Let be the random variable for the number of marks a given student receives on the exam.
10% of students obtain more than 75 marks, so
where follows a standard normal distribution. The critical value for an upper-tail probability of 10% is
where denotes the CDF of
, and
denotes the inverse CDF. We have
Similarly, because 20% of students obtain less than 40 marks, we have
so that
Then are such that
and we find
The formula for calculating the area of a circle is expressed as;
A = πr²
Since the area of the path is equal to the area of the pond, hence;
π(r+1.5)² - πr² = πr²
Add πr² to both sides
π(r+1.5)² - πr² + πr² = πr² + πr²
π(r+1.5)² = 2πr²
(r+1.5)² = 2r²
Expand the parenthesis
r²+3r + 2.25 = 2r²
r²+3r + 2.25 - 2r² = 0
-r² + 3r + 2.25 = 0
r² - 3r - 2.25 = 0
Multiply through by 2
2r² - 6.0r - 4.5 = 0
<em>This proves the required equation</em>
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Learn more on area of composite figures here: brainly.com/question/15981553
