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Elden [556K]
3 years ago
9

Mr. Brown's salary is $32,000 and it increases by 3% each year. What is the explicit rule for this sequence in simplified form?

Mathematics
1 answer:
katovenus [111]3 years ago
3 0

Answer:

This is the concept of geometric series. We are required to find the recursive formula for year n. Here we will use the formula;

nth=ar^(n-1)

where;

a=first term

r=common ratio

n=nth term

Thus

a=8.50

r=(8.85)/(8.50)=1.0412

thus the formula will be:

nth=8.50(1.0412)^n

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Answer:

0.4460 = 44.60% probability that none of the 8 surnames of these authors were among the 10 most common

Step-by-step explanation:

For each surname, there are only two possible outcomes. Either they are among the 10 most common, or they are not. Each author is independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

These names account for 9.6% of all U.S. residents.

This means that p = 0.096

8 authors in total.

This means that n = 8

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