MAT 230 Final Exam

Select the contrapositive of: If it snows tonight, then I will stay at home.
If I stay at home, then it will snow tonight.
If I do not stay at home, then it will not snow tonight.
If it does not snow tonight, then I will not stay at home.
none of the above.

Select the correct interpretations (may be more than one) of the notation
P(x) is true for all x
P(x) is true for at least one x
There is no x for which P(x) is true
There is an x such that P(x) is true

Let Q(x) be the statement, “x – 1 1. The first six Fibonacci numbers are: 1, 2, 3, 5, 8, 13. What is the next Fibonacci number?
19
21
23
25

Find f(4) if f is defined recursively by: f(0) = f(1) = 1 and for n > 1.
5
25
33
1214

Find the sequence for the recursive formula: ,
14, -4, 14, -4
6, 14, 86, 734
-3, 12, -3, 12
-3, 9, -3, 9

How many different license plates can be created with 7 numbers if any digit is allowed?
604,800
10,000,000
282,475,249
823,543

Find the value of C(16, 6).
8,008
924
5,765,760
12,870

Six women and eight men are on the faculty in the mathematics department at a school. How many ways are there to select a committee of four members of the department if at least one woman must be on the committee?
4242
126
931
1131

True of False? is a solution to the recurrence relation
True
False

If you deposit $10,000 in an account that yields 5% interest compounded yearly, what will be the balance at the end of 5 years?
$12,625
$13,382
$12,763
$14,186

Find a solution to the recurrence relation:

The Math Department has 4 committees that meet once a month. How many different meeting times must be used to guarantee that no one is…