Final answer:
Sonya's annual take-home pay, after FICA taxes of 7.65% on her annual salary of $36,590, would be $33,790.86.
Explanation:
To calculate Sonya’s annual take-home pay after FICA taxes, we first need to understand that FICA consists of two separate taxes: Social Security and Medicare. The total rate for these combined is 7.65% of the gross income. Sonya’s annual salary is $36,590.
First, we calculate the total FICA tax Sonya has to pay:
Social Security tax (6.2% of $36,590) = $2,268.58Medicare tax (1.45% of $36,590) = $530.56Add these two amounts to get the total FICA tax:
$2,268.58 (Social Security) + $530.56 (Medicare) = $2,799.14
Finally, subtract this total FICA tax from the annual salary to find Sonya’s take-home pay:
$36,590 (annual salary) - $2,799.14 (FICA taxes) = $33,790.86
A pyramid and prism have the same base area and height. The prism's base area is 8 square units and its height is 16 units. What is the volume of the pyramid? The volume of the pyramid is __________ cubic units. Enter the number that correctly fills in the blank in the previous sentence.
The volume of the pyramid with a base area of 8 square units and a height of 16 units is 42.67 cubic units.
The volume of a pyramid is calculated as one-third of the base area times the height. The base area of the given pyramid is 8 square units and the height is 16 units. Using the formula for volume V = rac{1}{3}Ah, where A is the base area and h is the height, the volume of the pyramid can be found as follows:
V = rac{1}{3} imes 8 imes 16
V = rac{1}{3} imes 128
V = 42.67 cubic units (rounded to two decimal places).
Therefore, the volume of the pyramid is 42.67 cubic units.
One side of the triangle is 8 in, and the other two sides are equal to a positive whole number of inches. What is the smallest possible perimeter of the triangle?
F. 9 in
G. 10 in
H. 11 in
J. 15 in
K. 17 in
Instructions:Select the correct answer. You’re given two side lengths of 10 centimeters and 8 centimeters. The angle between the sides measures 40°. How many triangles can you construct using these measurements? 0 1 2 infinitely many
Since we are given the lengths of 2 sides with the angle in between, therefore by cosine law we can only construct 1 triangle from this. By stating the angle in between, this constricts the possible number of triangles that can be formed into 1.
By calculation, the length of the 3rd side is calculated using cosine law:
c^2 = a^2 + b^2 – 2abcosθ
c^2 = 10^2 + 8^2 – 2(10)(8)cos40
c = 6.44 cm
ANSWER:
1 triangle
Write y less than 21
Answer:
21-y
Step-by-step explanation:
In mathematics the signs used for more than is + and for less than is -.
The question is asking us to write y less than 21 in mathematical statement form.
y less than 21 means 21-y,
Hence the mathematical statement for y less than 21 is 21-y.
Josh and his friends bought vanilla wafers for $4 per packet and chocolate wafers for $1 per packet at a carnival. They spent a total of $45 to buy a total of 27 packets of wafers of the two varieties.
Part A: Write a system of equations that can be solved to find the number of packets of vanilla wafers and the number of packets of chocolate wafers that Josh and his friends bought at the carnival. Define the variables used in the equations. (5 points)
Part B: How many packets of chocolate wafers and vanilla wafers did they buy? Explain how you got the answer and why you selected a particular method to get the answer. (5 points)
Vanilla wafers cost $4 per packet
and chocolate wafers for $1 per packet
They spent a total of $45 .
This means that the equation that can be formed using this information is:
4x+y=45
and they buy a total of 27 packets of wafers.
i.e. the equation formed with the help of this information is:
x+y=27
PART A:
The system of equations that can be solved to find the number of packets of vanilla wafers and the number of packets of chocolate wafers that Josh and his friends bought at the carnival is:
4x+y=45-------------------(1)
and x+y=27----------------(2)
PART B:
We will use the method of substitution because with the help of this method we could easily substitute the value of one variable in terms of the other variable and obtain the answer.
Using equation (2) we have:
y=27-x-------------------(3)
On putting this value of y in equation (1) we have:
4x+27-x=45
i.e.
4x-x+27=45
i.e.
3x+27=45
i.e.
3x=45-27
i.e.
3x=18
i.e.
x=6
and on putting the value of x in equation (3) we have:
y=27-6
i.e. y=21
Hence, number of vanilla wafers purchased = 6
and number of chocolates wafers purchased = 21
What is the constant of variation for the quadratic variation? 6y = 4x2
The triangle above is changed so that the exterior angle shown measures 128 how does this affect angles b and c
Answer:
the sum of the measures of angle B and angle C will also be 128 degrees meaning that the sum will decrease by 24 degrees.
the slopes of two lines are 5/6 and 2/p determine the value of p that will make the lines parallel
How do i solve this equation: 4/5a + 3 = 1/3a - 8
If the divisor is 40 what is the least three digit dividend that would give a reminder four
Select all of the following expressions that are equivalent to ab - 2 = c
a = c/b -2
b = c + 2/a
ab = c + 2
a - c/2 = b
b - 2/c = a
a = c + 2/b
Answer:
Option C.
