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finlep [7]
3 years ago
8

Jill Janzen’s gross weekly pay is $298. Her earnings to date for the year total $14,900. What amount is deducted from her pay ea

ch week for Social Security, which is taxed at 6.2%?
Mathematics
2 answers:
Sloan [31]3 years ago
8 0
298 x 0.062 = the amount that is deducted
298 x 0.062 = 18.476

The total amount of money she has earned this year is given to you just to confuse you. All you really need is the percent converted to a decimal, which is 0.062, and her weekly pay, which is $298. You multiply these two together to get 18.476, which when rounded becomes $18.48.

So, every week, $18.48 is deducted from her weekly pay.
Leviafan [203]3 years ago
4 0
I believe we pay 6.2% social security tax and another 1.45% for medicare. 
So you would pay approximately 18.48 for social security tax and another 4.32 for medicare each week.  Provided the 298. is your gross income. 
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The sum of three numbers is 26. Twice the first minus the second is the third less 2. The third is the second minus 3 times the
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Let a, b, c represent the three numbers. The problem statement gives rise to three equations:

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Adding the first two equations gives

... (a +b +c) +(2a -b) = (26) +(c -2)

... 3a +c = 24 +c . . . . . simplify

... 3a = 24 . . . . . . . . . . subtract c

... a = 8 . . . . . . . . . . . . divide by 3

Adding the second and third equations gives ...

... (2a -b) +(-3a +b) = (c -2) +(c)

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Using the third equation we can find b.

... -3·8 +b = -3 . . . . substitute for a and c

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The numbers are 8, 21, -3.

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The method above is sort of "ad hoc", taking advantage of the numbers in this particular set of equations. You can use more formal methods of Gaussian elimination or Cramer's Rule to solve these by just following a procedure. Or, your graphing calculator can do it for you.

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3 years ago
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2 years ago
Show tan(???? − ????) = tan(????)−tan(????) / 1+tan(????) tan(????)<br> .
anyanavicka [17]

Answer:

See the proof below

Step-by-step explanation:

For this case we need to proof the following identity:

tan(x-y) = \frac{tan(x) -tan(y)}{1+ tan(x) tan(y)}

We need to begin with the definition of tangent:

tan (x) =\frac{sin(x)}{cos(x)}

So we can replace into our formula and we got:

tan(x-y) = \frac{sin(x-y)}{cos(x-y)}   (1)

We have the following identities useful for this case:

sin(a-b) = sin(a) cos(b) - sin(b) cos(a)

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If we apply the identities into our equation (1) we got:

tan(x-y) = \frac{sin(x) cos(y) - sin(y) cos(x)}{sin(x) sin(y) + cos(x) cos(y)}   (2)

Now we can divide the numerator and denominato from expression (2) by \frac{1}{cos(x) cos(y)} and we got this:

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And simplifying we got:

tan(x-y) = \frac{tan(x) -tan(y)}{1+ tan(x) tan(y)}

And this identity is satisfied for all:

(x-y) \neq \frac{\pi}{2} +n\pi

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