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Math B Regents Exam Questions by Type - 4 Point Free Response Page 13
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70. A picnic table in the shape of a regular
octagon is shown in the accompanying
diagram. If the length of AE is 6 feet, find
the length of one side of the table to the
nearest tenth of a foot, and find the area of the
table's surface to the nearest tenth of a square
foot.
71. Graph and label the following equations, a
and b, on the accompanying set of coordinate
axes.
2
ay : = x
2
by : =−( x− 4)
+ 3
Describe the composition of transformations
performed on a to get b.
73. Two tow trucks try to pull a car out of a ditch.
One tow truck applies a force of 1,500 pounds
while the other truck applies a force of 2,000
pounds. The resultant force is 3,000 pounds.
Find the angle between the two applied
forces, rounded to the nearest degree.
74. A rectangular piece of cardboard is to be
formed into an uncovered box. The piece of
cardboard is 2 centimeters longer than it is
wide. A square that measures 3 centimeters
on a side is cut from each corner. When the
sides are turned up to form the box, its
volume is 765 cubic centimeters. Find the
dimensions, in centimeters, of the original
piece of cardboard.
75. To measure the distance through a mountain
for a proposed tunnel, surveyors chose points
A and B at each end of the proposed tunnel
and a point C near the mountain. They
determined that AC = 3,800 meters, BC =
2,900 meters, and m∠
ACB =110. Draw a
diagram to illustrate this situation and find the
length of the tunnel, to the nearest meter.
76. Team A and team B are playing in a league.
They will play each other five times. If the
probability that team A wins a game is 1 3 ,
what is the probability that team A will win at
least three of the five games?
2
77. Solve for x: log ( x + 3x) − log ( x+ 5)
= 1
4
4
72. Twenty high school students took an
examination and received the following
scores:
70, 60, 75, 68, 85, 86, 78, 72, 82, 88, 88, 73,
74, 79, 86, 82, 90, 92, 93, 73
Determine what percent of the students scored
within one standard deviation of the mean.
Do the results of the examination approximate
a normal distribution? Justify your answer.
78. A shoe manufacturer collected data regarding
men's shoe sizes and found that the
distribution of sizes exactly fits the normal
curve. If the mean shoe size is 11 and the
standard deviation is 1.5, find:
a the probability that a man's shoe size is
greater than or equal to 11
b the probability that a man's shoe size is
greater than or equal to 12.5
c Psize ( ≥ 12. 5)
Psize ( ≥ 8)