Answer:
Lana Powell has cumulative earnings of $110,000 at the end of September. In the first week in October she earns $2,000. The amount deducted for Social Security and Medicare from her check is (assume Social Security rate of 6.2% on $110,100 and Medicare of 1.45%):
Step-by-step explanation:
In the first week of October on the $ 2,000, we must deduct the two expenses, that of 6.2% and 1.45%, and then add them between them and subtract them from the $ 2000.
It would be the following: 2000 x 6.2% = $ 124; 2000 x 1.45% = 29; 124 + 29 = $ 153 is the amount to be deducted from the $ 2,000; $ 2000 - $ 153 = $ 1847.
Lana Powell's paycheck for the first week in October would have $124 deducted for Social Security and $29 for Medicare, resulting in a total deduction of $153. Her cumulative earnings are not considered here as she has exceeded the earnings threshold of $110,100 for Social Security tax.
Explanation:Lana Powell's earnings for the first week in October are subject to deductions for Social Security at a rate of 6.2% and Medicare at a rate of 1.45%. To calculate these deductions, you multiply her weekly earnings by the respective rates:
Social Security deduction = $[tex]2000*6.2/100 = $124[/tex]Medicare deduction = $[tex]2000*1.45/100 = $29[/tex]Therefore, the total amount deducted from Lana Powell's paycheck for Social Security and Medicare is $124 + $29 = $153.
Note that you do not consider her cumulative earnings in this case. The Social Security tax is applicable only up to a wage base limit of $110,100 and since her cumulative earnings have already exceeded this limit, she would not be paying any additional Social Security tax beyond this earnings threshold.
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A round-robin tournament has 66 pairings. How many teams are in the tournament?
Identify all the sets to which 0.41567 belongs. Choose from rational,irrational,whole,and integer
Answer:
1.) D
2.) C
3.) C
4.) B
5.) A
6.) D
7.) A
8.) D
9.) A
10.) D
Step-by-step explanation:
what is the length of a circle that has a central angle of 98 degrees and 6 cm rounded to the nearest 100th. using 3.14
Can someone please help me
which rectangular equation is equivalent to the polar equation r sin theta=-2
Answer:
The rectangular equation that is equivalent to the given polar equation is:
y= -2
Step-by-step explanation:
We know that the polar coordinate of a equation are related to the rectangular coordinates of the equation as:
[tex]x=r\sin \theta\\\\y=r\cos \theta[/tex]
where,
[tex]r=\sqrt{x^2+y^2}[/tex]
Now we are given that:
[tex]r\sin \theta=-2[/tex]
Also,
[tex]\theta=\arctan \dfrac{y}{x}[/tex]
Hence, on converting the given polar equation to the rectangular equation we get:
[tex]y=-2[/tex]
How many cubes with 5 inches side Will completely fill a cube that is 10 inches on each side
what is the average rate of change for this quadratic function please help
Quadrilateral ABCD has vertices A(-3, 4), B(1, 3), C(3, 6), and D(1, 6). Match each set of vertices of quadrilateral EFGH with the transformation that shows it is congruent to ABCD.
Answer:
Answers a little bit more simplified, all credit to the expert :)
E(4, 4), F(8, 3), G(10, 6) and H(8, 6) <-----> a translation 7 units right
E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6) <-----> a reflection across the y-axis
E(-3, -1), F(1, -2), G(3, 1), and H(1, 1) <-----> a reflection across the x-axis
E(-3, -1), F(1, -2), G(3, 1) and H(1, 1) <-----> a translation 5 units down
Step-by-step explanation:
Which of the following is a solution of x2 + 5x = −2?
5 plus or minus the square root of 33 divided by two.
5 plus or minus the square root of 17 divided by two
negative 5 plus or minus the square root of 33 divided by two.
negative 5 plus or minus the square root of 17 divided by two.
Answer:
negative 5 plus or minus the square root of 17 divided by two: [tex]x=\frac{-5\pm\sqrt{17}}{2}[/tex].
Step-by-step explanation:
We have the equation
[tex]x^2+5x=-2[/tex]
[tex]x^2+5x+2=0[/tex].
To solve it, we are going to use the general formula. This formula is used to find the solutions of quadratic equations.
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
where a is the coefficient of [tex]x^2[/tex], in this case a=1, b is the coefficient of x, in this case b=5 and c is the independent term, in this case c=2.
[tex]x=\frac{-5\pm\sqrt{5^2-4(1)(2)}}{2(1)}[/tex]
[tex]x=\frac{-5\pm\sqrt{25-8}}{2}[/tex]
[tex]x=\frac{-5\pm\sqrt{17}}{2}[/tex].
a scale model of a school building is 5 inches tall. If the building is 100 feet tall, find the scale of the model
Answer with Step-by-step explanation:
A scale model of a school building is 5 inches tall.
Actual size of the school building is 100 feet.
