
,

,

We find the probability of intersection using the inclusion/exclusion principle:

By definition of conditional probability,

For

and

to be independent, we must have

in which case we have

, which is true, so

and

are indeed independent.
Or, to establish independence another way, in terms of conditional probability, we must have

which is also true.
Answer:
We see that opposite angles are two angles between two secant lines (“secant lines” simply means two lines that cross each other) that share a vertex (that is why they are called “vertical” angles). We see also that they are not adjacent (which means next to each other) but opposite each other.
Step-by-step explanation:
Vemos que los ángulos opuestos son dos ángulos entre dos líneas secantes (“líneas secantes” simplemente significa dos líneas que se cruzan) que comparten un vértice (por eso se llaman ángulos “verticales”). También vemos que no son adyacentes (lo que significa uno al lado del otro) sino uno frente al otro.
Answer:
3100ft
Step-by-step explanation:
There are 2 sides to the prism that have an area of 50ft * 10ft or 500ft. The total of those will be 500ft * 2 or 1000ft. There are 2 more sides to the prism that have an area of 30ft * 10ft or 300ft. The total would be 300ft * 2 or 600ft. Then the last two sides to the prism have an area of 50ft * 30ft or 1500ft. Since we're imagining this prism to be a house, you can't paint the floor (well, I guess you could but I think they want us to leave that part out because you can't pick the house up to paint the bottom that would be ridiculous). So the surface area is each area added, or 1000ft + 600ft + 1500ft = 3100ft.
Answer:
10
Step-by-step explanation:
6²+8²
=100
√100
=10
Okay, y = -0.96x + 103. Now what?