Consider point P(x,y) such that P, X and Y are collinear,
As vectors
XP = XO + OZ where O(0,0)
XP = OZ - OX
XP= (x,y) - (-3,3)
XP = (x+3, y-3)
Similarly,
PY = (6-x, -3-y)
But XP= 2^PY
[x+3, y-3] = [2(6-x), 2(-3-y)]
Given both vectors are equal, as they go in the same direction, Solve for x and y accordingly:
x+3 = 12 - 2x
x = 3
y-3 = -6-2y
y = -1
Therefore, P(3,-1)
Answer:

Step-by-step explanation:
Start by finding how many integers there are from 10-30...
30-10+1=20+1=21
Note we have to add 1 since it is inclusive.
Now, let's find how many multiples of 4 or 5 there are from 10-30...
4*3=12
4*4=16
4*5=20
4*6=24
4*7=28
5*2=10
5*3=15
5*4=20
5*5=25
5*6=30
5+5-1=9
Note we have to subtract 1 since 20 is counted twice.
The probability would be...
