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kumpel [21]
3 years ago
6

Find the common ratio and the explicit formula -3, 9, -27, 81,​

Mathematics
1 answer:
Fofino [41]3 years ago
6 0

Answer:

see explanation

Step-by-step explanation:

These are the terms of a geometric sequence with n th term

a_{n}\\ = a(r)^{n-1}

where re a is the first term and r the common ratio

r = 9 ÷ - 3 = - 27 ÷ 9 = 81 ÷ - 27 = - 3 ← common ratio

and a = - 3, thus

[te x]a_{n}[/tex] = - 3(-3)^{n-1} ← explicit formula

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Answer

P(A) = 0.30

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P(A\ n\ B) = 0.22

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Explanation:

Given

See attachment for proper data presentation

n = 100 --- Sample

A = Supplier 1

B = Conforms to specification

Solving (a): P(A)

Here, we only consider data in sample 1 row.

Here:

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Solving (b): P(B)

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n(B) = (1) + (2) + (3)

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P(B) = 0.77

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Here, we only consider the similar cell in the yes column and sample 1 row.

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This is represented as: n(A n B)

n(A\ n\ B) = 22

The probability is then calculated as:

P(A\ n\ B) = \frac{n(A\ n\ B)}{Sample}

P(A\ n\ B) = \frac{22}{100}

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Solving (d): P(A u B)

This is calculated as:

P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)

This gives:

P(A\ u\ B) = \frac{30}{100} + \frac{77}{100} - \frac{22}{100}

Take LCM

P(A\ u\ B) = \frac{30+77-22}{100}

P(A\ u\ B) = \frac{85}{100}

P(A\ u\ B) = 0.85

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