1 feet=12 inches
100 feet=12×100 inches
= 1200 inches
5 inch is representing 1200 inches
1 inch represents 1200/5 inches
1 inch represents 240 inches
or 1 inch represents 12×20 inch
or 1 inch represents 20 feet
Scale of the model is:
1 inch represents 240 inches
1 inch represents 20 feet
Determine whether the cost for ordering multiple items that will be delivered is sometimes, always, or never proportional. Explain your reasoning.
Which expression is equivalent to (5^-2) (5^-1)
-1/125
-1/5
1/125
1/5
Evaluate the function rule for the given value. Y=6*4^x for x=-3
Answer:
[tex]y = \frac{3}{32}[/tex]
Step-by-step explanation:
Using the exponent rule:
[tex]a^{-n} = \frac{1}{a^n}[/tex]
Given the function:
[tex]y = 6 \cdot (4)^x[/tex] ......[1]
To evaluate the function rule for x = -3.
Substitute x = -3 in [1] we have;
[tex]y = 6 \cdot (4)^{-3}[/tex]
⇒[tex]y = 6 \cdot \frac{1}{4^3} = 6 \cdot \frac{1}{64}=\frac{3}{32}[/tex]
Therefore, the function rule for the given value when x = -3 is:
[tex]y = \frac{3}{32}[/tex]
Identify the values of a, b, and c that would be used in the quadratic formula to solve the equation 3x2− 5x + 5 = 0. A. a = 3, b = 5, c = 5 B. a = 3, b = −5, c = 5 C. a = 5, b = −5, c = 0 D. a = −3, b = 5, c = −5
A Sporting good store charges $30 for 12 cans of tennis balls. The tennis coach orders 100 cans of tennis balls for the tennis team. How much were the coach pay for the tennis balls?
What is the midpoint of GH? G(7,-5) H(9,-1)
if the lateral surface area of a square pyramid is 84ft^2 and the base edge is 6, what is the slant height?
A recipe for pastry has flour, butter and water mixed in the ratio 24 : 8 : 3 if fiona follows the recipe and uses 3 cups of flour, how many cups of butter should she use?
Fiona should use 1 cup of butter when using 3 cups of flour, according to the recipe's ratio of 24:8:3 for flour to butter to water.
Explanation:The question asks how much butter Fiona should use if she's using 3 cups of flour and the recipe calls for flour, butter, and water in the ratio of 24:8:3. To solve this, we take the ratio for butter (which is 8) and divide it by the flour ratio (which is 24), then multiply by the number of cups of flour Fiona is using (which is 3 cups).
Step-by-step Solution:
Write down the original ratio: 24 parts flour : 8 parts butter : 3 parts water.Calculate the ratio of butter to flour, which is 8/24. This simplifies to 1/3.Since Fiona is using 3 cups of flour, multiply the simplified butter ratio by the amount of flour: (1/3) * 3 cups = 1 cup. Thus, she would need 1 cup of butter.a game spinner has regions that are numbered 1 through 8. if the spinner is used twice, what is the probability that the first number is a 3 and the second is a 7?
The probability that the first number is a 3 and the second is a 7 is 1/64
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given:
spinner had region numbered from 1 to 8
So, the probability on the spinner has an equally likely chance of being selected= 1/8.
P(3) = 1/8
P(7) = 1/8
Thus, probability that the first number is a 3 and the second is a 7
=(1/8) * (1/8)
= 1/64
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Diana can earn money for the tickets she sells. Which of the following statements describes the variables in this situation correctly?
The variables in this situation are the price of the tickets and the quantity of tickets sold. The relationship between price, quantity, and revenue can be analyzed using the concept of price elasticity of demand. Diana should lower the price if demand is elastic, raise the price if demand is inelastic, and can maintain the same revenue if demand has unitary elasticity.
Explanation:The variables in this situation are the price of the tickets and the quantity of tickets sold. These two variables directly affect the total revenue generated by Diana from ticket sales. The relationship between price, quantity, and revenue can be analyzed using the concept of price elasticity of demand.
If demand for tickets is elastic, Diana should lower the price to increase total revenue. A decrease in price will result in a larger percentage increase in the quantity sold, leading to a higher total revenue. On the other hand, if demand is inelastic, Diana should raise the price to increase revenue. A certain percentage increase in price will result in a smaller percentage decrease in quantity sold, ultimately raising total revenue.
If demand has unitary elasticity, an equal percentage change in quantity will offset a moderate percentage change in price. In this case, Diana can earn the same revenue regardless of a moderate increase or decrease in ticket price.
Solve for x.
The length of a rectangle is equal to 2 times the width plus 3 feet. If the area of the rectangle is 20 square feet, what are the dimension of the rectangle?
what is the algebraic expression for the product of 9 and a number t
Which graph shows a triangle and its reflection image over the x-axis?
A. first picture
B. 2nd picture
C. picture 3
D. picture 4
A. is wrong
Answer-
In picture 4, the triangle is reflected over x axis.
