ANSWER
or
EXPLANATION
For
We make y the subject to obtain,
We can easily graph this function, because we just have to transform the graph of by shifting the intercept up to
.
As for the straight line, ,
We find the intercepts as follows,
When .
When .
We plot the points and
.
We now draw the two graphs on the same graph sheet. The intersection of the two graphs gives the solution to be
or
See graph
It is given in the question that
Ms. Velez will use both x gray bricks and y red bricks to build a wall around her garden. Gray bricks cost $0.45 each and red bricks cost $0.58 each. She can spend up to $200 on her project, and wants the number of red bricks to be less than half the number of gray bricks.
Maximum she can spend is $200. That is
And
And that's the required inequalities .
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.