Nina's property taxes will be $531.
We are starting with the amount of $2950. To find 18% of this amount, we just multiply the starting amount by 0.18
0.18 x 2950 = 531
The total amount of the taxes will be $531.
Length to width : 210/65 reduces to 42/13 or 42:13 or 42 to 13
Answer:
![(1) \ _8P_8 = 40320\\\\(2) \ _1_0P_4 = 5040\\\\(3) \ \frac{_1_0P_5}{_5P_3} = 504\\\\(4) \ \frac{_6P_2 \ . \ _8P_5}{_1_0P_6} = 1\frac{1}{3} \\\\(5) \ \frac{_8P_2 \ . \ _8P_6}{_7P_6 \ . \ _4P_2} = 18\frac{2}{3}](https://tex.z-dn.net/?f=%281%29%20%5C%20_8P_8%20%3D%2040320%5C%5C%5C%5C%282%29%20%5C%20_1_0P_4%20%3D%205040%5C%5C%5C%5C%283%29%20%5C%20%5Cfrac%7B_1_0P_5%7D%7B_5P_3%7D%20%3D%20504%5C%5C%5C%5C%284%29%20%5C%20%5Cfrac%7B_6P_2%20%5C%20.%20%5C%20_8P_5%7D%7B_1_0P_6%7D%20%3D%201%5Cfrac%7B1%7D%7B3%7D%20%5C%5C%5C%5C%285%29%20%5C%20%5Cfrac%7B_8P_2%20%5C%20.%20%5C%20_8P_6%7D%7B_7P_6%20%5C%20.%20%5C%20_4P_2%7D%20%3D%2018%5Cfrac%7B2%7D%7B3%7D)
Step-by-step explanation:
![(1) \ _8P_8 = \frac{8!}{(8-8)!} = \frac{8!}{0!} = 8! = 40320](https://tex.z-dn.net/?f=%281%29%20%5C%20_8P_8%20%3D%20%5Cfrac%7B8%21%7D%7B%288-8%29%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B0%21%7D%20%3D%208%21%20%3D%2040320)
![(2) \ _1_0P_4 = \frac{10!}{(10-4)!} = \frac{10!}{6!} = \frac{10\times 9\times 8 \times 7 \times 6!}{6!} = 10\times 9\times 8 \times 7 = 5040](https://tex.z-dn.net/?f=%282%29%20%5C%20_1_0P_4%20%3D%20%5Cfrac%7B10%21%7D%7B%2810-4%29%21%7D%20%3D%20%5Cfrac%7B10%21%7D%7B6%21%7D%20%3D%20%5Cfrac%7B10%5Ctimes%209%5Ctimes%208%20%5Ctimes%207%20%5Ctimes%206%21%7D%7B6%21%7D%20%3D%2010%5Ctimes%209%5Ctimes%208%20%5Ctimes%207%20%20%3D%205040)
![(3) \ \frac{_1_0P_5}{_5P_3} =\frac{(10!)/(10-5)!}{(5!)/(5-3)!} = \frac{(10!)/(5!)}{(5!)/(2!)} = \frac{10\times 9 \times 8\times 7\times 6}{5\times 4 \times 3} = 504](https://tex.z-dn.net/?f=%283%29%20%5C%20%5Cfrac%7B_1_0P_5%7D%7B_5P_3%7D%20%3D%5Cfrac%7B%2810%21%29%2F%2810-5%29%21%7D%7B%285%21%29%2F%285-3%29%21%7D%20%3D%20%5Cfrac%7B%2810%21%29%2F%285%21%29%7D%7B%285%21%29%2F%282%21%29%7D%20%3D%20%5Cfrac%7B10%5Ctimes%209%20%5Ctimes%208%5Ctimes%207%5Ctimes%206%7D%7B5%5Ctimes%204%20%5Ctimes%203%7D%20%3D%20504)
