Solve for the Social Security contribution if the percentage deduction is 8.5% for the income of $112, 000

Answer:

7,7, and 7

Step-by-step explanation:

If she vase is cubical we know that all 3 dimensions are the same. This means that x^3 = 343. So we know the answer is the cube root of 343, which is 7

The dimensions of the cubic vase are 7 by 7 by 7.

A three-dimensional object with six congruent square faces is called a cube. The cube's six square faces all have the same dimensions.

Given that the volume of the cubic vessel is 343 cubic inches.

The formula for the volume of a cube of side length a is:

V =a³

Substitute V= 343:

343 = a³

Or, a = ∛343

a = 7

Hence, the dimensions of the cubic vase are 7 by 7 by 7.

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The angular acceleration and angular speed of the pulley at t = 4.9 s areA) 48.7 rad/s² and B)85.89 rad/s, respectively.

Given data :Rotational inertia of pulley about its axle = I = 2.4×10⁻² kg-m²

Radius of pulley = r = 11 cm = 0.11 mForce acting on pulley = F = 0.6t + 0.3t² at t = 4.9 s

(a) Angular acceleration of the pulleyThe torque applied on the pulley,τ = F×r

Torque is given byτ = I×αwhere α is the angular accelerationI×α = F×rα = F×r / II = 2.4×10⁻² kg-m²r = 0.11 mF = 0.6t + 0.3t² = 0.6×4.9 + 0.3×(4.9)² = 10.617 Nτ = F×r = 10.617×0.11 = 1.16787 N-mα = τ / I = 1.16787 / 2.4×10⁻² = 48.7 rad/s²

Therefore, the angular acceleration of the pulley is 48.7 rad/s².

(b) Angular speed of the pulleyUsing the relation,ω² = ω₀² + 2αθwhere ω₀ = initial angular speed of pulley = 0θ = angular displacement of pulleyAt t = 4.9 s, the angular displacement of pulley is given byθ = ω₀t + ½ αt²

where ω₀ = initial angular speed of pulley = 0t = 4.9 sα = 48.7 rad/s²θ = 0 + ½×48.7×(4.9)² = 596.22 rad

Therefore,ω² = 0 + 2×48.7×596.22ω = 85.89 rad/s

Therefore, the angular speed of the pulley is 85.89 rad/s.Thus, the angular acceleration and angular speed of the pulley at t = 4.9 s are 48.7 rad/s² and 85.89 rad/s, respectively.

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Answer:

To solve this problem, let's break it down step by step.

1. Find the difference in height between the highest and lowest point of the handle:

The difference in height is 9 feet - 4 feet = 5 feet.

2. Calculate the circumference of the flywheel:

The circumference of a circle can be found using the formula C = πd, where C is the circumference and d is the diameter.

The diameter is given as 5 feet, so the circumference is C = π(5) = 5π feet.

3. Determine the vertical distance covered by the handle in one revolution of the flywheel:

Since the handle is attached to the edge of the flywheel, it moves in a circular path as the flywheel rotates.

The circumference of the flywheel represents the distance covered by the handle in one revolution.

Therefore, the vertical distance covered is also 5π feet.

4. Calculate the speed of the handle:

The wheel makes a complete turn every 2 seconds, which means it completes one revolution in 2 seconds.

Therefore, the speed of the handle is the vertical distance covered (5π feet) divided by the time taken (2 seconds):

Speed = (5π feet) / (2 seconds) = (5/2)π feet per second.

d. The extra variability is caused by variations in the df value.

T-statistics are used to test hypotheses about the mean of a population when the standard deviation of the population is unknown and the sample size is small.

The t-distribution is similar to the standard normal distribution (z-distribution) but it has flatter tails and is more spread out. This extra spread is caused by the fact that the t-distribution is based on the sample size, which is reflected in the degrees of freedom (df) value.

The larger the sample size, the closer the t-distribution is to the standard normal distribution, and the more similar the t- and z- statistics will be.

In contrast to this, as the sample size decrease, the t-distribution becomes more spread out and t- statistics are therefore more variable than z-scores.

This increased spread means that t-statistics have a higher chance of falling into the tails of the distribution, which leads to a greater likelihood of a type I error (rejecting a true null hypothesis) or a lower power (failing to reject a false null hypothesis).

