How has the court determined that a defendant waived his Miranda right?

"The prosecution had to prove by a preponderance of evidence that defendant knowingly and voluntarily waived his Miranda rights. [Citations.] A valid waiver may be express or implied. [Citation.] Although it may not be inferred 'simply from the silence of the accused after warnings are given or simply from the fact that a confession was in fact eventually obtained' [citation], it may be inferred where 'the actions and words of the person interrogated'clearly imply it. [Citation.] [] In determining whether a defendant waived his rights, the court must consider 'the totality of the circumstances surrounding the interrogation.' [Citation.]" (People v. Cortes (1999) 71 Cal.App.4th 62, 69.) "On appeal, we conduct an independent review of the trial court's legal determination and rely upon the trial court's findings on disputed facts if supported by substantial evidence. [Citation.]" (People v. Williams, supra, 49 Cal.4th at p. 425.)

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