![(4) \ \frac{_6P_2 \ . \ _8P_5}{_1_0P_6} = \frac{(6!)/(6-2)! \ \times\ (8!)/(8-5)!}{(10!)/(10-6)!} = \frac{(6!)/(4!) \ \times \ (8!)/(3!)}{(10!) /(4!)} = \frac{6! \ \times \ 8!}{10! \ \times \ 3!} \\\\= \frac{6\times 5 \times 4 \times 3! \ \times 8!}{10\times 9 \times 8! \ \times \ 3!} = \frac{6\times 5 \times 4}{10\times 9} = \frac{4}{3} = 1\frac{1}{3}](https://tex.z-dn.net/?f=%284%29%20%5C%20%5Cfrac%7B_6P_2%20%20%5C%20.%20%5C%20_8P_5%7D%7B_1_0P_6%7D%20%3D%20%5Cfrac%7B%286%21%29%2F%286-2%29%21%20%5C%20%5Ctimes%5C%20%20%288%21%29%2F%288-5%29%21%7D%7B%2810%21%29%2F%2810-6%29%21%7D%20%3D%20%5Cfrac%7B%286%21%29%2F%284%21%29%20%5C%20%5Ctimes%20%5C%20%288%21%29%2F%283%21%29%7D%7B%2810%21%29%20%2F%284%21%29%7D%20%3D%20%5Cfrac%7B6%21%20%5C%20%5Ctimes%20%5C%208%21%7D%7B10%21%20%5C%20%5Ctimes%20%5C%203%21%7D%20%5C%5C%5C%5C%3D%20%5Cfrac%7B6%5Ctimes%205%20%5Ctimes%204%20%5Ctimes%203%21%20%5C%20%5Ctimes%208%21%7D%7B10%5Ctimes%209%20%5Ctimes%208%21%20%5C%20%5Ctimes%20%5C%203%21%7D%20%3D%20%5Cfrac%7B6%5Ctimes%205%20%5Ctimes%204%7D%7B10%5Ctimes%209%7D%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20%3D%201%5Cfrac%7B1%7D%7B3%7D)
![(5) \ \frac{_8P_2 \ . \ _8P_6}{_7P_6 \ . \ _4P_2} = \frac{(8!)/(6!) \ \times \ (8!)/(2!)}{(7!)/(1!) \ \times \ (4!)/(2!)} = \frac{8! \ \times \ 8!}{7! \ \times \ 6! \ \times \ 4!} = \frac{(8 )\ \times \ (8 \times 7)}{4!} =\frac{(8 )\ \times \ (8 \times 7)}{4\times 3 \times 2}\\\\= \frac{56}{3} = 18 \frac{2}{3}](https://tex.z-dn.net/?f=%285%29%20%5C%20%5Cfrac%7B_8P_2%20%5C%20.%20%5C%20_8P_6%7D%7B_7P_6%20%5C%20.%20%5C%20_4P_2%7D%20%3D%20%5Cfrac%7B%288%21%29%2F%286%21%29%20%5C%20%5Ctimes%20%5C%20%288%21%29%2F%282%21%29%7D%7B%287%21%29%2F%281%21%29%20%5C%20%5Ctimes%20%5C%20%284%21%29%2F%282%21%29%7D%20%3D%20%5Cfrac%7B8%21%20%5C%20%5Ctimes%20%5C%208%21%7D%7B7%21%20%5C%20%5Ctimes%20%5C%206%21%20%5C%20%5Ctimes%20%5C%204%21%7D%20%3D%20%5Cfrac%7B%288%20%29%5C%20%5Ctimes%20%5C%20%288%20%5Ctimes%207%29%7D%7B4%21%7D%20%3D%5Cfrac%7B%288%20%29%5C%20%5Ctimes%20%5C%20%288%20%5Ctimes%207%29%7D%7B4%5Ctimes%203%20%5Ctimes%202%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B56%7D%7B3%7D%20%3D%2018%20%5Cfrac%7B2%7D%7B3%7D)
Answer:
$12.55
Step-by-step explanation:
25-6.75=18.25
18.25-3.70=14.55
14.55-2=12.55
Miguel has $12.55 left