1. (3x + y = 5 (x-4y=32
2 answers:
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Answer:
x=3
Step-by-step explanation:
We are given the equation
This can be rewritten as
Now using the quotient rule for logarithms we can combine these two
Next we can remove the log by using an inverse operation
Now we can solve for x
Answer:
a) There is a probability of 42% that the person will feel guilty for only one of those things.
b)There is a probability of 46% that a randomly selected person will not feel guilty for either of these reasons
Step-by-step explanation:
This probability problem can be solved by building a Venn like diagram for each probability.
I say that we have two sets:
-Set A, for those people that will feel guilty about wasting food.
-Set B, for those people that will feel guilty about leaving lights on when not in a room.
The most important information is that there is a .12 probability that a randomly selected person will feel guilty for both of these reasons. It means that
The problem also states that there is a .39 probability that a randomly selected person will feel guilty about wasting food. It means that P(A) = 0.39. The probability of a person feeling guilty for only wasting food is PO(A) = .39-.12 = .27.
Also, there is a .27 probability that a randomly selected person will feel guilty about leaving lights on when not in a room. So, the probability of a person feeling guilty for only leaving the lights on is PO(B) = 0.27-0.12 = 0.15.
a) What is the probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room?
This is the probability that the person feels guilt for only one of those things, so:
P = PO(A) + PO(B) = 0.27 + 0.15 = 0.42 = 42%
b) What is the probability that a randomly selected person will not feel guilty for either of these reasons
The sum of all the probabilities is always 1. In this problem, we have the following probabilies
- The person will not feel guilty for either of these reasons: P
- The person will feel guilty for only one of those things: PO(A) + PO(B) = 0.42
- The person will feel guilty for both reasons: PB = 0.12
So
`P + 0.42 + 0.12 = 1
P = 1-0.54
P = 0.46
There is a probability of 46% that a randomly selected person will not feel guilty for either of these reasons