Solution-
While reflecting a point over x axis, (x, y) → (x, -y) rule is followed.
Only the sign of y-coordinate is changed, keeping x-coordinate intact.
In the first picture, though the image is reflected, but it is reflected over y axis.
In the second picture, the image is first reflected over y axis, then it is translated 1 unit down.
We rotating a point 90° clockwise, (x, y) → (y. -x) rule is followed.
In the third picture, the triangle is rotated 90° clockwise and then translated 1 unit to right.
But, in case of the fourth picture, the figure is reflected over x axis. Only the y coordinates sign are changed, all the x coordinates are same as before.
Question text
Which volume formula or formulas show(s) a joint variation?
I V=8^3
II V=πr^2h
III V=Bh
Select one:
a. III only
b. I only
c. II and III only
d. I, II, and III
The correct answer is: c. II and III only
To determine which volume formula(s) exhibit joint variation, we need to consider if the volume (V) varies directly with two or more variables. In joint variation, V is directly proportional to the product of two or more variables.
Let's analyze each formula:
I. V = 8^3 → This is not a joint variation as V is solely dependent on the constant 8.
II. V = πr^2h → This shows joint variation as V varies directly with both r and h.
III. V = Bh → This also exhibits joint variation since V varies directly with both B (base area) and h (height).
How can ΔABC be mapped to ΔXYZ?
First, translate .
Next, rotate ΔABC about B to align the sides and angles.
To map ΔABC to ΔXYZ, you need to translate the triangle and then rotate it about a point.
Explanation:In order to map ΔABC to ΔXYZ, you can follow these steps:
First, translate ΔABC by moving it horizontally and vertically to a new position.Next, rotate ΔABC about point B to align the sides and angles with ΔXYZ.By performing these steps, you can map one triangle to another.
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Factor completely 36x2 − 49.
A (3x + 7)(12x − 7) B (3x − 7)(12x + 7) C (6x − 7)(6x − 7) D (6x + 7)(6x − 7)
A B C D ?
Answer:
The correct option is D.
Step-by-step explanation:
The given expression is
[tex]36x^2-49[/tex]
It can be written as
[tex](6x)^2-(7)^2[/tex]
Using the formula
[tex]a^2-b^2=(a-b)(a+b)[/tex]
[tex](6x)^2-(7)^2=(6x+7)(6x-7)[/tex]
Therefore the complete factor form of given expression is (6x+7)(6x-7). The correct option is D.
What is a quartic function with only the two real zeros given?
x = -4 and x = -1
A.
y = x4 + 5x3 + 5x2 + 5x + 4
B.
y = x4 - 5x3 - 5x2 - 5x - 4
C.
y = -x4 + 5x3 + 5x2 + 5x + 4
D.
y = x4 + 5x3 + 5x2 + 5x - 5
A soccer team has won 1/2 of the games they played. they won 12 games. how many games did they play? Show your working/calculations
they won 1/2 of their games and won 12 games
1/2 = 50% , multiply by 2 to make 100%
so 12 x 2 = 24 games were played
To calculate the number of games played by the soccer team, multiply the number of games they won (12) by 2, because winning 12 games represents winning [tex]\frac{1}{2}[/tex] of all games played. The soccer team thus played a total of 24 games.
To find how many games the soccer team played in total, we can set up a proportion using the information that they won [tex]\frac{1}{2}[/tex] of their games. This means for every game they won, they played two (since [tex]\frac{1}{2}[/tex] represents one out of two games). If the team won 12 games, and that represents [tex]\frac{1}{2}[/tex] of the total games, we can use a simple equation to solve for the total number of games (T).
The proportion is as follows: [tex]\frac{1}{2}[/tex] = [tex]\frac{12}{T}[/tex], where 12 is the number of games won, and T is the total number of games played.
To solve for T, we multiply both sides of the equation by T to get rid of the fraction: [tex]\frac{T}{2}[/tex] = 12. To find T, we then multiply both sides of the equation by 2 to isolate T on one side of the equation: T = 12 * 2.
Therefore, the team played a total of T = 24 games.
Which sequence is geometric and has 1/4 as its fifth term and 1/2 as the common ratio?
A rectangular vegetable garden will have a width that is 3 feet less than the length, and an area of 54 square feet. if x represents the length, then the length can be found by solving the equation: x(x−3)=54x(x-3)=54 what is the length, x, of the garden? the length is _____ feet.
Answer
Length of rectangular garden = x feet
As, Width is 3 feet less than Length.
Width = (x-3 ) feet
Area of Rectangle = Length × Breadth
Area = 54 square feet
→54 = x × (x-3)
→ x²-3 x-54=0
Splitting the Middle term
→x² - 9 x + 6 x- 54=0
→x × (x-9)+6 × (x-9)=0
→ (x+6)(x-9)=0
→x+6=0 ∧ x-9=0
x≠-6, as length can't be negative.
So, x=9
Length of Rectangular garden = 9 feet