The other day, critic ivor smallbrain gave a lecture to an audience consisting of 5 mathematicians. each mathematician fell asleep exactly twice during the lecture. for each pair of mathematicians, there was a moment during the lecture when they were both asleep. prove that there was a moment when three of the mathematicians were simultaneously asleep.

Any greatly appreciated! you in advance. jody bought 20 shares of amazon at the close price of $121.00. she bought 20 more shares a year later at the price of $127.00. two years later she's sold all of her shares at the price of $133.00. her broker charges $50 for each transaction. after all of these transactions how much money did jody make? a.$65.00b.$5288.00c.$210.00d.$310.00

Suppose a pendulum is l meters long. the time,t,in seconds that it tales to swing back and forth once is given by t=2.01

Evaluate the expression for the given value of the variable. ∣-4b-8∣+∣-1-b^2 ∣+2b^3 ; b=-2