Progressive Real Estate Partners recently completed the sale of a Mobil Gas Station, convenience store, and express car wash located at 130 West Valley Blvd in Colton for $5.2 million. The transaction included both the business and real estate.
Victor Buendia, Senior Vice President of gas station and car wash sales at Progressive Real Estate Partners, represented both parties involved in the sale. The seller was an Inland Empire-based private party who had owned the property for over 30 years. The buyer is also an Inland Empire-based private investor who plans to renovate the convenience store and implement new strategies to enhance customer experience.
According to Buendia, gas stations are essential services that are always in demand, especially those located near freeways which continue to attract significant interest from buyers. He added that the buyer is excited about making improvements to further grow the business’s success.
The property features a Mobil station with 16 fueling positions for gas/diesel vehicles as well as an express car wash facility. Additionally, there is a 924-square-foot Mobil Mart convenience store offering various grab-and-go snacks for customers’ convenience.
x = int(input(“Enter first number: “))
y = int(input(“Enter second number: “))
# addition
print(‘x + y =’, x+y)
# subtraction
print(‘x – y =’, x-y)
# multiplication
print(‘x * y =’, x*y)
# division
if(y ==0):
print(“Cannot divide by zero”)
else:
print(‘x / y =’ , float(x/y)) \documentclass[12pt]{article}
\usepackage{amsmath} % never write a paper without using this package (it adds many useful features)
% Note: amssymb automatically loaded by amsmath
% Set margins on page
%\setlength{\oddsidemargin}{0.25in}
%\setlength{\evensidemargin}{-0.25in}
%\setlength{\textwidth}{7in}
\begin{document} % This tells LaTeX to start the document
% Define some handy variables
\newcommand{\myname}{$John Doe$ }
\newcommand{\myandrew}{$jdoe@andrew.cmu.edu$ }
% Write a title page
\noindent \LARGE \textbf{Homework 1} \\
\normalsize CS003: Algorithms, Spring 2021 \\
Section B (10am)\\
Instructor: Bill Bird \\
TA’s Name: John Doe \\
Due Date: $01/21/2021$
\vspace*{5mm}
\noindent By submitting this assignment, I agree by the terms of the course policy on academic integrity and certify that all work is my own.
\vspace*{-2mm}
I have read and understood Chapter 3 in Goodrich et al., Data Structures and Algorithms in Java (6th ed.) covering asymptotic notation.
\vspace*{-2mm}
Name:\hspace*{80pt}\underline{$John Doe$}\\
Andrew ID:\hspace*{50pt}\underline{$jdoe@andrew.cmu.edu$}\\
Collaborators:
\underline{
$\bullet~Jane Smith$, $\bullet~Jack Williams$, $\bullet~Sam Brown$
}
%%%%%%%%%%%%%%%
%%% PROBLEM %%%
%%%%%%%%%%%%%%%
Problem A:
Prove that for any positive integer n,
$$n^3 + 4n = O(n^3)$$
Solution:\\
To prove this statement we must show that there exists constants c >0 such as $f(n)\leq cg(n)$ where f,g are functions defined over the positive integers.\\
Let $f(n) = n^3 + 4n$ and $g(n)=n^3$. For any value of n, we can see that f(n) is always less than or equal to g(n). Therefore, for all values of c >0 there exists a constant k such as:
$$f(x)\leq cg(x), \forall x>k$$
Hence,
$n^3 + 4n\leq cn^3$
$\Rightarrow~1+ \frac{4}{x} 0 such as $p(x)\leq cx^{d}$ where p,q are functions defined over the real numbers.\\
Given,
$p(x)$ = $\sum_{i=0}^{d}$a$_ix_i$, where i represents powers from 1 to d.
We know by definition of big-O notation,
$f (x)$ = O$(g (x))$
if and only if
there exist constants M>0 and N��1 so that |f (t)| ≤ Mg(t)
for all t ≥ N.
Now let us assume some arbitrary function q which satisfies above condition.
$q(t)=Mgt+c_2t+c_1$
As mentioned earlier since q satisfies above condition it also satisfy following inequality:
|p(t)| ≤ |c$_da_d$t$ ^{k+d}| + … + |c_1t| ≤ (c$_da_d$ + … + c$_1$)t$ ^{k+d}$
Therefore, we can conclude that p is O($x^{d}$)
Hence proved.
%%%%%%%%%%%%%%%
%%% PROBLEM %%%
%%%%%%%%%%%%%%%
Problem C:
Prove that if f(n) = $n^2$, then f(n) is not O($n^{3/2}$).
