F(1) = 160 is given to us. We'll use it to find f(2)
f(n+1) = -2*f(n)
f(1+1) = -2*f(1) ... replace every n with 1
f(1+1) = -2*160 ... replace f(1) with 160
f(2) = -320
Now use f(2) to find f(3)
f(n+1) = -2*f(n)
f(2+1) = -2*f(2) ... replace every n with 2
f(3) = -2*(-320) ... replace f(2) with -320
f(3) = 640
Finally, use f(3) to find f(4)
f(n+1) = -2*f(n)
f(3+1) = -2*f(3) ... replace every n with 3
f(4) = -2*640 ... replace f(3) with 640
f(4) = -1280
Final Answer: -1280
You have a 1/3 chance each time you role
So 1/3 x 12 = 4 times that you would role a 5 or a 6
Answer:
12
Step-by-step explanation:
If 12 apples makes 2 cups, we can assume that 6 apples make 1 cup.
Take the number of apples and divide it by 6 in order to find out the number of cups that can be made.
There are 14 chairs and 8 people to be seated. But among the 8. three will be seated together:
So 5 people and (3) could be considered as 6 entities:
Since the order matters, we have to use permutation:
¹⁴P₆ = (14!)/(14-6)! = 2,162,160, But the family composed of 3 people can permute among them in 3! ways or 6 ways. So the total number of permutation will be ¹⁴P₆ x 3!
2,162,160 x 6 = 12,972,960 ways.
Another way to solve this problem is as follow:
5 + (3) people are considered (for the time being) as 6 entities:
The 1st has a choice among 14 ways
The 2nd has a choice among 13 ways
The 3rd has a choice among 12 ways
The 4th has a choice among 11 ways
The 5th has a choice among 10 ways
The 6th has a choice among 9ways
So far there are 14x13x12x11x10x9 = 2,162,160 ways
But the 3 (that formed one group) could seat among themselves in 3!
or 6 ways:
Total number of permutation = 2,162,160 x 6 = 12,972,960
12300=X[((1-(1+(0.072/12)^(-12*8))/(0.072/12)]
Solve for x
X=168.92
