Answer:
Step-by-step explanation:
A binary string with 2n+1 number of zeros, then you can get a binary string with 2n(+1)+1 = 2n+3 number of zeros either by adding 2 zeros or 2 1's at any of the available 2n+2 positions. Way of making each of these two choices are (2n+2)22. So, basically if b2n+12n+1 is the number of binary string with 2n+1 zeros then your
b2n+32n+3 = 2 (2n+2)22 b2n+12n+1
your second case is basically the fact that if you have string of length n ending with zero than you can the string of length n+1 ending with zero by:
1. Either placing a 1 in available n places (because you can't place it at the end)
2. or by placing a zero in available n+1 places.
0 ϵ P
x ϵ P → 1x ϵ P , x1 ϵ P
x' ϵ P,x'' ϵ P → xx'x''ϵ P
Let's assume
boiling point is y
altitude is x
we are given
This relationship between altitude and boiling point is linear
At an altitude of 1000 feet, water boils at 210°F
so, first point is (1000,210)
so, x1=1000 , y1=210
At an altitude of 3000 feet, water boils at 206°F
so, second point is (3000,206)
so, x2=3000,y2=206
now, we can find slope
now, we can plug values
now, we can use point slope form of line
so, we can plug it
so, point slope form of line is
now, we can plug x=8000
and then we can solve for y
So,
the boiling point of water at an altitude of 8000 feet is 196°F..........Answer
Loosely, "varies inversely" means that as one quantity increases, the other decreases. Specifically, if x and y vary inversely, then y = k/x where k is some constant (a particular number).
Another way to write that relationship is xy = k. To find the value of k for this problem, you need a numbers for x and y that go together.
Suppose x = number of children and y = number of candies (it doesn't matter what order these go in as long as you keep track!).
"When 12 children are present, 140 pieces of candy are consumed." So when x = 12, the value of y = 140.
xy = k
(12)(140) = k
1680 = k
Now, when x = 8 children,
8y = 1680
y = 210
483,391. You can line the, up vertically and then use simple arithmetic and carrying to solve this problem
