Find the first, fourth, and eighth terms of the sequence.

1 answer:

6 0

$a(n)=-3\cdot2^{n}-1\\\\a_1=-3\cdot2^1-1=-3\cdot2-1=-6-1=-7\\a_4=-3\cdot2^4-1=-3\cdot16-1=-48-1=-49\\a_8=-3\cdot2^8-1=-3\cdot256-1=-768-1=-769\\\\if\ a(n)=-3\cdot2^{n-1}\ then\\\\a_1=-3\cdot2^{1-1}=-3\cdot2^0=-3\cdot1=-3\\a_4=-3\cdot2^{4-1}=-3\cdot2^3=-3\cdot8=-24\\a_8=-3\cdot2^{8-1}=-3\cdot2^7=-3\cdot128=-384$

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It is a well-known fact that 50% of the general population are rascals (P(R) = 0.5) and 50% of the general population are not ra

aleksley [76]

Answer:

The answer is D. 0.75

Step-by-step explanation:

Let call R the event that a person is rascal, RC a person is not rascal, TH a person use top hat and NTH a person don’t use top hat.

From the information on the question we have 4 options with their respective probability:

1. A person could be rascal and use top Hat: this probability is calculate as the multiplication of the probability of be a rascal (0.5) and use a top hat (0.9), then:

P(R y TH)=0.5*0.9=0.45

2. A person could be rascal and don’t use top Hat: this probability is calculate as the multiplication of the probability of be a rascal (0.5) and not use a top hat (0.9), then:

P(R y NTH)=0.5*0.1=0.05

3. A person could be not rascal and use top Hat: this probability is calculate as the multiplication of the probability of not be a rascal (0.5) and use a top hat (0.3), then:

P(RC y TH)=0.5*0.3=0.15

4. A person could be not rascal and not use top Hat: this probability is calculate as the multiplication of the probability of not be a rascal (0.5) and not use a top hat (0.7), then:

P(RC y NTH)=0.5*0.7=0.35

Then the probability that a person is a rascal given that he is wearing a top hat could be written and calculate as:

$P(R/TH)=\frac{P(R y TH)}{P(TH)}$