$12.80 × 1.075 = $13.76
$13.76 × 1.15 =$15.82
Answer:
6.4 m
Step-by-step explanation:
We have 2 expressions here. The first one is the fact that r = y. That's one of 2 equations. The second one involves whats' left after cutting off certain lengths of each color string. We cut 2.5 m from red, we cut 3.8 m from yellow. We know that what's left of red is 1.5 times the length of what's left of yellow. What's left of red is r - 2.5; what's left of yellow is y - 3.8. We know that r = 1.5y, so filling that in with our corresponding expressions gives us
r - 2.5 = 1.5(y - 3.8)
Distribute to get
r - 25 = 1.5y - 3.2
Now from the first expression, r = y, so fill in y for r to get an equation in one variable:
y - 2.5 = 1.5y - 3.2
Combine like terms:
-.5y = -3.2 and divide to get
y = 6.4
Check it to make sure it works. What's left of red should be 1.5 times the length of what's left of yellow and y = 6.4:
What's left of red: 6.4 - 2.5 = 3.9
What's left of yellow: 6.4 - 3.8 = 2.6
1.5 x 2.6 = 3.9, just like it should!
Let's analyze the increments for each step of the sequence:
Each step we add 3 to the previous number.
Since we need the 20th, from what we saw, in the 20th term we will have added three 20 times.
So the procedure is: calculate how much is 3 times 20 and then add that to the first term of the sequence.
So we add 60 to the first term to find the 20th term:
Answer: 124
The base case of 
is trivially true, since
but I think the case of 
may be a bit more convincing in this role. We have by the inclusion/exclusion principle
with equality if 
.
Now assume the case of 
is true, that
We want to use this to prove the claim for 
, that
The I/EP tells us
and by the same argument as in the case, this leads to
By the induction hypothesis, we have an upper bound for the probability of the union of the 
through 
. The result follows.
Answer:
1
Step-by-step explanation:
