Marcus earned $54,000 last year when the Social Security tax was 6.2% of income up to $94,200. His Medicare tax was 1.45%. How m
2 answers:
Given =
Marcus earned $54,000 last year. social s ecurity tax was 6.2% and medicare tax was 1.45%
Find out he pay in Social Security and Medicare taxes last year.
To proof
Marcus earned last year = $ 54000
Social Security tax = 6.2%
Medicare tax = 1.45%
First find out the social security tax
6.2 % written in the simpler form =
= 0.062
Social Security tax last year = .062×54000
= $ 3348
find out Medicare taxes
1.45% Medicare tax written in the simpler form =
= 0.0145
Medicare taxes last year = 0.0145 × 54000
= $743
Total tax last year = $743 + $3348
= $ 4131
Hence proved
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Answer:
From top to bottom, the boxes shown are number 3, 5, 6, 2, 4, 1 when put in ascending order.
Step-by-step explanation:
It is convenient to let a calculator or spreadsheet tell you the magnitude of the sum. For a problem such as this, it is even more convenient to let the calculator give you all the answers at once.
The TI-84 image shows the calculation for a list of vectors being added to 4∠60°. The magnitudes of the sums (rounded to 2 decimal places—enough accuracy to put them in order) are ...
... ║4∠60° + 3∠120°║≈6.08
... ║4∠60° + 4.5∠135°║≈6.75
... ║4∠60° + 4∠45°║≈7.93
... ║4∠60° + 6∠210°║≈3.23
... ║4∠60° + 5∠330°║≈6.40
... ║4∠60° + 7∠240°║≈ 3
_____
In the calculator working, the variable D has the value π/180. It converts degrees to radians so the calculation will work properly. The abs( ) function gives the magnitude of a complex number.
On this calculator, it is convenient to treat vectors as complex numbers. Other calculators can deal with vectors directly
_____
<em>Doing it by hand</em>
Perhaps the most straigtforward way to add vectors is to convert them to a representation in rectangular coordinates. For some magnitude M and angle A, the rectangular coordinates are (M·cos(A), M·sin(A)). For this problem, you would convert each of the vectors in the boxes to rectangular coordinates, and add the rectangular coordinates of vector t.
For example, the first vector would be ...
3∠120° ⇒(3·cos(120°), 3·sin(120°)) ≈ (-1.500, 2.598)
Adding this to 4∠60° ⇒ (4·cos(60°), 4°sin(60°)) ≈ (2.000, 3.464) gives
... 3∠120° + 4∠60° ≈ (0.5, 6.062)
The magnitude of this is given by the Pythagorean theorem:
... M = √(0.5² +6.062²) ≈ 6.08
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<em>Using the law of cosines</em>
The law of cosines can also be used to find the magnitude of the sum. When using this method, it is often helpful to draw a diagram to help you find the angle between the vectors.
When 3∠120° is added to the end of 4∠60°, the angle between them is 120°. Then the law of cosines tells you the magnitude of the sum is ...
... M² = 4² + 3² -2·4·3·cos(120°) = 25-24·cos(120°) = 37
... M = √37 ≈ 6.08 . . . . as in the other calculations.
Answer:
D. two acute angles
Step-by-step explanation:
Let us quickly plot the vertices on a graph to obtain the figure in the attachment.
Connecting the four points gives a square.
We know a square has the following properties.
A. four right angles
.......True
B. four vertices
................True
C. two sets of parallel lines
......True
D. two acute angles...................False.....A square has four right angles.
Therefore the correct choice is D
