If x is a prime number, what is the value of x? (1) 2 x + 2 is the cube of a positive integer. (2) The average of any x consecut
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Answer:
The length of the diagonal HJ is 10.82 units
Step-by-step explanation:
* Lets revise the rule of the distance between two points
- , where
and
are the two points
* Lets use this rule to find the length of the diagonal HJ
∵ The coordinates of point H are (-4 , 3)
∵ The coordinates of point J are (5 , -3)
∴ and
∴ and
- Lets find the length of the diagonal HJ by using the rule above
∴ HJ =
∴ HJ =
∴ HJ = 10.82
* The length of the diagonal HJ is 10.82 units
Answer:
And rounded up we have that n=2663
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We can assume an estimated proportion of since we don't have prior info provided. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=2663