please see photo attached
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:
The t-shirt shop sold 21 long sleeve shirts and 17 short sleeve shirts.
Step-by-step explanation:
To solve this problem, we should create a system of equations. Let's let short sleeve t-shirts be represented by the variable s and long sleeve t-shirts be represented by the variable l.
We know that the shop sold 38 total shirts, or in other words, the amount of long sleeve and short sleeve shirts combined is 38. If we write this as an equation, we get: s + l = 38.
We can make another equation with the prices of the shirts. If we take each type of shirt and multiply each price by the number sold and add them together, we should get the shop's total profits. Represented as an equation, this is: 10s + 15l = 485.
Now that we have two equations, we should try to solve the system. In this case, it is easiest to use substitution, so we are going to rewrite the first equation in terms of one variable.
s + l = 38
s = 38 - l
If we substitute this equivalent value for the variable s into the second equation, we get:
10s + 15l = 485
10(38 - l) + 15l = 485
Now we have an equation that only has one variable, so we can simplify both sides and then isolate the variable.
380 - 10l + 15l = 485
380 + 5l = 485
5l = 105
l = 21
Now, we can substitute this value for l back into the first equation to solve for the variable s.
s + l = 38
s + 21 = 38
s = 17
Therefore, the t-shirt shop sold 21 long sleeve shirts and 17 short sleeve shirts.
Hope this helps!
54 is the hypotenuse because it is the longest side. Square all of the sides. So 54^2=2916
51^2=2601
22^2=484
Now you have 2916=2601+484
Add the two and they will be greater than 2916. Because of that, you will have an acute triangle because 22^2+51^2>54^2
In short, its B
You are not giving enough information but in one of the calsses the average of student's height might be greater than the other class beacause one of the two classes needs to have 1 extra person than the other calss