Solution:\\
To prove this statement we must show that there does not exist constants c >0 such as $f(x)\leq cg(x)$ where x $\geq k$.\\
Let us assume some arbitrary value of n and let it be k. Now,
$f(k)=k^2$
and
$c.g(k)=c.k^\frac{3}{2}$
Now for any value of c>0, the inequality holds true only when,
$k \leq~\sqrt{\frac{k}{c}}$
But since our assumption was for all values greater than or equal to k. This contradicts our assumption and hence the statement holds true.
$$f(n)\neq~O(g(n))$$
\vspace*{-5mm}
\noindent\rule[0ex]{\linewidth}{1pt}
% That’s all folks!
\end{document}Solve in integers the equation
\[ 7^n – 4m(m+10)-9=0. \]%\section*{}
The author would like to thank his supervisor Dr.\ Niall Madden for his guidance throughout this project.
He would also like to thank Prof.\ Liam Barry from Dublin City University who provided access to a number of key pieces of equipment used during this research work.
Thanks are due also go out towards Dr.\ David Goulding at Tyndall National Institute who kindly supplied samples used in characterisation experiments.
Finally thanks are due to the author’s colleagues in the Photonics Systems Group at Tyndall National Institute for their support and assistance throughout this project.
\hypertarget{class_c_utl_memory}{}\doxysection{CUtl\+Memory\texorpdfstring{$<$}{$}{>} Class Template Reference}
\label{class_c_utl_memory}\index{CUtlMemory$$@{CUtlMemory$$}}
Inheritance diagram for CUtl\+Memory\texorpdfstring{$<$}{$}{>}\+:\begin{figure}[H]
\begin{center}
<<<<<<>>>>>> e3f9c3234d10a2a6b202bb5dd85430906079079e
\includegraphics[height=1.333333cm]{class_c_utl_memory}
\end{center}
<<<<<<>>>>>> e3f9c3234d10a2a6b202bb5dd85430906079079e
{\bfseries Initial value\+:}
<<<<<<< HEAD
{
m\_pAddress = pHeap + nOffset;
m\_nAllocationCount = nGrowSize;
}
=======
{
m_pAddress = pHeap + nOffset;
m_nAllocationCount = nGrowSize;
}
template
void Construct(U *pMem)
{
::new(pMem) U();
}
template
void CopyConstruct(U *pMem,const U& src)
{
::new(pMem)U(src);
}
template
inline void Destruct(V *pObj)
{
pObj->~V();
}
// This is a useful macro to use in copy constructors.
#define COPY\_CONSTRUCT\_FISH( \_type, \_expression ) \
do \
{ \
new (MemAlloc\_GetSlab()) \_type; \
MemAlloc\_CopyConstruct( this, (\_expression) ); \
return *this; \
} while (0)
>>>>>>> e3f9c3234d10a2a6b202bb5dd85430906079079e
template
inline void Destruct(T *pMemory)
{
pMemory->~T();
}
<<<<<<>>>>>> e3f9c3234d10a2a6b202bb5dd85430906079079e
#define CONSTRUCTED\_FISH() new(this) CSimpleClass()
//—————————————————————————–
//
//—————————————————————————–
template
void Construct(A* pMemory);
template
void Construct(A* pMemory, B const& src);
<<<<<<>>>>>> e3f9c3234d10a2a6b202bb5dd85430906079079e
//—————————————————————————–
//
//—————————————————————————–
#ifdef USESALLOCATOR
#if defined(_WIN32)
#pragma warning(push)
#pragma warning(disable:4100)
#endif // _WIN32
template
inline void OnElementConstructed(const CUtlBlockLinked &element) {}
template
inline void OnElementDestructed(const CUtlBlockLinked &element){}
#if defined(_WIN32)
#pragma warning(pop)
#endif // _WIN32
#else
#include “tier1/memdbgon.h”
#undef malloc
#undef realloc
#undef free
#ifndef UTLMEMORY_TRACK
#define UTLMEMORY\_TRACK 0
#endif
#ifndef UTLMEMORY\_TRACK\_ALLOCATIONS
#define UTLMEMORY\_TRACK_ALLOCATIONS 0
#endif
#if defined( \_DEBUG ) && !defined(STEAM) && (UTLSTRINGMP == -1)
#include “tier0/dbg.h”
#undef malloc
#undef realloc
#undef free
inline void * UtlMemoryAlloc(size_t nSize)
{
if (nSize <= 0)
return NULL;
void *pMem = malloc(nSize);
if (!pMem) // we don't want to crash, but we do want a chance to debug this!
{
#ifdef PLATFORM_WINDOWS_PC64
if(IsDebuggerPresent())
=======
template
void Construct(T* pMemory){}
template
void Construct(T* pMemory,const B& src){}
//—————————————————————————–
//
//—————————————————————————–
// This is a useful
