In 48 days, they would have consumed 108 gallons, and have 22 left, so yeah. 48 days
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: First train speed shall be 42 mi/hr
Second train speed shall be 84 mi/hr
Yes it is the valid answer, it gets annoying when almost everyone enters the wrong answer for a good laugh. Either way, hope this helps! Have a spectacular day.
Step-by-step explanation:
What is the 1st train's head start in miles?
Let +s+ = the speed of the 1st train in mi/hr
From 2PM to 4PM is 2 hrs
+d%5B1%5D+=+s%2A2+
---------------------
Let +d+ = distance the 2nd train travels until
it overtakes the 1st train
From 4PM to 6PM is 2 hrs
Start time when the 2nd train leaves
---------------------
Equation for 1st train:
(1) +d+-+2s+=+s%2A2+
Equation for 2nd train:
(2) +d+=+%28+s%2B42+%29%2A2+
--------------------
Substitute (2) into (1)
(1) +%28+s%2B42+%29%2A2+-+2s+=+s%2A2+
(1) +2s+%2B+84+-+2s+=+2s+
(1) +2s+=+84+
(1) +s+=+42+
and
+s%2B+42+=+42+%2B+42+
+s+%2B+42+=+84+
------------------
The 1st train's speed is 42 mi/hr
The 2nd train's speed is 84 mi/hr
---------------------------
check:
(2) +d+=+%28+s%2B42+%29%2A2+
(2) +d+=84%2A2+
(2) +d+=+168+
and
(1) +d+-+2s+=+s%2A2+
(1) +d+-+2%2A42+=+42%2A2+
(1) +d+=+84+%2B+84+
(1) +d+=+168+
Hey there,
The x-intercept is= 6/5 = 1.20000
The y-intercept is= 6/8 = 3/4 = 0.75000
:)
