Question 1
1 answer:
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A. We are going to form 7 digit numbers from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
where the first digit cannot be 0 or 1.
so we have 8 choices for the 1. digit, and 10 choices for all the other 6 digits.
this means there are
possible numbers.
b.
consider the numbers which start with 911. There are
such numbers, since for the 4th, 5th, 6th and 7th digits we have 10 choices.
then we remove this number, from the one we found in a:
There are in total
numbers which don't start with 911.
Answer:
a.
b.7,990,000
where the first digit cannot be 0 or 1.
so we have 8 choices for the 1. digit, and 10 choices for all the other 6 digits.
this means there are
b.
consider the numbers which start with 911. There are
then we remove this number, from the one we found in a:
There are in total
Answer:
a.
b.7,990,000
Answer:
32, <u>16</u>, <u>8</u>, <u>4</u>, <u>2</u>, 1
Explanation:
The geometric mean can be represented by .
Which is the mean of the product of n numbers, used to find the average of a geometric progression.
Don't get confused by geometric mean, it is only asking you about the next numbers in the geometric sequence given the first and sixth term.
The explicit rule for a geometric sequence can be modeled by:
Where is the nth term,
is the first term in the sequence, n is the term number, and r is the common ratio.
Since we already know the first term, will simply be 32.
Since we know it's geometric, there will be an exponential relationship, which means that we will use the geometric mean to find the common ratio.
There are 6 total terms, r is raised to the n – 1 so 6 – 1 = 5, and that will be the degree of this root.
=
=
.
Therefore: .
Using all the information we have, we can find the explicit rule:
-
= 32
→
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We can test that this works by substituting the number location of the term you want to find.
For instance: