-2x + 6y= 18 is in standard form, use y=mx+b to solve that.
we are given
first term is
![a_1=42](https://tex.z-dn.net/?f=%20a_1%3D42%20)
common ratio is
![r=\frac{3}{4}](https://tex.z-dn.net/?f=%20r%3D%5Cfrac%7B3%7D%7B4%7D%20%20)
now, we can find nth term
![a_i=a_1(r)^{i-1}](https://tex.z-dn.net/?f=%20a_i%3Da_1%28r%29%5E%7Bi-1%7D%20)
now, we can plug values
![a_i=42(\frac{3}{4})^{i-1}](https://tex.z-dn.net/?f=%20a_i%3D42%28%5Cfrac%7B3%7D%7B4%7D%29%5E%7Bi-1%7D%20)
now, we can write in sigma form
![sum=\sum _{i=1}^{\infty }\:42(\frac{3}{4})^{i-1}](https://tex.z-dn.net/?f=%20sum%3D%5Csum%20_%7Bi%3D1%7D%5E%7B%5Cinfty%20%7D%5C%3A42%28%5Cfrac%7B3%7D%7B4%7D%29%5E%7Bi-1%7D%20)
now, we can find sum
we can use formula
![sum=\frac{a}{1-r}](https://tex.z-dn.net/?f=%20sum%3D%5Cfrac%7Ba%7D%7B1-r%7D%20%20)
now, we can plug values
we get
![sum=\frac{42}{1-\frac{3}{4}}](https://tex.z-dn.net/?f=%20sum%3D%5Cfrac%7B42%7D%7B1-%5Cfrac%7B3%7D%7B4%7D%7D%20%20)
![sum=168](https://tex.z-dn.net/?f=%20sum%3D168%20%20)
so, option-D.................Answer
Answer:
The answer to this question can be defined as follows:
i) ![\bold{p(x)= -5x^2+ 217x- 1,401} \\](https://tex.z-dn.net/?f=%5Cbold%7Bp%28x%29%3D%20-5x%5E2%2B%20217x-%201%2C401%7D%20%5C%5C)
ii) x=22 units
iii) Maximum profit: 953.45
Step-by-step explanation:
Given value:
p(x) = 211 − 5x \\
C(x) = 1,401 + 16x
The formula for calculating the profit function value:
![\to \bold{P(x)= xp(x) - C(x)}](https://tex.z-dn.net/?f=%5Cto%20%5Cbold%7BP%28x%29%3D%20xp%28x%29%20-%20C%28x%29%7D)
![= x(211-5x)- 1,401 + 16x\\\\= 211x -5x^2-1,401+16x\\\\= -5x^2+ 217x- 1,401 \\](https://tex.z-dn.net/?f=%3D%20x%28211-5x%29-%201%2C401%20%2B%2016x%5C%5C%5C%5C%3D%20211x%20-5x%5E2-1%2C401%2B16x%5C%5C%5C%5C%3D%20-5x%5E2%2B%20217x-%201%2C401%20%5C%5C)
The formula for calculating the value for maximum profit:
![p'(x) = - 10x + 217 =0](https://tex.z-dn.net/?f=p%27%28x%29%20%20%3D%20%20-%2010x%20%2B%20217%20%3D0)
![217= 10x\\\\x= \frac{217}{10}\\\\x= 21.7](https://tex.z-dn.net/?f=217%3D%2010x%5C%5C%5C%5Cx%3D%20%5Cfrac%7B217%7D%7B10%7D%5C%5C%5C%5Cx%3D%2021.7)
So, the production level is 22 units
Maximum profit:
![\to p(21.7)= - 5 (21.7)^2+217 (21.7) -1,401\\\\](https://tex.z-dn.net/?f=%5Cto%20p%2821.7%29%3D%20-%205%20%2821.7%29%5E2%2B217%20%2821.7%29%20-1%2C401%5C%5C%5C%5C)
![=-5 (470.89) +217 (21.7) -1,401\\\\=-2354.45+ 4708.9-1,401\\\\= 953.45](https://tex.z-dn.net/?f=%3D-5%20%28470.89%29%20%2B217%20%2821.7%29%20-1%2C401%5C%5C%5C%5C%3D-2354.45%2B%204708.9-1%2C401%5C%5C%5C%5C%3D%20953.45)
Answer:
<h2>
9.1 inches</h2>
Step-by-step explanation:
1cm = 0.3937007874 inches.
As there are 2.54cm in an inch, to convert your cm figure to inches you need to divide your figure by 2.54.
9.05512 -> 9.1 inches
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