9514 1404 393
Answer:
133 1/3 km/hour
Step-by-step explanation:
Average speed is computed as ...
average speed = (total distance)/(total time)
= (80 km +120 km +200 km)/(2/3 + 1 + 1 1/3 hour) = 400 km/(3 hour)
= 133 1/3 km/hour
A) 25% = 25/100 = 0.25
b) 18% = 18/100 = 0.18
c) 40% = 40/100 = 0.40
d) 2% = 2/100 = 0.02
e) 0.15% = 0.15/100 = 0.0015
Let

where we assume |r| < 1. Multiplying on both sides by r gives

and subtracting this from
gives

As n → ∞, the exponential term will converge to 0, and the partial sums
will converge to

Now, we're given


We must have |r| < 1 since both sums converge, so


Solving for r by substitution, we have


Recalling the difference of squares identity, we have

We've already confirmed r ≠ 1, so we can simplify this to

It follows that

and so the sum we want is

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?
Answer: If the number of bills counted is odd, the ones digit is 5; if the number of bills is even, the ones digit is 0.
Explanation
1) Simulate the counting of the bills:
number of bills counted value ones digit
1 5 5
2 5 + 5 = 10 0
3 10 + 5 = 15 5
4 15 + 5 = 20 0
5 20 + 5 = 25 5
6 25 + 5 = 30 0
2) Pattern: you can see that the ones digit alreternate: 5, 0, 5, 0, 5, 0, ...
If the number of bills counted is odd the ones digit is 5, if the number of bills is even the ones digit is 0.
Answer:
(3,2)
Step-by-step explanation:
The system is
x + y = 5
x -y = 1
Add the equations to eliminate y
2x = 6----->x=3
Substitute this value in any equation
3+y = 5----->y=2
The solution is (3,2)