Answer:
12 units
Step-by-step explanation:
x is to 16 as 9 is to x
x/16 = 9/x cross multiply
x^2 = 144
x =12
In 1 hour you pick 60 lines, so in 8 hours you pick 60*8 = 480 lines
Answer:
8 one-dollar bills
3 five-dollar bills
2 ten-dollar bills
Step-by-step explanation:
Let x = # of one-dollar bills, y = # of five-dollar bills, and z = # of ten-dollar bills. Total amount in the wallet is $43, so the first equation would be 1x + 5y + 10z = 43. Next, there are 4 times as many one-dollar bills as ten-dollar bills, so x = 4z. There are 13 bills in total, so x + y + z = 13
x + 5y + 10z = 43
x = 4z
x + y + z = 13
x + 5y + 10z = 43
x + 0y - 4z = 0
x + y + z = 13
5y + 14z = 43
-y - 5z = -13
5y + 14z = 43
-5y - 25z = -65
-11z = -22
z = 2
x = 4z
x = 4*2 = 8
x + y + z = 13
8 + y + 2 = 13
10 + y = 13
y = 3
The formula of the present value of annuity due:
![PV=C*[\frac{1-(1+i)^{-n}}{i}]*(1+i)](https://tex.z-dn.net/?f=PV%3DC%2A%5B%5Cfrac%7B1-%281%2Bi%29%5E%7B-n%7D%7D%7Bi%7D%5D%2A%281%2Bi%29)
For your case:
C = $3000
i = 12% / 100 = 0.12
n = 3 * 2 = 6 (semiannually for 3 years means 6 payments)
So, the solution is:
![PV=3000*[\frac{1-(1+0.12)^{-6}}{0.12}]*(1+0.12)=3000*[\frac{1-0.5066}{0.12}]*1.12=](https://tex.z-dn.net/?f=PV%3D3000%2A%5B%5Cfrac%7B1-%281%2B0.12%29%5E%7B-6%7D%7D%7B0.12%7D%5D%2A%281%2B0.12%29%3D3000%2A%5B%5Cfrac%7B1-0.5066%7D%7B0.12%7D%5D%2A1.12%3D)
![=3000*[\frac{1-0.5066}{0.12}]*1.12=3000*4.1114*1.12=13814.32](https://tex.z-dn.net/?f=%3D3000%2A%5B%5Cfrac%7B1-0.5066%7D%7B0.12%7D%5D%2A1.12%3D3000%2A4.1114%2A1.12%3D13814.32)
Hello, again!!
So, the range is the outcome when you plug in any x. In other words, the y.
Because this is absolute value, the x will turn positive. However, the number will then turn negative.
Therefore, y will ALWAYS be negative.
The answer is C.
Hope this helps!! Let me know if you have ANY questions.
