Answer: a) 2092278989 b) 576, c) ![\dfrac{576}{2092278989}](https://tex.z-dn.net/?f=%5Cdfrac%7B576%7D%7B2092278989%7D)
Step-by-step explanation:
Since we have given that
Number of students = 16
Number of desks = 16
a) How many days must pass before the class must repeat a seating arrangement?
![16!=2092278989](https://tex.z-dn.net/?f=16%21%3D2092278989)
If the number of rows = 4
b) How many seating arrangements are there that put Larry, Moe, Curly, and Shemp in the front seats?
![4!\times 4!\\\\=24\times 24\\\\=576](https://tex.z-dn.net/?f=4%21%5Ctimes%204%21%5C%5C%5C%5C%3D24%5Ctimes%2024%5C%5C%5C%5C%3D576)
c) How many seating arrangements are there that put Larry, Moe, Curly, and Shemp in the front seats?
![\dfrac{576}{2092278989}](https://tex.z-dn.net/?f=%5Cdfrac%7B576%7D%7B2092278989%7D)
Hence, a) 2092278989 b) 576, c) ![\dfrac{576}{2092278989}](https://tex.z-dn.net/?f=%5Cdfrac%7B576%7D%7B2092278989%7D)
Step-by-step explanation:
(2/3) * (3/8)
= (2 * 3) / (3 * 8)
= 6 / 24
= 1/4.
Answer:
Coupon B
Step-by-step explanation:
Given
![Price = \$450](https://tex.z-dn.net/?f=Price%20%3D%20%5C%24450)
![Coupon\ A = \$80](https://tex.z-dn.net/?f=Coupon%5C%20A%20%3D%20%5C%2480)
![Coupon\ B = 20.5\%](https://tex.z-dn.net/?f=Coupon%5C%20B%20%3D%2020.5%5C%25)
Required
Which coupon is better
From the question, we have:
![Coupon\ A = \$80](https://tex.z-dn.net/?f=Coupon%5C%20A%20%3D%20%5C%2480)
![Coupon\ B = 20.5\%](https://tex.z-dn.net/?f=Coupon%5C%20B%20%3D%2020.5%5C%25)
Coupon B means that:
![Coupon\ B = 20.5\% * \$450](https://tex.z-dn.net/?f=Coupon%5C%20B%20%3D%2020.5%5C%25%20%2A%20%5C%24450)
![Coupon\ B = 0.205 * \$450](https://tex.z-dn.net/?f=Coupon%5C%20B%20%3D%200.205%20%2A%20%5C%24450)
![Coupon\ B = \$92.25](https://tex.z-dn.net/?f=Coupon%5C%20B%20%3D%20%5C%2492.25)
By comparison:
Coupon B gives him a better buy because: ![\$92.25 > \$80](https://tex.z-dn.net/?f=%5C%2492.25%20%3E%20%5C%2480)
Answer:
26
Step-by-step explanation:
Since x = -5, we can replace x with it's numerical -5, right? The problem tells you that x is equal to -5. So, just replace any x you see with -5.
So in this case,
![-3|x|+2x-1](https://tex.z-dn.net/?f=-3%7Cx%7C%2B2x-1)
turns into:
![-3|(-5)|+2(-5)-1](https://tex.z-dn.net/?f=-3%7C%28-5%29%7C%2B2%28-5%29-1)
You can use a calculator or solve it by hand to see what the answer is.
![-3|(-5)|+2(-5)-1\\-3(5)+2(-5)-1\\-15+(-10)-1\\-25-1\\-26](https://tex.z-dn.net/?f=-3%7C%28-5%29%7C%2B2%28-5%29-1%5C%5C-3%285%29%2B2%28-5%29-1%5C%5C-15%2B%28-10%29-1%5C%5C-25-1%5C%5C-26)