The volume of a cube (V) is given in terms of its side length (s) as
... V = s³
You have
... 27n²⁷ = s³
You may recognize that 27 = 3³, so this can be written as
This result matches your second selection
... 3n⁹ units
State two numbers such that the lesser number is 25% less than the greater number
2 answers:
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Answer:
Part a: From column 1 of the attached Wage and Tax statement, the gross pay is $34854.
Part b: From column 17 of the attached Wage and Tax statement, she paid $1762.39 in state income tax.
Part c: It should be $2160.95 instead of $2164.44
Part d: It should be $505.38 instead of $467.68
Part e: FICA Tax is $2665.38
Part f: She owes the difference $16.52 to the Federal Tax.
Step-by-step explanation:
As data was missing from the question, the complete question is found online and is attached herewith.
Part a:
From column 1 of the attached Wage and Tax statement, the gross pay is $34854.
Part b:
From column 17 of the attached Wage and Tax statement, she paid $1762.39 in state income tax.
Part c:
For 2012, Social Security Tax is given as 6.2% of the gross pay so
Item 4 should then be
6.2% x Gross Income
6.2% x 34854
.062 * 34854 = 2160.95
It should be $2160.95 instead of $2164.44
Part d
For 2012, Medicare Tax is given as 1.45% of the gross pay so
Item 6 should then be
1.45% x Gross Income
1.45% x 34854
.0145 * 34854 = 505.38
It should be $505.38 instead of $467.68
Part e
FICA tax is given as sum of Social security tax and Medicare taxes. This is given as
FICA Tax=Social Security Tax+Medicare Tax
FICA Tax=$2160+$505.38
FICA Tax=$2665.38
FICA Tax is $2665.38
Part f
From the attached table, with $32104 as the taxable income, as the head of household she owes $4199 in Federal tax.
From the attached wages and tax statement in column 2, she paid $4182.48. Thus she owes the difference $16.52 to the Federal Tax.
Answer:
For n = 3, there are 134 possibilities
Step-by-step explanation:
First, lets calculate the generating function.
For each square we have 2 possibilities: red and blue. The Possibilities between n² squares multiply one with each other, giving you a total of 2^n² possibilities to fill the chessboard with the colors blue or red.
However, rotations are to be considered, then we should divide the result by 4, because there are 4 ways to flip the chessboard (including not moving it), that means that each configuration is equivalent to three other ones, so we are counting each configuration 4 times, with the exception of configurations that doesnt change with rotations.
A chessboard that doesnt change with rotations should have, in each position different from the center, the same colors than the other three positions it could be rotated into. As a result, we can define a <em>symmetric by rotations chessboard</em> with only (n²-1)/4 + 1 squares (the quarter part of the total of squares excluding the center plus the center).
We cocnlude that the total of configurations of symmetrical boards is
Since we have to divide by 4 the rest of configurations (because we are counted 4 times each one considering rotations), then the total number of configutations is
If n = 3, then the total amount of possibilities are