Normal Distribution problem

The length of time that light bulbs will be functional is normally distributed with a mean of 800 hours and a standard deviation of 160 hours. If testing determines that 0.3% of the bulbs fail within the first x hours then x in hours is:

The corresponding z -score for 0.3% or 0.003
0.5 -0.003= 0.497
z-score will be -2.75
(x-800)/ 160 = -2.75

x= 360 hrs.

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Numbers -Word Problems

The number 210 can be written as the sum of consecutive positive integers in several ways. When written as the sum of the greatest possible number of consecutive positive integers, what is the largest of these integers?

Sum to n terms 1,2,3,.........n is n(n+1) / 2.This will give us greated number of consecutive positive integers.

n(n+1)/2 = 210
so n(n+1)= 420
20*21= 420
so answer is 20

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Euclid's Algorithm

A pair of positive integers (x, y) satisfies the equation 31x + 29 y = 1125. What is x + y? ans - x+y=37

31x+29y=1125

31x+29y=1 we get for x=-14 and y=15

general solution is x =-14*1125+29*t y = 15*1125-31t

14*1125/29 <= t<= 15*1125/31 t is an integer
we get t as 544

plug in t back in the equations above
to get x =26 and y=11
so x+y=37

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Asymptotes

Find the asymptotes of the function

(x^2-4x+5)

f(x)= ---------------

x + 3
Answer: vertical asymptote is x=-3 because f(x) is not defined at that value.
If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.
for slant/oblique asymptote divide numerator by denominator
x+3 ) x^2-4x+5 (x-7
x^2+3x
___________________
-7x+5
-7x-21
__________________
26
y= f(x) = (x-7) + 26 / (x+3)

y= x-7 is the slant/oblique asymptote.

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