Who knows forty-five?
Please cite/link your sources, if possible. At some point in the next few days, I will:
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45 are the days from the Exodus until the arrival of the Jewish People at Mount Sinai. Correspondingly, Hashem describes Himself (through the metaphor of the prophet Hosea's actions) as having acquired His spouse, the Jewish People, with "a chomer of barley and a lesech of barley" - totaling 45 se'ah. (Hosea 3:2 and Radak there)
Forty-five are the Amida blessings that you'll say on a "Friday" (using the non-Jewish definition of Friday): 19 for Friday Shachris, 19 for Friday Mincha, 7 for Shabbos Maariv.
Speaking of davening, forty-five are the minutes after 8AM at which many newer Centrist Orthodox synagogues on the East Coast begin services on Shabbos morning. Many older synagogues figured 9AM was a good time, but it turns out for the US East Coast that starting 15 minutes earlier can mean making Sof Zman Krias Shema (latest time for saying the Shema, the first quarter of daylight hours) much more often.
(I looked at a sunrise/sunset chart for Brooklyn. If my math is right, assuming 34 minutes from start to Krias Shema, the number of additional days a year at which you'll make Shema in time by switching from 9 to 8:45 is ... 45.)
Also, isn't there someone with the opinion that Shabbos ends 45 minutes after sunset (in New York)?
The shem מ״ה (that is, יו״ד ה״א וא״ו ה״א)
45 times the Torah warns us regarding a convert (e.g. to love, not cheat, not cause suffering)
corresponding to the
45 times the Torah warns us against idol worship.
45 are the maximum Hallel days in a year (in the diaspora):
So that's 27 + Rosh Chodesh. How many of those are there?
The following months always have two days of Rosh Chodesh [...]: Cheshvan, Adar (and Adar II), Iyar, Tammuz, and Elul. The following months always have one day of Rosh Chodesh: Tishrei, Shevat, Nisan, Sivan, and Av. The months of Kislev and Tevet [...] some years both have two days. (source)
We don't celebrate Rosh Chodesh in Tishrei, and Rosh Chodesh Tevet falls in Chanukah so has already been counted. The others total 18.