space is Cauchy sequence but
the converse need not to be true.
EK
2x7
(3) Write the definition of continuous map between two normed spaces and write
with prove the equivalent statement to definition.
(4) Let be a subset of a normed space X over a field F, show that A is bounded set iff
for any sequence in A and any sequence in F converge to zero the
sequence converge to zero in F.
އ
Establish the identity.
1 + cos u
1 - cos u
1 - cos u
1 + cos u
= 4 cot u csc u
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