Commutative means 'you can swap them'. I.e., a+b = b+a, addition is commutative. Subtraction is not.
The first answer: <span>2(6a − 3) = (6a − 3) ⋅ 2 is an example where 2 and (6a-3) are the factors that can be swapped, because multiplication is commutative.</span>
Answer:
a) P ( E | F ) = 0.54545
b) P ( E | F' ) = 0
Step-by-step explanation:
Given:
- 4 Coins are tossed
- Event E exactly 2 coins shows tail
- Event F at-least two coins show tail
Find:
- Find P ( E | F )
- Find P ( E | F prime )
Solution:
- The probability of head H and tail T = 0.5, and all events are independent
So,
P ( Exactly 2 T ) = ( TTHH ) + ( THHT ) + ( THTH ) + ( HTTH ) + ( HHTT) + ( HTHT) = 6*(1/2)^4 = 0.375
P ( At-least 2 T ) = P ( Exactly 2 T ) + P ( Exactly 3 T ) + P ( Exactly 4 T) = 0.375 + ( HTTT) + (THTT) + (TTHT) + (TTTH) + ( TTTT)
= 0.375 + 5*(1/2)^4 = 0.375 + 0.3125 = 0.6875
- The probabilities for each events are:
P ( E ) = 0.375
P ( F ) = 0.6875
- The Probability to get exactly two tails given that at-least 2 tails were achieved:
P ( E | F ) = P ( E & F ) / P ( F )
P ( E | F ) = 0.375 / 0.6875
P ( E | F ) = 0.54545
- The Probability to get exactly two tails given that less than 2 tails were achieved:
P ( E | F' ) = P ( E & F' ) / P ( F )
P ( E | F' ) = 0 / 0.6875
P ( E | F' ) = 0
LORAN follows an hyperbolic path.
The equation of the hyperbola is: 
The coordinates are given as:

The center of the hyperbola is

The distance from the center to the focal points is given as:

Square both sides

The distance from the receiver to the transmitters is given as:

Divide both sides by 2

Square both sides

We have:

This gives

The equation of an hyperbola is:

So, we have:


Hence, the equation of the hyperbola is: 
Read more about hyperbolas at:
brainly.com/question/15697124
Answer: -3
Step-by-step explanation:
the number at the end of the equation is the y-intercept. it's called "slope-intercept" form because the 2x that is at the beginning represents the slope, and the -3 at the end represents the y-intercept.
hope this helps!
Answer:
5.83 units
Step-by-step explanation:
We write the coordinate points of Maple Station (-3,5) and Town Center (0,0). We label the points left to right as
and substitute the values.
5.83 units