For an F distribution, the number of degrees of freedom for the numerator a. must be larger than the number of degrees of freedom for the denominator. b. can be larger, smaller, or equal to the number of degrees of freedom for the denominator. c. must be smaller than the number of degrees of freedom for the denominator. d. must be equal to the number of degrees of freedom for the denominator.

b. can be larger, smaller, or equal to the number of degrees of freedom for the denominator.

Step-by-step explanation:

The distribution of all possible values of the f statistic is called an F distribution with various degree of freedom. For an F distribution, the F statistic is greater than or equal to zero and as the degrees of freedom for the numerator and for the denominator get larger, the curve approximates the normal.

For an F distribution, the number of degrees of freedom for the numerator can be larger, smaller, or equal to the number of degrees of freedom for the denominator.

(1)  Rotation of 90° counterclockwise about the origin (2) Translation 2 units right .

Step-by-step explanation:

We have been asked to determine a sequence of transformations that maps △ABC to △A′B′C'.

To map △ABC to △A′B′C′ first of all we have to rotate △ABC 90° counterclockwise (positive rotation) about the origin. After rotating △ABC 90° our new coordinates will be A(-3,-4), B(-3,-1) and C (-1,-2).

We can see that distance between A and origin is and distance between A' and origin is also . Distance between A and A' is , which forms a right triangle.

To map △ABC to △A′B′C′ completely we will translate our △A′B′C' 2 units right. After translation our coordinates will be A'(-1,-4), B'(-1,-1) and C'(1,-2).

Therefore, a sequence of transformations that maps △ABC to △A′B′C′ is (1) rotation of 90° counterclockwise about the origin and (2) translation 2 units right.