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elena55 [62]
3 years ago
11

I need to find the approximate sum. ​

Mathematics
1 answer:
Bad White [126]3 years ago
7 0

Answer:

135 to nearest whole number.

Step-by-step explanation:

∑ 5(4/3)^(k-1)   from k = 1 to k = 8.

First term = 5 , second term = 5*4/3

This is a Geometric series with first term a1 = 5 and common ratio r  = 4/3.

The sum of n terms = a1(r^n - 1) / (r - 1).

The sum of 8 terms is given by  5 * (4/3)^8 - 1) /  ( 4/3 - 1)

= 135 to the nearest whole number.

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Answer:

0.967 = 96.7% probability the rock sample actually contains raritanium

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Positive reading

Event B: Contains raritanium

Probability of a positive reading:

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0.5% of 100-13 = 87%(false positive, positive when there is no raritanium). So

P(A) = 0.98*0.13 + 0.005*0.87 = 0.13175

Positive when there is raritanium:

98% of 13%

P(A) = 0.98*0.13 = 0.1274

What is the probability the rock sample actually contains raritanium?

P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1274}{0.13175} = 0.967

0.967 = 96.7% probability the rock sample actually contains raritanium

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( Hope this helps!! ) <3


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