2/3=.6 repeating
12/.6 repeating = 18
13 balls of yarn would be used to make 18 scarves.
There's more ways than one to solve this, just as there's more ways than one to skin a cat.
Two paralle lines have the same slope, so the desired new line looks exactly like the given line 3x + 5y = 6, except that the constant, 6, is replaced by another value.
Write out 3x + 5y = c
Replace x with 0 and y with 3. Then 3(0) + 5(3) = c, and c = 15.
Thus, the equation of the new, parallel, line is 3x + 5y = 15.
The price for each instructor will be the same at 3 hours. How I determined this answer:
First off, you need to add the initial price and hourly price for each person together, so you already know how much it will cost for 1 hour, including the initial fee. Here's how you do it:
Ieda: $11.00 (hourly price) + $8.50 (initial fee) = $19.50 (for 1 hour)
Thanh: $10.50 (hourly price) + $10.00 (initial fee) = $20.50 (for 1 hour)
Now that you have the price for 1 hour including the initial fee, now you need to find the price for each hour after that. Here's how I did that:
I created a graph that looked like this:
Hours: 1 2 3
Ieda: 19.50 30.50 41.50
Thanh: 20.50 31.00 41.50
Here's how I figured out the price for each hour:
Ieda:
Hour 1 (including initial price):
$11.00 + $8.50 = $19.50
Hour 2 (excluding initial price): Only add the hourly price after Hour 1!
$19.50 + $11.00 = $30.50
Hour 3 (excluding initial price):
$30.50 + $11.00 = $41.50
Thanh:
Hour 1 (including initial price):
$10.50 + $10.00 = $20.50
Hour 2 (excluding initial price):
$20.50 + $10.50 = $31.00
Hour 3 (excluding initial price):
$31.00 + $10.50 = $41.50
So, looking at the graph, their prices are the same once each instruction reaches 3 hours. ($41.50)
I hope I was able to help you! :)
Answer:
Step-by-step explanation:
2^0 is less than or equal to 1!, because 1<= 1
if 2^n <= (n+1)!, we wish to show that 2^(n+1) <= (n+2)!, since
(n+2)! = (n+1)! * (n+2), and (n+1)!>= 2^n, then we want to prove that n+2<=2, which is always true for n>=0
