Which of the following is not a subset of {1, 2, 3}? {0} {1, 2, 3} Ø
1 answer:
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Answer:
The net pay of the Raquel be $601 .
Step-by-step explanation:
As given
Raquel has gross pay of $732 and federal tax withholdings of $62.
Social Security tax that is 6.2% of her gross pay .
6.2% is written in the decimal form.
= 0.062
Social Security tax = 0.062 × Gross pay
= 0.062 × 732
= $ 45.38 (Approx)
As given
Medicare tax that is 1.45% of her gross pay .
1.45% is written in the decimal form.
= 0.0145
Medicare Tax = 0.0145 × Gross pay
= 0.0145 × 732
= $ 10.6 (Approx)
As given
State tax that is 21% of her federal tax.
21% is written in the decimal form.
= 0.21
State tax = 0.21 × Federal tax
= 0.21 × 62
= $13.02
Total amount of the tax = Federal tax + Social Security tax + Medicare Tax + State tax
Putting all the values in the above
= $62 + $45.38 +$10.6 + $13.02
= $ 131
Raquel’s net pay = Gross pay - Total amount of taxes
= $732 - $131
= $ 601
Therefore the net pay of the Raquel be $601 .
Answer:
The Coordinates of Point C are C(5,2)
The slope of CD is 3
The possible coordinates of point D(a,b) are (6, 5) and (4, -1)
Step-by-step explanation:
According to the Question,
- Given, The end points of AB are A(2,3) and B(8,1). The perpendicular Bisector of AB is CD, and point C lies on AB. The length of the CD is √10 units.
Now, Let The Coordinates of Point C are C( x , y ) .
- Thus, C( x , y ) =
The Coordinates of Point C are C( x , y ) = ⇒C(5, 2).
- And, The slope of AB =
⇒
⇔
.
Thus, The slope of CD is =
⇔ 3.
- Let the coordinate of D be (a, b) then
⇒ √{ (b - 2)² +(a - 5)² } = √10
on squaring both sides we get,
⇒ a² - 10a + 25 + b² - 4b + 4 = 10
⇒ a² + b² - 10a - 4b = - 19 ⇔⇔ (Equation 1)
- We Know, the slope of CD = 3
⇒Thus, (b - 2)/(a - 5) = 3
⇒ b - 2 = 3a - 15
⇒ b = 3a - 13 ⇔⇔ (Equation 2)
- Putting value of Equation 2 into Equation 1, We get
⇒a² + (3a - 13)² - 10a - 4(3a - 13) = - 19
⇒a² + 9a² - 78a + 169 - 10a - 12a + 52 = - 19
⇒10a² - 100a + 240 = 0
⇒a² - 10a + 24 = 0
⇒(a - 4)(a - 6) = 0
⇒a = 4 or a = 6
Now,
- When a = 4 , b = 3(4) - 13 ⇒ 12 - 13 ⇒ b = -1
- When a = 6, b = 3(6) - 13 ⇒ 18 - 13 ⇒ b = 5
Therefore, the possible coordinates of point D(a,b) are (6, 5) and (4, -1).