In 2003 the social security tax rate was 6. 2% and the maximum taxable income was $87,000. 0. If Linda earned $54,122, how much did she contribute to social security?

Answer:

first one is D and the second one is B

Step-by-step explanation:

Have a great day! :)

Answer:

3. 73 4. -18

Step-by-step explanation:

3.

45 - (-28)

45 + 28

73

4.

-55 - (-37)

-55 + 37

- 18

Following this algorithm will generate random variables X1, X2, and X3 with the given multivariate distribution and covariance matrix.

1. Define the mean vector and covariance matrix:
  - Mean vector (µ): [E[X1]=1, E[X2]=2, E[X3]=3]
  - Covariance matrix (Σ): Provided in the question (not given in this case, so you would need to plug in the matrix values)

2. Perform a Cholesky decomposition of the covariance matrix:
  - Find a lower triangular matrix L such that Σ = LL^T, where L^T is the transpose of L.

3. Generate three independent standard normal random variables:
  - Let Z1, Z2, and Z3 be standard normal random variables (mean=0, variance=1).

4. Transform the standard normal random variables:
  - Compute X = µ + LZ, where X = [X1, X2, X3], µ is the mean vector, L is the lower triangular matrix from step 2, and Z = [Z1, Z2, Z3].

5. Extract the random variables X1, X2, and X3 from the transformed vector X.

Following this algorithm will generate random variables X1, X2, and X3 with the given multivariate distribution and covariance matrix.

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Answer: side AB is 5.7 units

Step-by-step explanation:

If you look at the congruence marks on the angles, you can see that side AB and side KL correspond. Since we know KL is 5.7, AB must be 5.7 as well. :)

When two solids are similar with a scale factor of p:q, their corresponding areas have a ratio of (p/q)^2 and their corresponding volumes have a ratio of (p/q)^3.

This means that if you were to take two similar solids and enlarge one by a factor of p and the other by a factor of q, the ratio of their areas would be (p/q)^2 and the ratio of their volumes would be (p/q)^3. This property is very useful in geometry and can be used to solve many problems involving similar solids. If two solids are similar with a scale factor of p:q, then their corresponding areas have a ratio of p²:q², and their corresponding volumes have a ratio of p³:q³.

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In a 4 x 4 x 4 design, there are three main effects, three 2-way interactions, and one 3-way interaction.

In a factorial design, the number of main effects and interactions can be determined by examining the number of factors and their levels. In a 4 x 4 x 4 design, there are three factors, each with four levels.

For each factor, there is one main effect. Since there are three factors in the design, there are three main effects.

To determine the number of possible interactions, we consider the possible combinations of factors. In a 4 x 4 x 4 design, we can have 2-way interactions, 3-way interactions, and a 4-way interaction.

2-way interactions: There are three pairs of factors (A-B, A-C, B-C), resulting in three 2-way interactions.

3-way interactions: There is only one combination of three factors (A-B-C), resulting in one 3-way interaction.

4-way interaction: Since there are no additional factors beyond the three factors, there is no 4-way interaction.

Therefore, in a 4 x 4 x 4 design, there are three main effects, three 2-way interactions, and one 3-way interaction.

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The probability of the sets are solved and

a) n(P U Q) = 85%

b) n(P ∩ Q) = 20%

c) n(only P) = 35%

d) n(only Q) = 30%

Given data ,

P and are the subsets of universal set U

And , n (p) = 55% n (Q) = 50% and n(PUO)complement = 15%

Now , we'll use the formula for the union and intersection of sets:

n(P U Q) = n(P) + n(Q) - n(P ∩ Q)

n(P ∩ Q) = n(P) + n(Q) - n(P U Q)

n(only P) = n(P) - n(P ∩ Q)

n(only Q) = n(Q) - n(P ∩ Q)

We're given that:

n(P) = 55%

n(Q) = 50%

n(P U Q)' = 15%

To find n(P U Q), we'll use the complement rule:

n(P U Q) = 100% - n(P U Q)'

n(P U Q) = 100% - 15%

n(P U Q) = 85%

Now we can substitute the values into the formulas above:

(i)

n(P U Q) = n(P) + n(Q) - n(P ∩ Q)

n(P ∩ Q) = n(P) + n(Q) - n(P U Q)

n(P ∩ Q) = 55% + 50% - 85%

n(P ∩ Q) = 20%

(ii)

n(P ∩ Q) = 20%

(iii) n(only P) = n(P) - n(P ∩ Q)

n(only P) = 55% - 20%

n(only P) = 35%

(iv)

n(only Q) = n(Q) - n(P ∩ Q)

n(only Q) = 50% - 20%

n(only Q) = 30%

Hence , the probability is solved

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The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.

Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.

The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.

In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

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Answer:

The digit you replace that box with is 6.

The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is,

⇒ x²+ (y - 6)² = 36

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Now, We know that;

The standard form for finding the equation of a circle is expressed as;

⇒(x - a)² + (y - b)² = r²

where; (a, b) is the center of the circle and r is the radius of the circle.

Here, we have;

⇒ Diameter = 12 units

⇒ Radius = 12/2 = 6 units

Since, The center lies on the y-axis,

Hence, the center will be at (0, 6).

Substituting into the formula, we will have;

⇒ (x - 0) + (y - 6)² = 6²

⇒ x² + (y - 6)² = 36

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Amy buys 12 envelopes for 26p each, so the total cost is 12 x 26 = 312p. She pays with a £5 note, which is equal to 5 x 100 = 500p. Therefore, she gets 500 - 312 = 188p in change. This is equal to £1.88.

Mathematics deals with the relationship between two numbers or quantities using the notions of ratio and proportion. Two numbers are compared in a ratio, which is often represented as a fraction. For example, the ratio of pounds to oranges in a basket could be 3:2, implying that there are three apples for every two oranges. Contrarily, proportion is the connection between two ratios. It is an equation, in other words, when two ratios are equal. The ratio of apples to oranges in a basket may be 3:2, whereas the ratio of apples to all the other fruits in the basket might be 9:11. In this case, the two ratios are proportionate since 3/2 = 9/11.

How to solve?

Amy buys 12 envelopes for 26p each, so the total cost is 12 x 26 = 312p. She pays with a £5 note, which is equal to 5 x 100 = 500p. Therefore, she gets 500 - 312 = 188p in change. This is equal to £1.88.

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Answer: $46.40

Step-by-step explanation: The cost after discount is $17.40. List price $29 per shirt. 40% off of $29 is $11.60. So for the first shirt he will pay $29 and the second he will pay $17.40. In total he pays $46.40 in the two shirts.

Answer:

64 degrees

Step-by-step explanation:

since it is in between the both of them and they both share the 62 degree angle

The number of ways to choosing coins with at least 15 quarters and 20 dimes is 4354.

In the given question, if the pile contains only 15 quarters and only 20 dimes but at least 30 of each other kind of coin, then we have to find the collections of 30 coins can be chosen.

Number of coins only of quarters = 15

Number of coins only of dimes = 20

The number of ways to choosing coins with at least 15 quarters and 20 dimes= Total- \((^{18}C_{3}+^{13}C_{3})\)

The number of ways to choosing coins with at least 15 quarters and 20 dimes= \(^{33}C_{3}-(^{18}C_{3}+^{13}C_{3})\)

Using \(^{n}C_{r}=\frac{n!}{r!(n-r)!}\)

The number of ways to choosing coins with at least 15 quarters and 20 dimes= \(\frac{33!}{3!(33-3)!}-(\frac{18!}{3!(18-3)!}+\frac{13!}{3!(13-3)!})\)

The number of ways to choosing coins with at least 15 quarters and 20 dimes= \(\frac{33!}{3!30!}-(\frac{18!}{3!15!}+\frac{13!}{3!10!})\)

Simplifying

The number of ways to choosing coins with at least 15 quarters and 20 dimes= \(\frac{33\times32\times31\times30!}{3\times2\times1\times30!}-(\frac{18\times17\times16\times15!}{3\times2\times1\times15!}+\frac{13\times12\times11\times10!}{3\times2\times1\times10!})\)

The number of ways to choosing coins with at least 15 quarters and 20 dimes= 11×16×31-(3×17×16+13×2×11)

The number of ways to choosing coins with at least 15 quarters and 20 dimes= 5456-(816+286)

The number of ways to choosing coins with at least 15 quarters and 20 dimes= 5456-1102

The number of ways to choosing coins with at least 15 quarters and 20 dimes= 4354

If the pile contains only 15 quarters and only 20 dimes but at least 30 of each other kind of coin, the number of ways to choosing coins with at least 15 quarters and 20 dimes is 4354.

