Explanation:
In order to prove that affirmation, we define the function g over the interval [0, 1/2] with the formula 
If we evaluate g at the endpoints we have
g(0) = f(1/2)-f(0) = f(1/2) - f(1) (because f(0) = f(1))
g(1/2) = f(1) - f(1/2) = -g(0)
Since g(1/2) = -g(0), we have one chance out of three
- g(0) > 0 and g(1/2) < 0
- g(0) < 0 and g(1/2) > 0
- g(0) = g(1/2) = 0
We will prove that g has a zero on [0,1/2]. If g(0) = 0, then it is trivial. If g(0) ≠ 0, then we are in one of the first two cases, and therefore g(0) * g(1/2) < 0. Since f is continuous, so is g. Bolzano's Theorem assures that there exists c in (0,1/2) such that g(c) = 0. This proves that g has at least one zero on [0,1/2].
Let c be a 0 of g, then we have

Hence, f(c+1/2) = f(c) as we wanted.
Answer:
Step-by-step explanation:
20 problems
correct=+4
false=-1
unanswered=0
Uncorrectly:5 => -5
unanswered:2 =>0 points
20x4=80 points in total(only correct awnsers)
=>20-5+2=13 correct awnsers
13x4=52
52-5=47
It will be nice if you give me brainliest. Good luck!
There are 36 combinations, 5 combinations equal 8
(2,6) (3,5) (4,4) (5,3) (6,2) all equal 8
The chance of rolling 8 is 5/36 (combinations that equal 8/total combinations)
5/36=.13888...
32/40 is the fraction to 32:40 and if u simplify it, it would be 4/5
Answer:
y=5/4x
Step-by-step explanation:
(A fraction)