15. e. Since
AB and
CD are parallel lines cut by a trans-
versal, angle
f is equal to the sum of angles
c and
b . However, angle
f and angle
g are not equal—
they are supplementary. Therefore, the sum of
angles
c and
b is also supplementary—and not
equal—to
g .
16. b. The surface area of a cube is equal to 6
e 2
, where
e is the length of an edge of a cube. The surface
area of a cube with an edge equal to one unit is
6 cubic units. If the lengths of the edges are
decreased by 20%, then the surface area becomes
6(
4
5
)
2
=
9
2
6
5
cubic units, a decrease of
=
=
2
9
5
=
1
3
0
6
0
= 36%.
17. c. For the median and mode to equal each other,
the fifth score must be the same as one of the
first four, and, it must fall in the middle position
when the five scores are ordered. Therefore,
Simon must have scored either 15 or 18 points
in his fifth game. If he scored 15 points, then his
mean score would have been greater than 15:
17.4. Simon scored 18 points in his fifth game,
making the mean, median, and mode for the
five games equal to 18.
18. a. To go from
g (
2
5
) to
g (–
1
5
), you would multiply
the exponent of
g (
2
5
) by (–
1
2
). Therefore, to go
from 16 (the value of
g (
2
5
)) to the value of
g (–
1
5
),
multiply the exponent of 16 by (–
1
2
). The expo-
nent of 16 is one, so the value of
g (–
1
5
) = 16 to
the (–
1
2
) power, which is
1
4
.
