Answer:
Let the number of digits be n and the number of elements in set be s.
<h3>When n = 1</h3>
- The set contains 1-digit numbers, 1 through 9,
- The set consists of 10 - 1 = 9 numbers.
<h3>When n = 2</h3>
- The set contains 2-digit numbers, 10 through 99,
- The set contains 100 - 10 = 90 numbers.
<h3>When n = 3</h3>
- The set contains 3-digit numbers, 100 through 999,
- The set contains 1000 - 100 = 900 numbers.
The pattern we see helps us determine the relationship between s and n as follows.
When set contains n-digit numbers, the set contains:
- s = 10ⁿ - 10ⁿ⁻¹ = 10ⁿ⁻¹(10 - 1) = 9*10ⁿ⁻¹ elements
We have s known, substitute it into equation above and solve for n:
- 900000000 = 9*10ⁿ¹
- 100000000 = 10ⁿ⁻¹
- 10⁸ = 10ⁿ⁻¹
- n - 1 = 8
- n = 9
The numbers in the set s are 9-digit long.
You will need to use GCF 12 equals 11 altitude
Answer:
B is a function
Step-by-step explanation:
A function only has one Y value for each X value.
A) this one is not a function because there are 2 points at x = 0
B) this one is a function because each X value has only 1 Y value
C) this is not a function because there are 2 points at x = 1
D) this is not a function because there are 2 points at x = 2
Using the Fundamental Counting Theorem, it is found that for each case, the total number of outcomes is:
a) 60,466,176.
b) 5,961,600.
<h3>What is the Fundamental Counting Theorem?</h3>
It is a theorem that states that if there are n things, each with ways to be done, each thing independent of the other, the number of ways they can be done is:
Item a:
No restrictions, hence for each of the five characters, there are 36 outcomes, hence .
Then, the possible number of passwords is:
Item b:
The letters and the digits have to be alternated, hence:
- Starting with a letter, .
- Starting with a digit, .
Then, the possible number of passwords is:
To learn more about the Fundamental Counting Theorem, you can take a look at brainly.com/question/24314866