Prove the hyperbolic function 1 - tanh2x = sech2x.

Ernest is purchasing a $175,000 home with a 30-year mortgage. he will make a $15,000 down payment. use the table below to find his monthly pmi payment.

Write two subtraction equations that are equivalent to 5 + 12 = 17.

The number if marbles of different colors stored in a hat is listed below: 4 red marbles 10 green marbles 7 blue marbles. without looking in the hat, dan takes out a marble at random. he replaces the marble and then takes out another marble from the hat. what is the probability that dan takes out a blue marble in both draws?