the next number is 17 thank you
Answer:
D. taking two marbles from a box without replacing the first marble are dependent events
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Answer:
Let's say that the whole book have 5a pages.
First day: a + 12
Second day: (4a)1/4+15= a + 15
Third day: (1/3)[ 4a - (a+15)] +18= a + 13
Forth day: 70
So we get this:
(a + 12) + (a + 15) + (a + 13) + 70 = 5a
a + 12 + a + 15 + a + 13 + 70 = 5a
3a + 110 = 5a
3a - 5a = -110
-2a = -110
a = 55
5a = 5(55) = 275
So the total pages are in the book is:
275 pages
Assume P(xp,yp), A(xa,ya), etc.
We know that rotation rule of 90<span>° clockwise about the origin is
R_-90(x,y) -> (y,-x)
For example, rotating A about the origin 90</span><span>° clockwise is
(xa,ya) -> (ya, -xa)
or for a point at H(5,2), after rotation, H'(2,-5), etc.
To rotate about P, we need to translate the point to the origin, rotate, then translate back. The rule for translation is
T_(dx,dy) (x,y) -> (x+dx, y+dy)
So with the translation set at the coordinates of P, and combining the rotation with the translations, the complete rule is:
T_(xp,yp) R_(-90) T_(-xp,-yp) (x,y)
-> </span>T_(xp,yp) R_(-90) (x-xp, y-yp)
-> T_(xp,yp) (y-yp, -(x-xp))
-> (y-yp+xp, -x+xp+yp)
Example: rotate point A(7,3) about point P(4,2)
=> x=7, y=3, xp=4, yp=2
=> A'(3-2+4, -7+4+2) => A'(5,-1)
