4/12=1/3
8/14=4/7
6/8=3/4
3/6=1/2
5/15=1/3
Ur counter example would mean making that conjecture false.
x^3 > 3x + 3....subbing in 2
2^3 > 3(2) + 3
8 > 6 + 3
8 > 9....this is not true...so ur answer is C. 2
Where’s the rest of the problem
Answer:
The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.
Step-by-step explanation:
We have the standard deviation for the population, so we can use the normal distribution. If we had the standard deviation for the sample, we would have to use the t-distribution.
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, 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 lower end of the interval is the sample mean subtracted by M. So it is 30 - 1.68 = 28.32 characters.
The upper end of the interval is the sample mean added to M. So it is 30 + 1.68 = 31.68 characters.
The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.
Let
be the data set. The variance of the data is
where
is the mean of the data. You have
so if each data point was multiplied by 2.4, you have a "new" mean of
So in the variance formula, you have
so the standard deviation of the new data set would be
The original standard deviation was
so the new one would be
.