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Prior research has established that valence-trustworthiness and power-dominance are the two main dimensions of voice evaluation at zero-acquaintance. These impressions shape many of our interactions and high-impact decisions, so it is crucial for many domains to understand this dynamic. Yet, the relationship between acoustical properties of novel voices and personality/attitudinal traits attributions remains poorly understood. The fundamental problem of understanding vocal impressions and relative decision-making is linked to the complex nature of the acoustical properties in voices. In order to disentangle this relationship, this study extends the line of research on the acoustical bases of vocal impressions in two ways. First, by attempting to replicate previous finding on the bi-dimensional nature of first impressions: using personality judgements and establishing a correspondence between acoustics and voice-first-impression (VFI) dimensions relative to sex (Study 1). Second (Study 2), by exploring the non-linear relationships between acoustical parameters and VFI by the means of machine learning models. In accordance with literature, a bi-dimensional projection comprising valence-trustworthiness and power-dominance evaluations is found to explain 80% of the VFI. In study 1, brighter (high center of gravity), smoother (low shimmers), and louder (high minimum intensity) voices reflected trustworthiness, while vocal roughness (harmonic to noise-ratio), energy in the high frequencies (Energy3250), pitch (Quantile 1, Quantile 5) and lower range of pitch values reflected dominance. In study 2, above chance classification of vocal profiles was achieved by both Support Vector Machine (77.78%) and Random-Forest (Out-Of-Bag = 36.14) classifiers, generally confirming that machine learning algorithms could predict first impressions from voices. Hence results support a bi-dimensional structure to VFI, emphasize the usefulness of machine learning techniques in understanding vocal impressions, and shed light on the influence of sex on VFI formation.