Does the point (2
3
, 2) lie on the circle that is centered at the origin and contains the point (0, -4)? Explain?

  no

Step-by-step explanation:

We assume the point of interest is (2/3, 2). If the circle is centered at the origin and contains the point (0, -4), its radius is 4. For a circle centered at the origin, the magnitude of the sum of coordinates of any point on the circle must be at least equal to the radius.

The sum of the given coordinates is 2 2/3, which is less than 4. The point is inside the circle, not on it.

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation: