Consider the parametric equations

x = cos(2t) - sin(2t), y= cos(2t) + =sin(2t t <

a. Eliminate the parameter t to find a Cartesian equation for the parametric curve.

Hint: Multiply y by v2, then square both equations and add them together.

b. Sketch the parametric curve, indicating with arrows the direction in which the curve is traced.

In a test for esp (extrasensory perception), a subject is told that cards only the experimenter can see contain either a star, a circle, a wave, or a square. as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. a subject who is just guessing has probability 0.25 of guessing correctly on each card. a. the count of correct guesses in 20 cards has a binomial distribution. what are n and p? b. what is the mean number of correct guesses in 20 cards for subjects who are just guessing? c. what is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?