Answer:
x^2 + 5x - 14
Step-by-step explanation:
We can assume that if there is 2 options for x, this is a quadratic equation that equals 0.
Therefore, we can put this into brackets as one bracket must equal 0.
(x - 2) (x + 7)
After this we expand, which is a process easier to search up
The answer is:
x^2 + 7x - 2x - 14
We can simplify this to:
x^2 + 5x - 14
x^2 represents x squared in case you were wondering
Therefore, the answer is:
x^2 + 5x - 14
Explanation:
Marginal distribution: This distribution gives the probability for each possible value of the Random variable ignoring other random variables. Basically, the values of other variables is not considered in the marginal distribution, they can be any value possible. For example, if you have two variables X and Y, the probability of X being equal to a value, lets say, 4, contemplates every possible scenario where X is equal to 4, independently of the value Y has taken. If you want the probability of a dice being a multiple of 3, you are interested that the dice is either 3 or 6, but you dont care if the dice is even or odd.
Conditional distribution: This distribution contrasts from the previous one in the sense that we are restricting the universe of events to specific condition for other variable, making a modification of our marginal results. If we know that throwing a dice will give us a result higher than 2, then to in order to calculate the probability of the dice being a multiple of 3 using that condition, we have two favourable cases (3 and 6) from 4 total possible results (3,4,5 and 6) discarding the impossible values (1 and 2) from this universe since they dont match the condition given (note that the restrictions given can also reduce the total of favourable cases).
The joint distribution calculates the probabilities for two different events (related to two different random variables) occuring simultaneously. If we want to calculate the joint probability of a dice being multiple of 3 and greater than 2 at the same time, our possible cases in this case are 3 and 6 from 6 possible results. We are not discarding 1 or 2 as possible results because we are not assuming, that the dice is greater than 2, that is another condition that we should met in the combination of events.
Answer:
8,566,379,470 people
Step-by-step explanation:
Let's start simple. In order to find the population increase on January 1, 2006, we need to multiply 6,486,915,022 by 1.4% and add it to 6,486,915,022.
- 6,486,915,022*1.4% = 90,816,810.308
- 90,816,810.308+6,486,915,022 = 6,577,731,832.31 people on January 2006.
Note that the above two steps gives the same answer as 6,486,915,022*1.014.
So we need to do this for each year. 20 years pass between 1/1/2005 and 1/1/2025.
We need to do 6,486,915,022*1.014*1.014*1.014... 20 times.
This is equivalent to 
.
Multiplying it out gives us 8566379470.2 = 8,566,379,470 people.
Answer:
400 m^2.
Step-by-step explanation:
The largest area is obtained where the enclosure is a square.
I think that's the right answer because a square is a special form of a rectangle.
So the square would be 20 * 20 = 400 m^2.
Proof:
Let the sides of the rectangle be x and y m long
The area A = xy.
Also the perimeter 2x + 2y = 80
x + y = 40
y = 40 - x.
So substituting for y in A = xy:-
A = x(40 - x)
A = 40x - x^2
For maximum value of A we find the derivative and equate it to 0:
derivative A' = 40 - 2x = 0
2x = 40
x = 20.
So y = 40 - x
= 40 - 20
=20
x and y are the same value so x = y.
Therefore for maximum area the rectangle is a square.
