, and
. Subtracting this from the numerator gives a remainder of
, and
. Subtracting this from the previous remainder gives a new remainder of
is not a multiple of
, so we're done. Then
F(n)=6.5n+4.5 find the 5th term of the sequence defined by the given rule
1 answer:
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You can see the three diagram attached. Each link is labeled with the probability: you have probability 1/6 that a six is rolled, and 5/6 that it is not rolled.
To answer the questions, find the path that brings you to the desired outcome, and multiply all the labels you meet.
First question:
To get three sixes, you have to choose the left path at each roll. The probability is always 1/6, so the answer is
Second question:
To get no sixes, you have to choose the right path at each roll. The probability is always 5/6, so the answer is
Third question:
To get exactly one six, it can either be the first, second or third roll.
In all cases, you have to choose the left path once and the right path twice: left-right-right mean that you get the six in the first roll, right-left-right means that you get the six in the second roll, right-right-left means that you get the six in the third roll.
In every case, the left turn has probability 1/6, and the right turn has probability 5/6. The probability of each combination is thus
And since there are three of these combinations, The answer is
Fourth question:
Since the question suggests to use what we already achieved, let's do it: having at least one six is the complementary event of having no sixes at all. If an event has probability p, its complementary has probability 1-p. So, since the probability of no sixes is known, the probability of at least one six is
Answer:
Step-by-step explanation:
An <em>inverse</em> function is any function that "undoes" another function. If we think of the function as some kind of machine that takes in a number
as input and produces a number
as an output, when we give inverse function
the number
as in input, we get
, our original input, as the output
We need a function that undoes , and the natural choice for undoing an exponent is with a logarithm. Here, our base is
, so we'll choose
as our inverse function. Let's see how that works:
is the power we have to raise
to to get
, which is
, so
And we have our function.