Answer:
(a) Orthogonal, (b) Neither, (c) Parallel, d( Orthogonal
Step-by-step explanation:
a and b are parallel is a=kb
a and b if a dot b = 0
(a) a dot b = (9)(-4)+6(6)=-36+36=0
a and b are orthogonal
(b) a dot b = 40-7-21=12
a=kb -> there is no k value satisfying the equation
a and b are neither parallel or orthogonal
(c) a dot b = -12-108-48=-168
a=kb -> k=-3/4 satisfies the equation
a and b are parallel
(d) a dot b= 9-3-6=0
a and b are orthogonal
We know:x^2+y^2+x−6y+9=0So, we complete the square as such:x^2+y^2+x−6y+9=x^2+x+y^2−6y+9=(x+1/2)^2+(y−3)^2=(1/2)^2=1/4
1. Introduction. This paper discusses a special form of positive dependence.
Positive dependence may refer to two random variables that have
a positive covariance, but other definitions of positive dependence have
been proposed as well; see [24] for an overview. Random variables X =
(X1, . . . , Xd) are said to be associated if cov{f(X), g(X)} ≥ 0 for any
two non-decreasing functions f and g for which E|f(X)|, E|g(X)|, and
E|f(X)g(X)| all exist [13]. This notion has important applications in probability
theory and statistical physics; see, for example, [28, 29].
However, association may be difficult to verify in a specific context. The
celebrated FKG theorem, formulated by Fortuin, Kasteleyn, and Ginibre in
[14], introduces an alternative notion and establishes that X are associated if
∗
SF was supported in part by an NSERC Discovery Research Grant, KS by grant
#FA9550-12-1-0392 from the U.S. Air Force Office of Scientific Research (AFOSR) and
the Defense Advanced Research Projects Agency (DARPA), CU by the Austrian Science
Fund (FWF) Y 903-N35, and PZ by the European Union Seventh Framework Programme
PIOF-GA-2011-300975.
MSC 2010 subject classifications: Primary 60E15, 62H99; secondary 15B48
Keywords and phrases: Association, concentration graph, conditional Gaussian distribution,
faithfulness, graphical models, log-linear interactions, Markov property, positive
Answer:
2 8/11 = b
Step-by-step explanation:
2b + 8 - 5b + 3 = -13 + 8b - 5
combine like terms
11 - 3b = -18 + 8b
add 3b
11 = -18 + 11b
add 18
29 = 11b
divide by 11
2 8/11 = b
Answer: 2 1/4
Step-by-step explanation:
