Final answer:
The American Totalizator Company provided parimutuel betting systems for racetracks. Eckert and Mauchly, known for inventing the ENIAC, were not directly involved with the company, but their work influenced the evolution of electronic computing in various industries, including betting systems.
Step-by-step explanation:
The American totalizator company refers to American Totalisator, a company that used to provide parimutuel betting systems for racetracks. It created mechanical and later electronic systems that allowed many bettors to pool their bets on horse and greyhound races to determine fair odds and payoffs.
Regarding Eckert and Mauchly, these names refer to John Presper Eckert and John William Mauchly, the inventors of the ENIAC, one of the earliest electronic general-purpose digital computers. Although they were not directly involved with American Totalisator, their development of electronic computing paved the way for the kinds of complex calculations and data processing needed in tote systems. Eventually, the influence of their work led to the replacement of mechanical machines with electronic systems in many industries, including parimutuel betting.