There are 50 students in our class. (1) What is the probability that Jack and Mike have the same birthday? (2) What is the probability that no one has the same birthday as the professor? (3) What is the probability that there are two and only two having the same birthday?

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Find the arc length parameter along the given curve from the point where tequals=0 by evaluating the integral s(t)equals=integral from 0 to t startabsolutevalue bold v left parenthesis tau right parenthesis endabsolutevalue d tau∫0tv(τ) dτ. then find the length of the indicated portion of the curve r(t)equals=1010cosine tcost iplus+1010sine tsint jplus+88t k, where 0less than or equals≤tless than or equals≤startfraction pi over 3 endfraction π 3.

Aregular hexagon has sides of 2 feet. what is the area of the hexagon? 12 ft2 12 ft2 24 ft2 6 ft2