35
le side of a = 1,052 + 1.08t and subtracted from the right side, and then
both sides are divided by 1.08.
QUESTION 10.
Choice B is correct. Substituting 1,000 for a in the equation a = 1,052 + 1.08t
gives 1,000 = 1,052 + 1.08t, and thus t =
−52
_
1.08
≈ − 48.15. Of the choices given,
−48°F is closest to −48.15°F. Since the equation a = 1,052 + 1.08t is linear,
it follows that of the choices given, −48°F is the air temperature when the
speed of a sound wave is closest to 1,000 feet per second.
Choices A, C, and D are incorrect, and might arise from errors in
calculating
−52
_
1.08
or in rounding the result to the nearest integer. For exam-
ple, choice C could be the result of rounding −48.15 to −49 instead of −48.
QUESTION 11.
Choice A is correct. Subtracting 3x and adding 3 to both sides of
3x − 5 ≥ 4x − 3 gives −2 ≥ x. erefore, x is a solution to 3x − 5 ≥ 4x − 3 if and
only if x is less than or equal to −2 and x is NOT a solution to 3x − 5 ≥ 4x − 3 if
and only if x is greater than −2. Of the choices given, only −1 is greater than
−2 and, therefore, cannot be a value of x.
Choices B, C, and D are incorrect because each is a value of x that is less than
or equal to −2 and, therefore, could be a solution to the inequality.
QUESTION 12.
Choice C is correct. e average number of seeds per apple is the total
number of seeds in the 12 apples divided by the number of apples, which
is 12. On the graph, the horizontal axis is the number of seeds per apple
and the height of each bar is the number of apples with the correspond-
ing number of seeds. e rst bar on the le indicates that 2 apples have
3 seeds each, the second bar indicates that 4 apples have 5 seeds each,
the third bar indicates that 1 apple has 6 seeds, the fourth bar indicates
that 2 apples have 7 seeds each, and the h bar indicates that 3 apples
have 9 seeds each. us, the total number of seeds for the 12 apples
is (2 × 3) + (4 × 5) + (1 × 6) + (2 × 7) + (3 × 9) = 73, and the average
number of seeds per apple is
73
_
12
= 6.08. Of the choices given, 6 is closest
to 6.08.
Choice A is incorrect; it is the number of apples represented by the tallest
bar but is not the average number of seeds for the 12 apples. Choice B is
incorrect; it is the number of seeds per apple corresponding to the tallest
bar, but is not the average number of seeds for the 12 apples. Choice D is
incorrect; a student might choose this by correctly calculating the average
number of seeds, 6.08, but incorrectly rounding up to 7.