The area of a trapezium is 550 cm2 and the length of the parallel sides is 23cm and 27cm, find the distance between them.
1 answer:
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Answer:
So on this case the 95% confidence interval would be given by (602.66;705.66)
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".
represent the sample mean
population mean (variable of interest)
s=165.23 represent the sample standard deviation
n=42 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,41)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (602.66;705.66)
<h3>Answer: Choice (3) 28</h3>
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Explanation:
We start with one block at the very left side. This is algebraically written as . The small subscript '1' means we're dealing with the first term, and that is set equal to 1. In other words, the first term is 1.
The second term is three since we have three blocks as the next figure down the line. So . We can then see that
and
The sequence of the first four terms are: 1, 3, 6, 10.
The notation tells us "to get the nth term
, we add the previous term (
) to the value of n".
For example, if we wanted the third term, we would add the second term a2 onto the value of n = 2. In order to know a2, we need the diagram or you would have to use the recursive formula to find it.
Furthermore, it means that to find the fifth term , we do the following
The fifth figure will have 15 small little blocks to it. You can draw this out by copying the fourth figure, and then adding 5 smaller blocks to the very bottom portion. The sixth figure is basically a copy of the fifth one, but we have six little blocks along the bottom. This is the "plus n" being applied in the recursive formula.
So the 6th figure will have 15+6 = 21 blocks in total while the 7th figure has 21+7 = 28 blocks. This points us to choice (3).
Side note: These are known as triangular numbers. Note how the gaps between consecutive values of 1,3,6,10,15,21,28 is +2,+3,+4,+5,+6,+7.