Intuitively, you might expect that any amount between $25,000 and $28,333 is a possible value
of the average salary. To see that $26,000 is possible, in the weighted mean above, use the
respective weights 9 and 1 instead of 2 and 1. To see that $28,000 is possible, use the
respective weights 7 and 3.
4. Which of the following could
be the units digit of
where n is a positive integer?
Indicate all such digits.
A. 0
B. 1
C. 2
D. 3
E. 4
F. 5
G. 6
H. 7
I. 8
J. 9
Explanation
The units digit of
is the same as the units digit of for all positive integers n. To see why
this is true for
compute
by hand and observe how its units
digit results from the
units digit of
Because this is true for
every positive integer n, you need to consider only
powers of 7. Beginning with
and proceeding consecutively, the units digits of 7,
and are 7, 9, 3, 1, and 7, respectively. In
this sequence, the first digit, 7, appears again, and
the pattern of four digits, 7, 9, 3, 1, repeats without end. Hence, these four digits are the only
possible units digits of and therefore of
The correct answer consists of Choices B (1),
D (3), H (7), and J (9)
.
28
Numeric Entry Questions
Description
Questions of this type ask you either to enter your answer as an integer or a decimal in a single
answer box or to enter it as a fraction in two separate boxes — one for the numerator and one for
the denominator. You will use the computer mouse and keyboard to enter your answer.
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