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Answer:

As x increase, y decreases.

The rate of change for y as a function of x is not constant, therefore the function is non-linear.

For all values of x, the function y > 0.

The y-intercept of the graph is the function value y = 8.

When x = 1, the function value y = 5.

It is shown that the curl of F is zero (∇ x F = 0), indicating that F is a conservative vector field. However, the potential function f is not unique and can have different forms depending on the choice of arbitrary functions g(y, z), h(x, z), and k(x, y).

The vector field F is given by F(x, y, z) = (2xz² - ysin(xy))i + (3z - zsin(xy))j + (2x²z + 3y)k.

To show that ∇ x F = 0, we need to calculate the curl of F.

To find a function f such that F = ∇f, we need to find the potential function f whose gradient is equal to F.

(a) To show that ∇ x F = 0, we calculate the curl of F.

The curl of F is given by the cross product of the del operator (∇) and F.

Using the determinant form of the curl, we have:

∇ x F = ( ∂/∂x, ∂/∂y, ∂/∂z ) x (2xz² - ysin(xy), 3z - zsin(xy), 2x²z + 3y)

Expanding the determinant and simplifying, we get:

∇ x F = ( ∂(2x²z + 3y)/∂y - ∂(3z - zsin(xy))/∂z)i + ( ∂(2xz² - ysin(xy))/∂z - ∂(2x²z + 3y)/∂x)j + ( ∂(3z - zsin(xy))/∂x - ∂(2xz² - ysin(xy))/∂y)k

Evaluating the partial derivatives, we find that each term cancels out, resulting in ∇ x F = 0.

Therefore, the curl of F is zero.

(b) To find a function f such that F = ∇f, we need to find the potential function whose gradient is equal to F.

This means finding f such that ∇f = F.

By comparing the components, we can determine the potential function.

Equating each component, we have:

∂f/∂x = 2xz² - ysin(xy)

∂f/∂y = 3z - zsin(xy)

∂f/∂z = 2x²z + 3y

Integrating each component with respect to its corresponding variable, we find:

f = ∫(2xz² - ysin(xy)) dx + g(y, z)

f = ∫(3z - zsin(xy)) dy + h(x, z)

f = ∫(2x²z + 3y) dz + k(x, y)

where g(y, z), h(x, z), and k(x, y) are arbitrary functions of the remaining variables.

Thus, the potential function f is not unique and depends on the choice of these arbitrary functions.

In summary, we have shown that the curl of F is zero (∇ x F = 0), indicating that F is a conservative vector field.

However, the potential function f is not unique and can have different forms depending on the choice of arbitrary functions g(y, z), h(x, z), and k(x, y).

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The complete question is:

Consider the vector field

F(x, y, z) = (2xz²-ysin(xy))i + (3z-zsin(xy))j + (2x²z+3y)k

a. Show that ∇ x F = 0.

b. Find a function f such that F=∇f.

Answer: y=42

Step-by-step explanation:

Answer:

b = 10.06 in

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ (10.5)² = b² + (3)²

→ 110.25 = b² + 9

→ b² = 110.25 - 9

→ b = √101.25

→ [ b = 10.06 in ]

Hence, value of b is 10.06 in.

Answer:

No it's not!

Pythagorean theorem

15² + 9² = it's not 20

15² + 9² = 17 so

NO

The perimeter of the triangle and the square are both equal to 72 units.

To find the perimeter of the triangle, we need to add the length of the base to the sum of the lengths of the two equal sides and the length of the remaining side. Therefore, the perimeter of the triangle can be expressed as:

Perimeter of Triangle = 2x + 2(2x) + (x - 8)

Simplifying this expression, we get:

Perimeter of Triangle = 5x - 8

Therefore, the perimeter of the square can be expressed as:

Perimeter of Square = 4(x + 2)

Simplifying this expression, we get:

Perimeter of Square = 4x + 8

Now, since we know that the perimeters of the triangle and the square are equal, we can set the expressions for their perimeters equal to each other and solve for x:

5x - 8 = 4x + 8

Simplifying this equation, we get:

x = 16

Now that we have found the value of x, we can substitute it back into the expressions for the perimeters of the triangle and the square to find their values.

