Find the vertex for the equation: y=-2x^2+16x-31
1 answer:
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4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.
Start with
Taken mod 4, the last two terms vanish and we're left with
We have , so we can multiply the first term by 3 to guarantee that we end up with 1 mod 4.
Taken mod 7, the first and last terms vanish and we're left with
which is what we want, so no adjustments needed here.
Taken mod 9, the first two terms vanish and we're left with
so we don't need to make any adjustments here, and we end up with .
By the Chinese remainder theorem, we find that any such that
is a solution to this system, i.e. for any integer
, the smallest and positive of which is 149.
Answer:
We need a sample size of at least 75.
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
So it is z with a pvalue of , so
Now, we find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
The standard deviation is the square root of the variance. So:
With a .95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is
We need a sample size of at least n, in which n is found when M = 5. So
We need a sample size of at least 75.