Answer:
1) 1/10
2) 1/2
3) 1/5
Step-by-step explanation:
1)
1 favorable outcome and 10 total outcomes.

2)
5 favorable outcomes and 10 total outcomes

3)
2 favorable outcomes and 10 total outcomes

This is a geometric sequence with first term 1 and common ratio -1/2. r=-1/2.
a(n) = a(1)*(r)^(n-1).
Check: If n=2 our formula must return -1/2. Does it?
a(2) = 1(-1/2)^(2-1) = (-1/2)^1 = - 1/2. Yes.
a(3) should be 1/4. Is it? a(3) = (-1/2)^(3-1) = 1/4 Yes.
Then a(8) = (-1/2)^(8-1) = (-1/2)^7 = -1 / 2^7 = -1/128 (answer)
Answer:
Regina drank 2/4 gal. of orange juice
Step-by-step explanation:
She starts off at 3/4 which makes the equation: 3/4 - 1/4=x
3/4-1/4 equals 2/4 which gets reduced and simplified to 1/2.
Recall the Pythagorean identity,

So we have



But squaring any real number always gives a non-negative number, so there are no real solutions to this equation.