Answer: D) -2 |x| - 2
<u>Step-by-step explanation:</u>
A v-shaped graph is an absolute value graph.
The general form of an absolute value equation is: y = a |x - h| + k
where (h, k) represents the vertex and "a" represents the vertical stretch (aka slope).
The vertex of the given graph is (0, 2), however the graph is inverted (upside-down) which is a reflection across the x-axis. Therefore,
<h2> --> y = -2 |x| - 2</h2>
<span>In statistics, an outlier is an observation point that is distant from other observations.
Given the points
15, 23, 24, 26, 27 and 35
Notice, that the points 15 and 35 are distance from the other points and hence are outliers.
The mean of the observations including the outliers is given by

The mean of the observations without the outliers is given by

Therefore, </span>when <span>the outliers are removed,
the mean remains the same.</span>
Mean = 12000
Standard Deviation = 2000
We have to find how many standard deviations is 14,500 away from the mean.
This can be achieved by calculating the z-score
Z-score tells us how many standard deviations above or below is a sample value from the mean. A positive z value shows, sample value is above the mean.
z score can be calculated as = (Sample Value - Mean )/Standard Deviation)
So,
Z-score =
This means, 14,500 is 1.25 standard deviations above the mean value 12,000.
<span>1. take English and niether of the other two?
</span>36-6 that we know take all 3
This leave 30.
Subtract the 6 from those taking history and English. Leaves 10.
Subtract the 10 from those taking English.
This leaves 20.
Subtract the 6 from those taking political science and English. Leaves 8.
Subtract 8 from those taking English.
Leaves 12
<span>
2. take none of the three courses? </span>
<span>
3. take history, but niether of the other two
</span>Do the same with history as we did with English.
32-6 = 26 -10=16-10=6
<span>
4. take political science and history but not english
</span>16-6 (that take all 3) = 10
Hope at least the partial answer helps!