(1 pt) find a parametrization of the ellipse centered at the origin in the xy-plane that has major diameter 14 along the x-axis, minor diameter 10 along the y-axis, and is oriented counter-clockwise. your parametrization should make the point (7,0) correspond to t=0. use t as the parameter for all of your answers.

Step-by-step explanation:

The parametrization of an ellipse center at origin and counter-clockwise is given by the formulas:

Where “a” is the radius of the major axis along the x-axis and “b” is the radius of the minor axis along the y-axis. Since the major diameter along the x-axis is 14 then its radius is its half, thus a=7. Similarly, since the minor diameter along the y-axis is 10, then its radius is half of it, thus b=5

Therefore, the parametric equations for the ellipse become:

Notice at t=0 we get:

which satisfies that the parametrization at t=0 makes the point (7,0)

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.