Find the slope of the line that passes through (9, 8) and (4, 6).
2 answers:
You might be interested in
Answer:Remember that the general formula of geometric sequence is
where
is the nth term
is the difference
is the place of the term in the sequence
Also, to find we will use the formula:
where
is the current term in the sequence
is the previous term
a) Lets find the three first terms of our sequence to check what type of sequence we have:
We know for our problem that the initial value of the computer is $1250, so our first term is 1250. In other words .
To fin our second term , we are going to subtract 10% of the value to our original value:
and , so
To find our third term we are going to subtract yet again 10% to our current value:
and , so
Now that we have our sequence lets check if we have a consistent to prove we have a geometric sequence:
- with , and :
- with , and :
Look! our s are the same, so we can conclude that we have a geometric sequence.
b) To do this we just need to replece the values of our sequence in the general formula of a geometric sequence. We know from our previous point that and . So lets replace those values in geometric sequence formula to find our explicit formula:
c) To find the value of the computer at the beginning of the 6th year, we just need to find the 6th therm in our geometric sequence:
We can conclude that the value of the computer at the beginning of the 6th year will be $738.1125
Step-by-step explanation:
i did some research i dont know if it helped out not but id appreciate brainliest if it did..... thank you.
Answer:
a)
the smallest n that maximizes the expected payoff is n=5.
b) 4
Step-by-step explanation:
a)
The expected amount of $ won for each die would be the average of 1, 2, 3, 4 and 5 which is $3.
Let W(n) the expected money won when rolling n dice.
n =1
If the gambler rolls only one die, the expected money won would be $3 times the probability of not getting a 6, which is 5/6.
So
n=2
If the gambler rolls 2 dice, the expected money won would be $3 times the probability of not getting a 6 in any of the dice. Since the outcome of the rolling does not depend on the previous rollings, the probability is
and
n=3
Similarly, since the probability of not getting a 6 in 3 dice equals
and the formula for the expected money won with n dice would be
In the picture attached there is a plot of the values of the expected money won for n=1 to 20 (See picture)
For n=5 and n=6 we get the maximum profit expected of $6.02816=$6 rounded to the nearest integer.
Hence, the smallest n that maximizes the expected payoff is n=5.
b)
The probability that face k (k=1,2,...or 6) shows up is 1/6,
as this face can be in any of the 10 positions of the arrangement, there are 10 ways that face k can show up.
The probability that face k (k=1,2,...or 6) shows up twice is
as this face can be in any of the (combinations of 10 taken 2 at a time) positions of the arrangement, there are C(10;2) ways that face k can show up twice.
The probability that face k (k=1,2,...or 6) shows up three times is
as this face can be in any of the (combinations of 10 taken 2 at a time) positions of the arrangement, there are C(10;3) ways that face k can show up twice.
So, we infer that the expectation is
and the expected number of distinct dice values that show up is 4.
