A security alarm requires a four-digit code. The code can use the digits 0–9 and the digits cannot be repeated. What is the appr
2 answers:
Answer: 0.02381
Step-by-step explanation:
Given: A security alarm necessitates a four-digit code. The digits can be from 0 to 9 and must not be repeated.
The overall number of combinations for the security alarm will be (without repeating any digits):
If only odd numbers are considered, the ways to formulate the security alarm will be (without repeating any digits):
Thus, the probability that the code is composed of only odd numbers will be
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a) The sequence is geometric.
b) The subsequent term is 486
c) The rule is:
The 20th term will be: a_{20}=6973568802
Step-by-step explanation:
The series 6, 18, 54, 162, ... depicts the number of push-ups Kendall performed each week, starting from her initial week of exercise.
Part a) Is this sequence arithmetic or geometric?
An arithmetic sequence has a constant difference between consecutive terms.
In the given series 6, 18, 54, 162,
18-6 = 12
54-18= 36
The differences are not constant, thus it isn’t arithmetic.
A geometric sequence maintains a constant ratio between consecutive terms.
In this series 6, 18, 54, 162,
18/6 = 3
54/18 = 3
162/54 = 3
The ratios remain constant; therefore, the sequence is geometric.
The sequence in question is geometric.
Part b) How can you determine the next number in the series?
The next number can be calculated using the following formula:
where a_n= nth term
a= first term
r= common ratio
The next number represents the 5th term of the sequence.
To find the 5th term:
Thus, the next term in the sequence is 486
Part c) What is the rule for determining the 20th week? Calculate the 20th week.
The rule for determining the 20th week is:
Here n=20
Calculating the 20th week