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The method to produce randomly generated numbers in Dart is the Random() class. This class provides different methods to generate random numbers such as nextInt(), nextDouble(), and nextBool().

Example:

import 'dart:math';

void main() {
  // create a random number generator
  Random rng = Random();

  // generate a random integer between 0 and 9
  int randomInt = rng.nextInt(10);
  print(randomInt);

  // generate a random double between 0.0 and 1.0
  double randomDouble = rng.nextDouble();
  print(randomDouble);

  // generate a random boolean value
  bool randomBool = rng.nextBool();
  print(randomBool);
}