Using the concept of probability and the arrangements formula, there is a
0.002 = 0.2% probability that the first 8 people in line are teachers.
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- A probability is the <u>number of desired outcomes divided by the number of total outcomes.</u>
- The order in which they are positioned is important, and all people will be positioned, and thus, the arrangements formula is used to find the number of outcomes.
The number of possible arrangements from a set of n elements is given by:

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The desired outcomes are:
- First 8 people are teachers, in <u>8! possible ways.</u>
- Last 4 are students, in <u>4! possible ways.</u>
Thus, 
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For the total outcomes, <u>number of arrangements of 12 people</u>, thus:

The probability is:

0.002 = 0.2% probability that the first 8 people in line are teachers.
A similar problem is given at brainly.com/question/24650047
The value of the fractions will be:
1. 8 13/20
2. 2 4/5
3. 5/6
<h3>How to explain the fraction?</h3>
1. 6 1/4 + 2 2/5
LCM of 20
6 1/4 + 2 2/5.
6 5/20 + 2 8/20
= 8 13/20
2. 1 1/5 × 2 1/3
= 6/5 × 7/3
= 42/15
= 14/5
= 2 4/5
3. 3 1/3 - 2 1/2
= 3 2/6 - 2 3/6.
= 5/6
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1
X^2 = 8^2 + 5^2
x^2 = 64 + 25
x^2 = 89
x =
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9.4339811321
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ANSWER

EXPLANATION
The sum of an arithmetic sequence whose first term and last terms are known is calculated using

From the given information, the first term of the series is

and the last term of the series is

The sum of the first 26 terms is



The equation that would let us determine the number of people or population at a certain year is calculated through the equation,
A(t) = A(o)(2^(t - 1950)/50)
Substituting the known values,
A(t) = (2.5 million people)(2^(2100 - 1950)/50))
A(t) = 20 million
<em>Answer: 20 million people</em>