Using "Proof by Contraposition",sho that: if n is any odd integer and m is any even integer, then, 3m^3+2m^2 is odd.

At t=0 the current to a dc electric motor is reversed, resulting in an angular displacement of the motor shaft given by 𝜃(𝑡) = (250 𝑟𝑎𝑑/𝑠 )𝑡 − (20.0 𝑟𝑎𝑑/𝑠 2 )𝑡 2 − (1.50 𝑟𝑎𝑑/𝑠 3 ) 𝑡 3 . (a) At what time is the angular velocity of the motor shaft zero? (b) Calculate the angular acceleration at the instant that the motor shaft has zero angular velocity. (c) How many revolutions does the motor shaft turn through between the time when the current is reversed and the instant when the angular velocity is zero? (d) How fast was the motor shaft rotating at t=0 when the current was reversed? (e) Calculate the average angular velocity for the time period from t=0 to the time calculated in part (a). A

Use the table to determine the total of the servicecharge. Service charges for Gary Baxter's account were the basic charge, 8 bills paid, 1 overdraft, $450 cash advance, and 3 regional ATM transactions.
$\begin{array}{|lc|}\hline \text{ Online Banking Service }& \text{ Service Charge }\\ \text{ Basic Monthly Charge }& \$6.95\\ \text{ Bill Payment-first 5 N/C }& 0.50\\ \text{ Printed Statement }& 4.00\\ \text{ Replace Lost Card }& 5.00\\ \text{ Overdraft }& 25.00\\ \text{ International Wire Transfer }& 20.00\\ \text{ ATM Transaction Charges }\\ \text{ Local Network }& \text{ N/C }\\ \text{ Regional Network }& 1.00\\ \text{ National Network }& 2.00\\ \text{ Out-of-Network }& 3.00\\ \text{ Cash Advance }-2.00\mathrm{\%}\text{ of }\text{ Amt }& \$10.00\mathrm{Max}\\ \hline\end{array}$

Use the definition of Laplace Transform to determine the Laplace Transforms for 
the following time-domain function

f(t)=sin(3t)

B. G. Cosmos, a scientist, believes that the probability is ${\displaystyle \frac{2}{5}}$ that aliens from an advanced civilization on Planet X are trying to communicate with us by sending high-frequency signals to Earth. By using sophisticated equipment, Cosmos hopes to pick up these signals. The manufacturer of the equipment, Trekee, Inc., claims that if aliens are indeed sending signals, the probability that the equipment will detect them is ${\displaystyle \frac{3}{5}}$. However, if aliens are not sending signals, the probability that the equipment will seem to detect such signals is $\frac{1}{10}$. If the equipment detects signals, what is the probability that aliens are actually sending them?