Answer:
The minimum sample size needed is 125.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.

In which
z is the zscore that has a pvalue of
.
The margin of error is:

For this problem, we have that:

99% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
What minimum sample size would be necessary in order ensure a margin of error of 10 percentage points (or less) if they use the prior estimate that 25 percent of the pick-axes are in need of repair?
This minimum sample size is n.
n is found when 
So






Rounding up
The minimum sample size needed is 125.
183848%
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To work out the decrease, do original amount - new amount and then take that answer and divide it by the original amount, and then multiply by 100.
So you would do:
36.24 - 30.80 = 5.44
5.44 ÷ 36.24 × 100 = 15% to the nearest percent.
30 divided by 5 is 6, so the other term is (x+6). (x+5)(x+6) becomes x^2+11x+30, so k is equal to 11.