Answer:
F' = (7, 6)
R' = (-1, 7)
I' = (-2, -5)
O' = (6, -6)
Step-by-step explanation:
The reflection rule across the y-axis states that (x, y) ---> (-x, y). Thus, all x coordinates must be converted to their negative counterparts. The -7 from F becomes 7, the 1 from R becomes -1, the 2 from I turns into -2, and the -6 from O changes to 6.
Answer:
a) Ann has a 1/3 chance of winning in the first round
b) The chance of Ann winning for the first time in the fourth round is 8/81
c) The probability that Ann's first win occurs after the fourth round is 16/81
Step-by-step explanation:
a) Each strategy is played with a probability of 1/3. Given any strategy, there’s a 1/3 chance that Bill will choose the strategy that allows Ann to win. Consequently, the probability of Ann securing a victory in the first round (or any round) is
1/3 * 1/3 + 1/3 * 1/3 + 1/3 * 1/3 = 1/9 + 1/9 + 1/9 = 1/3.
Thus, the likelihood of Ann winning the initial round is 1/3.
b) The chances of Ann winning a round stand at 1/3; therefore, her chances of not winning are 2/3. This must happen three times before her first victory. Thus, the probability that Ann's first win occurs in the fourth round is
(2/3)³ * 1/3 = 8/81.
c) The first victory happens after the fourth round if she remains unsuccessful in the first four rounds, translating to a possibility of (2/3)⁴ = 16/81.
Answer:
The appropriate ratio to convert 45 cm into feet is 1 foot / 2.54 cm since the centimeters will cancel out.
Step-by-step explanation:
We aim to find the ratio that will allow us to convert from centimeters to feet for 45 cm.
The right ratio here is 1 foot / 2.54 cm, as the cm unit will be eliminated, resulting only in feet.
This works as follows;
1 foot / 2.54 cm * 45 cm.
This simplifies to;
(45 cm * 1 foot) / 2.54 cm.
Answer:
Step-by-step explanation:
Player A has a red marble and a blue marble, while Player B also has a red marble and a blue marble.
Therefore, the probability of selecting one marble is equal, at 0.5.
Due to the independence of A and B's choices, the joint event is calculated by multiplying the probabilities.
Let A represent the amount that player A wins.
If both players select one marble, the sample space can be considered as
(R,R) (R,B) (B,R) (B,B)
Probability 0.25 0.25 0.25 0.25
A's winnings 3 -2 -2 1
E(A) 0.75 -0.5 -0.5 0.25 = 0
Thus, the game is even, offering equal expected values for both A and B.
It does not influence the outcome whether you are A or B.
Here, 'a' relates to 0.
There are two scenarios for 'r' and 't'.
Scenario 1.
Both are positioned on the same side to the right of 'a'.
In this case, 'r' would equal 5, and 't' would equal 7.
The midpoint between 'r' and 't' is 
.
Scenario 2.
If both are found to the left of 'a'.
Then 'r' would equal -5, while 't' would equal -7.
The midpoint is 
.
Scenario 3.
If 'r' is right of 'a' and 't' is left of 'a'.
Thus 'r' equals 5 and 't' equals -7.
The midpoint is 
.
Scenario 4.
If 'r' is left of 'a' while 't' is right of 'a'.
In this case, 'r' corresponds to -5 and 't' corresponds to 7.
The midpoint is 
.
The potential midpoint coordinates for 'rt' are 6, -6, 1, and -1.
