How many equal sections divide a directed line segment if it is to be partitioned with a 5:7 ratio
2 answers:
Answer: The line segment can be divided into 12 equal sections.
Step-by-step explanation: We are given to find the number of equal sections that divide a directed line segment if it is to be partitioned with a 5 : 7 ratio.
We know that
if a line directed line segment is partitioned in the ratio a : b, then we can divide the line segment in (a + b) equal sections.
So, the number of equal sections in which the given line segment can be divided is given by
Thus, the line segment can be divided into 12 equal sections.
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Answer:
Option D.
Step-by-step explanation:
Suppose that we have a set of N values:
{x₁, x₂, ..., xₙ}
The median is the value in the middle, and the mean is calculated as:
Because here we have "the median" then we will assume that N is odd, and there is only one median, the value "k" (if N was even, the median would be the mean of the two middle values, that case is really similar to the case where N is odd, so solving only one of the cases is enough)
Now we add 7 to all the values greater than the median
We subtract 7 to all values smaller than the median.
Then the median remains unchanged (because we did not add nor subtract anything to the median).
The new mean will be:
So the mean does not change.
Because the mean is computed as the sum of the numbers divided by N, and the mean does not change, and N does not change, then the sum of the numbers does not change.
Finally, the standard deviation is computed as:
Because M does not change, if we add or subtract numbers to some of the values, the standard deviation will change (Because all the terms are squared, so the added and subtracted sevens don't cancel like in the previous cases)
Then the only value that does not have the same value in both the original and new data sets is the standard deviation.