Find the coordinates of p so that p partitions the segment ab in the ratio 1: 3 if a(5,8) and b(−1,4).
a. (-6.5, -9)
b. (-1.5, -1)
c. (3.5, 7)
d. (-4, -6)

The coordinates of point P are (3.5 , 7) ⇒ answer C

Step-by-step explanation:

* Lets explain how to solve the problem

- If the point (x , y) divide a line whose endpoints are (x1 , y1) , (x2 , y2)

 at ratio m1 : m2 from the point (x1 , y1), then the coordinates of the

 point (x , y) are

* Lets solve the problem

∵ A is (5 , 8) and B is (-1 , 4)

∵ P divides AB in the ratio 1 : 3

∴ m1 = 1 and m2 = 3

- Let A = (x1 , y1) and B = (x2 , y2)

∴ x1 = 5 , x2 = -1 and y1 = 8 , y2 = 4

- Let P = (x , y)

∴

∴

∴ The coordinates of point P are (3.5 , 7)

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560