Step-by-step explanation:
The given expression is ab - 2 = c
Option a : a = [tex]\frac{c}{b}[/tex] - 2
ab = c - 2b
Not equivalent to the original expression.
Option b : b = c + [tex]\frac{2}{a}[/tex]
ab = ac + 2 ⇒ [tex](\frac{ab-2}{a})[/tex] = c
Not equivalent
Option c : ab = c + 2
ab - 2 = c
Equivalent to original expression
Option d : a - [tex]\frac{c}{2}[/tex] = b
2a - c = 2b
Not equivalent
Option e : b - [tex]\frac{2}{c}[/tex] = a
bc - 2 = ac ⇒ c (b-a) = 2 ⇒ c = [tex]\frac{2}{b-a}[/tex]
Not equivalent
Option f : a = c + [tex]\frac{2}{b}[/tex]
ab = bc + 2
[tex](\frac{ab-2}{b} )[/tex] = c
Not equivalent
Paul has grades of 63 and 81 on his first two tests. What must he score on his third test in order to have an average of at least 70
draw a diagram of eli's walking pattern
The value of 4 in 3,492 is how many times the value of 4 in 704?
1. Solve -2n + 5 > 7.
2. Kia experimental probability of striking out at baseball is 13%. Out of 30 times at bat about how many times will she strike out?
What is a proportion?
0, 7, 26, 63, _ , 215.
What is the missing number in the given sequence?
What is the pattern?
Regroup hundreds as Tens:
8 hundreds 9 tens =
What are the solutions to the equation (2x-5)(3x-1)=0?
The answer is C. x = [tex]\frac{5}{2}[/tex] 0r x = [tex]\frac{1}{3}[/tex]
write an integer for the situation below : 13 feet below the sea level
Which class has 32% girls?
The correct answer to the question *interquartile range
HELPPP PLEASEEEEEE!?!?!
a straight line is 180 degrees so we can find C by subtracting 140 from 180
180-140 = 40 degrees
all 3 inside angles need to equal 180 so now we have
180 = 40 + (2x) + (x+2)
180 = 40 +3x +2
180=42+3x
138=3x
x= 138/3 = 46
check : 2x= 2*46 = 92
x+2 = 46+2 = 48
92 +48 +40 = 180
so x = 46 degrees
so angle B = 2x46 = 92 degrees
Ali needs 4/10 yard of red ribbon and 5/10 yard of blue ribbon to make a tail for her kite. how much ribbon does Ali need in all?
Consider the following pair of equations: −x − y = −5 y = x + 1 If the two equations are graphed, at what point do the lines representing the two equations intersect? (−2, 3) (3, −2) (2, 3) (3, 2)
Find the length of the missing side. If necessary, round to the nearest tenth. side A = 38 side b =b side c = 34
A. 51
B. 36
C. 72
D. 17
The length of the missing side = side B = 17 (D) or 51(A)
Further explanationTriangles are flat fields bounded by 3 intersecting sides and 3 angles
This side can be the same length or different.
If at an angle there is an angle of 90 degrees, this triangle is said to be a right angle
There is a hypotenuse in this triangle which is the sum of the two sides
[tex]\large{\boxed{\bold{C^2=A^2+B^2}}[/tex]
where c = hypotenuse
a and b = side/leg
This formula is known as the Pythagorean theorem which states that:
the hypotenuse or the longest side in a right triangle equal to the sum of the squares of the other sides.
or
the sum of the squares of the length of the two sides equals the square of the length of the hypotenuse
While the angle formulas used are
sin a = opposite / hypotenuse cos a = adjacent / hypotenuse tan a = opposite / adjacent
From the problem it is known that side A = 38 ,side b = b, side c = 34
There are 2 possible solutions to this problem because the image does not exist:
1. side A as the hypotenuse side (the longest side) 2. side B as hypotenuse sidePossible Solution no 1
A² = C²+B²(A=hypetenuse)
B² = A²-C²
B² = 38² - 34²
B² = 288
B = √288
B = 16.97, round to the nearest tenth ⇒ 17 (answer D)
Possible Solution no 2
B² = A²+C²(B=hypotenuse)
B² = 38² + 34²
B² = 2600
B = √2600
B = 50.99, round to the nearest tenth ⇒ 51 (answer A)
Learn more
the Sin rule
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trigonometric ratio
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the triangle angle
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Prove the converse of the Pythagorean Theorem
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Use Pythagoras' theorem
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Keywords: Pythagoras' theorem, the trigonometric, hypotenuse
DOES ANYONE KNOW THE ANSWER???
99PTS (08.06)The data set shows the number of cars parked in the restaurant parking lot during the lunch hour each day for two weeks: 8 7 14 10 13 27 11 10 14 7 12 9 14 9 Which of the following statements is true based on the data set?
{ y=x^2-2x-6
y=4x+10
What is the equation of the line passing through the points (2, –1) and (5, –10) in slope-intercept form?