Find the vertices and foci of the hyperbola with equation quantity x plus 2 squared divided by 144 minus the quantity of y minus 4 squared divided by 81 = 1.

Step-by-step explanation:

Given the equation of the hyperbola

Since the x part is added, then

Also, this hyperbola's foci and vertices are to the left and right of the center, on a horizontal line paralleling the x-axis.

From the equation, clearly the center is at (h, k) = (–2, 4). Since the vertices are a = 12 units to either side, then they are at (-14,4) and (10,4).

From the equation

The foci, being 15 units to either side of the center, must be at (–17, 4) and (13, 4)

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

its 60

4 x 12 = 48

3 x 4 = 12

48 + 12 = 60

yeeeet