We will use the segment addition postulate.
PQ + QR = PR
4x - 1 + 3x - 1 = 54
7x - 2 = 54
7x = 56
x = 8
So QR is 3(8) - 1 or 24 - 1 which is 23.
Answer:
QR is 23
Step-by-step explanation:
80
120
48
144
Answer:
144
Step-by-step explanation:
first digit of the code: only 2 and 4 are the only even numbers availible, so only 2 possibilities for the first digit.
2nd digit of code: 2,5,7,9,1 so 6 possibilities for the 2nd digit.
3rd digit of code: 2,5,7,9,1 so 6 possibilities for the 3rd digit.
4th digit of code: only 7 and 9 are greater tyhan 6 so only 2 possibilities for the 4th digit.
SO...
2 x 6 x 6 x 2 = 144
The states of nature must be mutually exclusive and collectively exhaustive.
The states of nature in decision theory are defined as mutually exclusive and collectively exhaustive, meaning that they are the only possible outcomes of a chance event, and only one of them can occur at a given time.
In other words, the states of nature represent all the possible outcomes of a chance event, and they are mutually exclusive because they cannot occur simultaneously. For example, if the states of nature are "rain" and "no rain," then either it will rain or it will not rain at a given time, but not both.
The term "collectively exhaustive" means that the set of states of nature includes all possible outcomes, so that there are no other possibilities beyond the ones listed. This ensures that the decision maker has considered all possible outcomes when making a decision.
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