Refresher - MATHEMATICS Quiz 4
PROBLEM 1:
From the set numbers 14, 8, 6, 2, find the mean absolute deviation.
Solution
Mean value:
2 + 6 + 8 + 14
x=
4
x = 7.5
Mean absolute deviation:
1
MAD = (x - x)
n
1
MAD = ⎡⎣ (2 - 7.5) + (6 - 7.5) + (8 - 7.5) + (14 - 7.5) ⎤⎦
4
MAD = 3.5
, Refresher - MATHEMATICS Quiz 4
PROBLEM 2:
From the top of a lighthouse, 175 ft. above the water, the angle of
depression of a boat due south is 18˚50’. Calculate the speed of the boat
if after it moves due west for 2 min, the angle of depression is 14˚20’.
Solution: D
175
tan 14˚20' =
AB
AB = 684.89 ft. 175
N
14 20’
o
A
175
tan 18˚50' =
AC 18 50’
o
AC = 513.08 ft.
C
2 2 2
(BC) = (AB) - (AC)
BC2 = (684.89)2 - (513.08)2
BC = 453.70 ft.
D=Vt
453.70 = V(2)
V = 227 ft. / min
PROBLEM 1:
From the set numbers 14, 8, 6, 2, find the mean absolute deviation.
Solution
Mean value:
2 + 6 + 8 + 14
x=
4
x = 7.5
Mean absolute deviation:
1
MAD = (x - x)
n
1
MAD = ⎡⎣ (2 - 7.5) + (6 - 7.5) + (8 - 7.5) + (14 - 7.5) ⎤⎦
4
MAD = 3.5
, Refresher - MATHEMATICS Quiz 4
PROBLEM 2:
From the top of a lighthouse, 175 ft. above the water, the angle of
depression of a boat due south is 18˚50’. Calculate the speed of the boat
if after it moves due west for 2 min, the angle of depression is 14˚20’.
Solution: D
175
tan 14˚20' =
AB
AB = 684.89 ft. 175
N
14 20’
o
A
175
tan 18˚50' =
AC 18 50’
o
AC = 513.08 ft.
C
2 2 2
(BC) = (AB) - (AC)
BC2 = (684.89)2 - (513.08)2
BC = 453.70 ft.
D=Vt
453.70 = V(2)
V = 227 ft. / min
