Are women allowed to give a speech when their audience is 50% men as well?
This is not proper for a religious crowd. [1] Poskim advise against this. Some even forbid it outright. [2]
However, if the crowd is not religious, and the purpose is to teach them Torah, there could be some room for leniency in very specific scenarios, and one should seek guidance from a Rav. [3]
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[1] Men need to look at the speaker, and to have men looking at a woman speak for a long period of time is not Tznius. We find in the Poskim that by the age of 9 it is important to have only male teachers.
[2] See Shaarei Yosher III: 21. Shevet Halevi 3:14. Mishnah Halachos 5:218. 11: 58. L’horos Nasan 1 EH 60:5. Igros Moshe OC 5: 12. See also ibid. 2:36.
[3] See also the end of question #2806 (2).
#2806 (7)