Perimeter of Triangle = 5x - 8 = 5(16) - 8 = 72

Perimeter of Square = 4x + 8 = 4(16) + 8 = 72

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Answer:

Extrapolation, because a key that is 12 keys from middle c is outside the data set.

Step-by-step explanation:

Given

See attachment for the data set

Required

Which option answers the question

From the attached dataset, we can see that 12 is not within the range of the data set.

When one makes predictions about a datum or set of data outside the range of the original dataset, then one is extrapolating.

Hence, (d) is correct

Answer:

d

Step-by-step explanation:

trust me

Answer:

\(\boxed{\textsf{ The correct option is Option B \textbf{Chemical Change}.}}\)

Step-by-step explanation:

Alkali metals such as Pottasium must be transported in special sealed containers because they have the ability to born or exclude upon contact with water due to their high reactivity. This is an example of Chemical Change .

Alkali metals like Pottasium (K) , Sodium (Na) , etc react vigorously with water . So they should be prevented in coming in contact to water . They are generally stored in kerosene . Here's an example of reaction of Alkali Metals with water .

★ Reaction of Sodium and Water :-

\(\boxed{\sf\underset{Sodium}{Na}+\underset{Water}{H_2O}\longrightarrow \underset{Sodium\ Hydroxide}{NaOH}+\underset{Hydrogen}{H_2} }\)

The equation that can be used to find f, the number of offices on each floor of this building, is,

18f = 396.

The correct option is b.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

There are 18 floors in the building.

Each floor has the same number of offices.

Altogether, there are 396 offices in the building.

So, the equation that can be used to find f, the number of offices on each floors of this building

18f = 396

f = 22

Therefore, the required equation is 18f = 396.

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A person weighing 173 pounds can burn 10.7 calories per minute.

The given equation is ŷ=2.2+0.05x.

To solve this question, we can use the equation given, ŷ=2.2+0.05x. We can insert the known weight value, 173 pounds, to calculate the anticipated calories burned per minute.

y = 2.2 + 0.05x

y = 2.2 + 0.05 × 173

y = 10.7

Therefore, a person weighing 173 pounds can burn 10.7 calories per minute.

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"Your question is incomplete, probably the complete question/missing part is:"

By observing a set of data values, Thomas used a calculator for the weight (in pounds) and predicted the number of calories burned per minute to get an equation for the least-squares line: ŷ=2.2+0.05x

Based on the information gathered by Thomas, select the statement that is true.

a) A person weighing 149 pounds can burn 9.8 calories per minute.

b) A person weighing 134 pounds can burn 8.9 calories per minute.

c) A person weighing 125 pounds can burn 8.3 calories per minute.

d) A person weighing 173 pounds can burn 10.7 calories per minute.

Answer:

A person weighing 134 pounds can burn 8.9 calories a minute.

Step-by-step explanation:

A major disadvantage of correlations is that they cannot make a cause-and-effect statement.

Correlations are statistical measures that describe the size and direction of a relationship between variables.

Correlations are expressed as numbers. Correlations establish that relationships exist but do not explain if the change in one variable is caused by the change in another variable's value.

The disadvantages of correlations include:

Thus, a major disadvantage of correlations is that they cannot make a cause-and-effect statement.

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The number of columns in the first matrix must equal the number of rows in the second matrix in order to multiply matrices with different dimensions.

    3. Determine the dot product of the corresponding row in matrix A          and the corresponding column in matrix B for each element in matrix C.

    4: The final response is matrix C, which is the union of the 2x3 matrix A and the 3x4 matrix B.

     Therefore, the result is a 2x4 matrix, which is produced by taking the dot product of the rows and columns of matrix A and matrix B.

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Answer:

\(\sf -3xy\left(2x^2-3xy+4y^2\right)\)

Step-by-step explanation:

\(\sf -6x^3y+9x^2y^2-12xy^3\)

To factor the GCF of 6x³y + 9x²y2 - 12xy³ let's apply the exponent rule:-

\(\boxed{\sf a^{b+c}=a^ba^c}\)

\(\boxed{\sf x^3y=xx^2y,\:x^2y^2=xxyy,\:xy^3=xyy^2}\)

\(\sf -6xx^2y+9xxyy-12xyy^2\)

Rewrite,

\(\sf 2\cdot \:3xx^2y+3\cdot \:3xxyy+4\cdot \:3xyy^2\)

Now, factor out the common term \(\sf -3xy\):-

__________________________

Answer:

It's C. I'm sure

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Market Size: Qualitative data, Nominal scale. Promotion: Qualitative data, Nominal scale. Week: Qualitative data, Ordinal scale.

a) The categorical qualitative variables from the ones listed above are as follows  :Market Size.

