(a) <em>X</em> has a probabiliity density of
If the lower quartile is 5 and the upper quartile is 9, then
Computing the integrals gives the following system of equations:
5 - <em>a</em> = 0.25 (<em>b</em> - <em>a</em>) ==> 0.75<em>a</em> + 0.25<em>b</em> = 5 ==> 3<em>a</em> + <em>b</em> = 20
<em>b</em> - 9 = 0.25 (<em>b</em> - <em>a</em>) ==> 0.25<em>a</em> + 0.75<em>b</em> = 9 ==> <em>a</em> + 3<em>b</em> = 36
Eliminate <em>a</em> :
(3<em>a</em> + <em>b</em>) - 3 (<em>a</em> + 3<em>b</em>) = 20 - 3×36
-8<em>b</em> = -88
==> <em>b</em> = 11 ==> <em>a</em> = 3
and so P(<em>X</em> = <em>x</em>) = 1/(11 - 3) = 1/8 for all 3 < <em>x</em> < 11.
(b)
(c) The distribution function is then
(-x³ +3x +4) -(2x³ +7x² -9) = -x³ +3x +4 -2x³ -7x² +9 . . . . eliminate parentheses
= x³(-1-2) +x²(-7) +x(3) +(4+9)
= -3x³ -7x² +3x +13 . . . matches the second choice.
Ur outlier is 22....so we will remove it.
now we find the mean (average) of the data set...
(9+4+10+9+5+2+10+3+3+5) / 10 = 60/10 = 6...this is ur mean
now we subtract the mean from every data value...and find its absolute value
9 - 6 = 3....| 3| = 3
4 - 6 = -2...|-2| = 2
10 - 6 = 4..|4| = 4
9 - 6 = 3....|3| = 3
5 - 6 = -1..|-1| = 1
2 - 6 = -4...|-4| = 4
10 - 6 = 4..|4| = 4
3 - 6 = -3...|-3| = 3
3 - 6 = -3...|-3| = 3
5 - 6 = -1...|-1| = 1
now we find the mean (average) of these numbers...that is ur MAD
(3+2+4+3+1+4+4+3+3+1) / 10 = 28/10 = 2.8
ur answer : on average, the height of the plant varies 2.8 inches from the mean of 6 inches
Answer:
A
Step-by-step explanation:
We see that triangle QRS is located in Quadrant III. (See attachment for labelling of quadrants)
Reflecting it over the x-axis means that we flip it over the x-axis, or we flip it vertically. Doing so, QRS will end up in Quadrant II.
Now, we need to rotate QRS 180 degrees about the origin. The quadrants are all 90 degrees away from each other, which means that if we rotate QRS about the origin 180 degrees, we'll end up two quadrants away from Quadrant II: we'll end in Quadrant IV.
Look at each of the answer choices. The only choice that features Q'R'S' (the image of QRS) in the fourth quadrant is the first choice, or A. So that's the answer.
<em>~ an aesthetics lover</em>