Which simplified fraction is equal to 0.53 (the 3 is repeating)
2 answers:
<h3>Answer: Choice B. 8/15</h3>
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Explanation:
x = 0.53333333... the 3's go on forever
10x = 5.3333333..... we have infinitely many 3's here as well
100x = 53.333333..... same story
Each time we multiply both sides by 10, we move the decimal point over 1 spot to the right.
Focus on this system of equations
Note how the decimal points line up so we can see both right sides have the same 33333... pattern
If we subtract those equations straight down, the left hand side turns into 90x because 100x-10x = 90x
The right hand side terms subtract to 48. The infinite number of 3's after the decimal will cancel out when we subtract. So we basically have 53-5 = 48.
After those subtractions, we now have the new equation 90x = 48
Divide both sides by 90 and reduce
90x = 48
90x/90 = 48/90
x = 48/90
x = (6*8)/(6*15)
x = 8/15
8/15 = 0.53333333....
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Answer:
A sample size of 345 is needed so that the confidence interval will have a margin of error of 0.07
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 of the interval is given by:
In this problem, we have that:
99.5% confidence level
So , z is the value of Z that has a pvalue of
, so
.
Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.07?
This is n when M = 0.07. So
A sample size of 345 is needed so that the confidence interval will have a margin of error of 0.07