Sarah was answered, by conceiving a child, on Rosh HaShanah: Rosh HaShanah 10b, 11a Rachel was answered, by conceiving a child, on Rosh HaShanah: Rosh HaShanah 10b, 11a Chanah was answered, by conceiving a child, on Rosh HaShanah: Rosh HaShanah 10b, 11a Joseph was freed from the Egyptian jail on Rosh HaShanah: Rosh HaShanah 10b, 11a-b
On Rosh HaShanah, the slavery in Egypt halted: Rosh HaShanah 11a, 11b
