supermanaccz

Disjoint events cannot happen at the same time. In other words, they are mutually exclusive. Put in formal terms, events A and B are disjoint if their intersection is zero: ... Disjoint events are disjointed, or not connected. Another way of looking at disjoint events are that they have no outcomes in common

A compound event is one in which there is more than one possible outcome.

Determining the probability of a compound event involves finding the sum of the probabilities of the individual events and, if necessary, removing any overlapping probabilities.

I hope this helped, 

Supermanaccz

Idenpendent events are events that do not effect each other. 

The occurring of A does not affect the outcome of B.

For example, 

rolling a 6 on a die and flipping a head on a coin. 

These events do not affect each other.

I hope this helped,

supermanaccz

I hope this helped :)

If by surfaces you mean area, here you go:

For the first shape, the area is:

17 * 15 which is 255.

For the second shape, we first need to find the height. 

To find the height we can use the Pythagorean theorem. 

5^2 - 3^2 = x^2 —————>  x = 4.

The area is 5 *4 ÷ 2 which also is 10.

The area for the third shape is:

17 *18÷2 which is 153.

To find the area for the final shape, we also need to find the height using the Pythagorean theorem. 

13^2 - 5^2 = x^2 ——————> x = 12

7*12 = 84. 

The area of the shapes in order is:

225, 10, 153, and 84.

Both 15^6 and  7^6 are squares, so we can factor 15^6 - 7^6  as the difference of squares:

15^6-7^6 = (15^3-7^3)(15^3+7^3)

We can pound out the computation from here (yuck!), or we can factor 15^3-7^3  as a difference of cubes and 15^3+7^3 as a sum of cubes:

[(15^3-7^3)(15^3+7^3) = [(15-7)(15^2+15*7 + 7^2)][(15+7)(15^2-15*7 + 7^2)]

The largest of these factors is 379. 

I did a better solution on paper, but I can't attach a file, sorry!

I think you meant x^6=64, nbot x^6=0... Here you go!

The obvious two solutions to this equation is 2 and -2 since, (±2)⁶ = 64 but the question asked for the complex numbers too, so there are more solutions.

The first step in order to approach this problem is to factor x⁶ = 64. 

We can re-write this problem into x⁶ - 2⁶ = 0
And also, (x³)²-(2³)²=0

After using difference of cubes and sum of cubes(search it up if you don't know what it is)

I got: (x-2)(x^2+2x+2^2)*{(x+2)(x^2-2x+2^2)}=0
 

We need to solve ±(x-2)=0,

(x^2+2x+2^2)=0

(x^2-2x+2^2)=0

After you do, you have your six conjugates. I'll leave the solving for you!

The time it took for you to type in all those numbers deserves a thumbs up :)

The symbol f(x) represents a function. 

f is the function, x is the input. 

f(1) = 3

f(2) = 6

You can figure out that the function is times 2

f(x) = 2x

Here is a function problem:

f(x) = ax^2 + bx + c

f(0) = 4

f(1) = 15

f(2) = 36

What is product abc?

Anyone is welcome to answer this problem :)

Notes: Function does not have to be f, it could be any letter

p(x) or b(x) both work!

I hope this helped, 

Supermanaccz

The other two y coordinates are the same as the other ones, respectively. 

3,17, so one of the y coordinate is 17

9, -4, so one of the y coordinate is -4

The sum of these two values is 13

I hope this helped, just check over my answer. 

:)