This variable represents the size of the customer base (small, medium, or large market).Promotion: Type represents which promotion the store ran (Promotion 1, 2, or 3. They ran three different promotions for a new product to see which one is more effective.).

b) The numerical (quantitative) variables from the ones listed above are as follows: Sales: (In Thousands) represents the number sales (in $1000) made in the specified week of December (Week).Age: Store represents the age of the store in years. Week: Number represents the week in which the promotion ran (Week 1, 2, 3, 4 - captured sales of new product over four weeks) c) Level of measurement for each variable is given as follows :Sales: Quantitative data, Ratio scale.Age: Quantitative data, Ratio scale.

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-3----------------___________________

Answer:

y = -3

Step-by-step explanation:

5(y + 2/5) = -13

5y + 2 = - 13

5y = -15

y = - 3

check:

5 (-3 + 2/5) = -13 ?

5 (-2.6) = -13 ?

-13 = - 13

Answer:

96730322328

Step-by-step explanation:

I hope this helps

Answer:

addition

Step-by-step explanation:

18 ( d - 9 ) = 198

      3

divide both side by 18

d - 9 = 198  

3          18

d - 9 = 11

3

multiply both sides by 3

d - 27 = 33

add 27 to both sides

d = 33 + 27

lastly, add them together

d = 60

therefore, the last step is addition

Answer:

25.5

Step-by-step explanation:

Answer is a 21

This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

What is the standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a wider range.

Standard deviation determines how far numbers deviate from the mean. The Standard deviation of the two sets will be the same if the numbers from the respective means are placed in the same order.

This is what 10, 15, and 20 will be on a number line

10_ _ _ _15 _ _ _ _20

(15 is the mean and 10 and 20 are 5 steps away from the mean)

i) Z - X = 10

This is what Z and X will be on the number line

X _ _ _ _ _ Z

ii) Z - Y = 5

This is what Z and Y will on the number line.

Y_ _ _ _ _ Z

Together, their relative placement on the number line:

X _ _ _ _ _  Y  _ _ _ _ _  Z

This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

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Based on the given confidence interval, there is evidence to support the claim that the true average echo duration of lightning flashes is 0.8 seconds.

To determine if the evidence supports the claim that the true average echo duration of lightning flashes is 0.8 seconds, we need to check if the value 0.8 falls within the confidence interval.

The 95% two-sided confidence interval for the true average echo duration is (0.743, 0.877). Since the value 0.8 falls within this interval, it means that the true average echo duration of lightning flashes of 0.8 seconds is within the range of values that is supported by the data.

Therefore, based on the given confidence interval, there is evidence to support the claim that the true average echo duration of lightning flashes is 0.8 seconds.

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so we know the equation to get the total forces is

\(\cfrac{Kg\cdot m}{s^2} ~~ \begin{cases} Kg=kilograms\\ m=meters\\ s=seconds \end{cases}\implies Kg\cdot \cfrac{m}{s^2}\implies Kg\cdot (acceleration)\)

the idea being, well, we have to do unit conversion, we know the object has a mass of 80 grams, hmmm that's not Kilograms, however since there are 1000 grams in a Kg, we can just convert that, and the acceleration of it is 20 m/s², so

\(\stackrel{ Kilograms }{\cfrac{80}{1000}}\cdot \stackrel{ accelaration }{20}\qquad \impliedby \textit{sum of the forces}\)

The coordinates of the image A(5,-9) for the translation (x,y) → (x - 2,y + 3) is; A'(3, -6)

In transformation, there are different operations such as dilation, reflection, translation, e.t.c

Now, in translation in transformation, we simply refer to the way we move an object from one point to another without changing the dimensions. However, in this question, we are told that the rule of transformation is;

(x, y) → (x - 2, y + 3)

If the coordinates of A(5, -9), then we can say that;

A(5, -9) → A'(5 - 2, -9 + 3)

= A'(3, -6)

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