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The mode is 18.5.

What is mode?

In statistics, there  are most repeated value among the given set of data. Those are called mode. Among the given set of data, mode is the value which has the maximum frequency. Sometimes, it may be possible to have more than one value which has the equal maximum frequency.

Formula for mode for grouped data is given by:

Mode = l + [(f₁-f₀)/(2f₁-f₀-f₂)]×h.-------------------(1)

Where, l = lower class limit of modal class, h = class size, f₁ = frequency of modal class, f₀ = frequency of class preceding to modal class, f₂ = frequency of class succeeding to modal class.

In the given problem l= 15.5

                                   f₀= 8

                                  f₁= 10

                                  f₂= 8

                                  h= 6

Putting all the values in equation (1) we obtain mode

                     mode= 15.5 +{(10-8)/(2×10-8-8)} ×6

                              = 15.5+(2/4)×6

                              = 15.5+ 3

                               = 18.5

Hence, the mode is 18.5.

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Given the provided coordinates of the points, The shape that is formed is a parallelogram because the slopes of the opposite sides are same.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

slope between (1,1) and (4,4),

m1 = 4-1/4-1 =3/3 =1

slope between (4,-2) and (7,1),

m2= 1+2/7-4 = 3/3 =1

m1=m2

similarly, slope between (1,1) and (4,-2),

m3= -2-1/4-1 = -3/3 =-1

slope between (7,1) and (4,4)

m4= 1-4/7-4 = -3/3 =-1

m3=m4

So, slopes of opposite sides are same that means they are parallel, The shape is parallelogram.

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So, by definition, a primary key must be unique and must have a value that is not null.

A primary key is a column or set of columns in a relational database table that uniquely identifies each row or record in that table.

By definition, a primary key must be unique, which means that no two rows in the table can have the same value in the primary key column(s).

This uniqueness constraint is enforced by the database management system (DBMS) when inserting, updating, or deleting data in the table.

In addition to being unique, a primary key must also have a value that is not null, which means that every row in the table must have a value in the primary key column(s).

This ensures that each row can be uniquely identified and accessed.

The primary key is used as a reference by other tables in the database, which may have relationships with the primary key column(s) in the table.

For example, a foreign key is a column in one table that references the primary key column(s) in another table.

This allows the DBMS to enforce referential integrity between the tables, which means that data in the database is consistent and accurate.

In summary, a primary key is a fundamental concept in relational database design, and it plays a critical role in ensuring data integrity and consistency.

By definition, a primary key must be unique and must have a value that is not null, which allows each row in the table to be uniquely identified and accessed.

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Step-by-step explanation:

TYhe vertex of this parabola would be the minimum point....this could be found by graphing..... or use the Quadratic formula to find the zeroes....

 the minumum is exactly in the middle of them

a = 1.2      b = - 216       c = 27 616

Plugging into the Quad Formula results in x = 90 +- 122.12 i

     exactly in the middle is x = 90 machines

Height and base of a triangle with given area 48 square meters is 12meters and 8 meters respectively.

As given ,

Area of the triangle = 48 square meters

Let 'y' meters represents the height of the triangle

Then 'y - 4' meters represents the base of a triangle.

Area of a triangle = ( 1/2 ) × base × height

Substitute the values we get

48 = ( 1 / 2) × ( y - 4 ) × y

⇒ 96 = y² - 4y

⇒ y² - 4y - 96 = 0

⇒ y² - 12y + 8y - 96 = 0

⇒ ( y - 12 ) ( y + 8 ) =0

⇒ y = 12 or y = -8

Height cannot be negative.

⇒y = 12meters

Base = 12 -4

        = 8 meters

Therefore, height and base of a triangle with given area is 12 meters and 8 meters respectively.

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Answer:

x = 5, y = 7

Step-by-step explanation:

x – y = -2 ——— 1

5x – 4y = -3 —– 2

x = -2 + y ——— 3

3 in 2 ≈ 5(-2 + y) – 4y = -3

-10 + 5y – 4y = -3

y = -3 + 10

y = 7

Putting y = 7 in 3, we have;

x = -2 + (7)

x = 5

Hence (x, y) = (5, 7)

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

What is derivative?

The derivative of a function in calculus measures the function's sensitivity to changes in its input variable. Specifically, at a particular point, it represents the function's rate of change with respect to its input variable at that moment.

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

This limit represents the instantaneous rate of change or slope of the function at the point x = a. The difference quotient is the change in the function value divided by the change in the input variable (or the distance between two points on the graph of the function).

The derivative is a fundamental concept in calculus, and it has many applications in various fields of science, engineering, and economics. It allows us to calculate important quantities such as velocity, acceleration, and marginal cost, and it is used to optimize functions and solve many real-world problems.

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The solution to the given system of linear equations is x = 4, y = 20

From the question, we are to determine solution to the given system of equations

The given system of equations is

x+y=6x=y+4

Thus, we can write that

x + y = 6x ----------- (1)

and

6x = y + 4 ------------(2)

Solve the two equations simultaneously

From equation (1)

x + y = 6x

y = 6x - x

y = 5x --------- (3)

Substitute into equation (2)

6x = y + 4

6x = 5x + 4

6x - 5x = 4

x = 4

Substitute the value of x into equation (3)

y = 5x

y = 5(4)

y = 20

Hence, the solution to the given system of linear equations is x = 4, y = 20

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The value that would complete the table to make the relationship between the two quantity proportional is 4.

When two quantities are proportional, their relationship is constant for all values and as one quantity rises, the other rises as well.

A proportional relationship exists between two quantities if they can be written in the general form y = kx, where k is the proportionality constant. In other words, the ratio between these amounts never changes. In other words, no matter which pair of the two numbers you divide, you always obtain the same number k.

The value that would complete the table to make the relationship between the two quantity proportional is 4.

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The function f(x, y) = x³ - 3y² + 3xy - 3y represents a surface in a three-dimensional space. Here  there are no local maxima or minima in the function f(x, y) = x³ - 3y² + 3xy - 3y.

In order to find the critical points, we need to take the partial derivatives of f(x, y) with respect to x and y, and set them equal to zero:

∂f/∂x = 3x² + 3y = 0

∂f/∂y = -6y + 3x - 3 = 0

Solving these equations simultaneously, we find the critical point at (x, y) = (1, 1/2).

To determine the nature of this critical point, we need to examine the second-order partial derivatives of f(x, y). Calculating the second partial derivatives, we find:

∂²f/∂x² = 6x

∂²f/∂y² = -6

∂²f/∂x∂y = 3

Evaluating these second partial derivatives at the critical point (1, 1/2), we have:

∂²f/∂x² = 6

∂²f/∂y² = -6

∂²f/∂x∂y = 3

Since the determinant of the Hessian matrix (∂²f/∂x²)(∂²f/∂y²) - (∂²f/∂x∂y)² = (6)(-6) - (3)² = -36 - 9 = -45 is negative, and ∂²f/∂x² = 6 > 0, we conclude that the critical point (1, 1/2) is a saddle point. Therefore, there are no local maxima or minima in the function f(x, y) = x³ - 3y² + 3xy - 3y.

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The decimal representation of the amount Maggie spent is the ratio of the amount spent and the total amount in her wallet expressed as a decimal.

The decimal representation of the amount spent can be calculated thus ;

Therefore, the decimal representation of the amount spent is 0.6

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The question is : The maximum load that a truck can carry is 3500 kg. If it is known that each trip carries at least 2800 kg, how many packages weighing 70 kg can it transport on each trip?

The truck can transport 10 packages weighing 70 kg each on each trip.

To determine the number of packages of 70 kg that can be transported on each trip, we need to find the difference between the maximum load capacity of the truck and the minimum weight already being transported.

Maximum load capacity: 3500 kg

Minimum weight already being transported: 2800 kg

Therefore, the remaining weight capacity for additional packages is:

3500 kg - 2800 kg = 700 kg

Since each package weighs 70 kg, we can divide the remaining weight capacity by the weight of each package to determine the number of packages that can be transported:

700 kg ÷ 70 kg = 10 packages

Therefore, the truck can transport 10 packages weighing 70 kg each on each trip.

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Answer:

10 feet

Step-by-step explanation:

a²+b²+=c²

a=8ft

b=6ft

Answer:

2.5 x 60

Step-by-step explanation:

im pretty sure thats how you get your answer

Answer:

Step-by-step explanation:

\( speed=\frac{2.5 \:miles}{\frac{1}{3}hour}=2.5\times 3 = 7.5 miles/hour \)