Solve 3^5x-1 ≤ 30. Round to the nearest ten-thousandth. A.
{x | x ≤ 0.4000}
B.
{x | x ≤ 1.8000}
C.
{x | x ≤ 3.0959}
D.
{x | x ≤ 0.8192}

A 4 digit PIN is selected. What is the probability that there are no repeated digits?

There are 10 possible values for each digit of the PIN (namely: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9), so there are 10 × 10 × 10 × 10 = 104 = 10000 total possible PINs.

To have no repeated digits, all four digits would have to be different, which is selecting without replacement. We could either compute 10 × 9 × 8 × 7, or notice that this is the same as the permutation  10P4 = 5040.

The probability of no repeated digits is the number of 4 digit PINs with no repeated digits divided by the total number of 4 digit PINs. This probability is

10

P

4

10

4

=

5040

10000

=

0.504

Step-by-step explanation: