11. A work day is 8 hours. You earn $48 for one work day What is the hourly pay rate? b. At that rate how much would you earn in 5 hours? Ker notes​

Answer:

1. mean: 5

2. median: 6

3. mode: 80% or 8

4. range: 7

Step-by-step explanation:

Answer:

mean = 5

median = 6

mode = 80%(aka 8)

range = 7

Step-by-step explanation:

Answer:

-s-6>-7

Step-by-step explanation:

Just ask!

Hope this helps. :)

Answer:

-s-6>-7 (top right)

Step-by-step explanation:

s = -18         > means what is on the left is bigger than what is on the right

top right one = - s - 6 ­> - 7

top right one = - ( - 18) - 6 > -7

top right one = 18 - 6 > -7

top right one = 12 is bigger than -7

Answer:

Is this slope or do you want me to solve x and y

Step-by-step explanation:

K = k1 + k2In matrix form, the stiffness matrix is given by: k = [(EIL^-3)(7/3L  2/3L; 2/3L  4/3L)]The above equation represents the stiffness matrix for the beam element with an additional node in the center (higher-order element).

Galerkin’s method is used to derive the stiffness matrix for a given beam element. Here's how to derive the stiffness matrix using Galerkin's method: Derive stiffness matrix using Galerkin's method:

Given, a beam element with an additional node in the center is a higher-order element. It can be represented by the following figure:

The beam element can be divided into two equal sub-elements of lengths L/2 each. Using Galerkin's method, the stiffness matrix of the beam element can be derived. The Galerkin's method uses the minimization principle of the potential energy.

The principle states that the energy of the system is minimum when the potential energy of the system is minimum. Galerkin’s method uses the shape functions of the element to interpolate the unknown displacements. In the Galerkin method, the approximate displacement field is taken as the same as the interpolation functions multiplied by the nodal parameters. Let us assume that there are m degrees of freedom for a beam element.

In matrix form, we have: {u} = [N]{d}Where,{u} is the vector of nodal displacements[N] is the matrix of shape functions[d] is the vector of nodal parameters Thus, the potential energy can be written asV = 1/2∫[B]^T[D][B]dA

where,[B] is the strain-displacement matrix[D] is the matrix of elastic moduli The strain-displacement matrix is given by[B] = [N]'[E]

Where [N]' is the derivative of the shape functions with respect to the axial coordinate The matrix of elastic moduli is given by[D] = (EIL^-3)[l  -l; -l  l]

where E is the Young’s modulus of the beam material, I is the area moment of inertia of the beam, and L is the length of the beam. Using Galerkin's method, the stiffness matrix of the beam element is derived as follows:

Step 1: Determine the shape functions and nodal parameters For this higher-order beam element, there are three degrees of freedom. Thus, there are three shape functions and three nodal parameters. The shape functions are given by: N1 = 1 - 3(ξ - 1/2)^2 N2

= 4ξ(1 - ξ) N3 = ξ^2 - ξ

where ξ is the dimensionless axial coordinate. The nodal parameters are given by: d1, d2, d3

Step 2: Determine the strain-displacement matrix The strain-displacement matrix is given by[B] = [N]'[E]The derivative of the shape functions with respect to the axial coordinate is given by:[N]' = [-6ξ + 3, 4 - 8ξ, 2ξ - 1]Therefore, the strain-displacement matrix is given by[B] = [N]'[E] = [-6ξ + 3, 4 - 8ξ, 2ξ - 1][E]

Step 3: Determine the matrix of elastic moduli The matrix of elastic moduli is given by[D] = (EIL^-3)[l  -l; -l  l]

where E is the Young’s modulus of the beam material, I is the area moment of inertia of the beam, and L is the length of the beam.

Step 4: Determine the stiffness matrix The stiffness matrix can be obtained by integrating the product of the strain-displacement matrix and the matrix of elastic moduli over the element. Therefore, the stiffness matrix is given by: k = ∫[B]^T[D][B]dA Knowing that the beam element can be divided into two equal sub-elements of lengths L/2 each, we can obtain the stiffness matrix for each sub-element and then combine them to obtain the stiffness matrix for the whole element.

The stiffness matrix for the first sub-element can be obtained by integrating the product of the strain-displacement matrix and the matrix of elastic moduli over the sub-element. Therefore, the stiffness matrix for the first sub-element is given by:k1 = ∫[B1]^T[D][B1]dA

where [B1] is the strain-displacement matrix for the first sub-element. The strain-displacement matrix for the first sub-element can be obtained by replacing ξ with ξ1 = 2ξ/L in the strain-displacement matrix derived above. Therefore,[B1] = [-3ξ1 + 3, 4 - 8ξ1, ξ1 - 1][E]The stiffness matrix for the second sub-element can be obtained in the same way as the first sub-element. Therefore, the stiffness matrix for the second sub-element is given by:k2 = ∫[B2]^T[D][B2]dA

where [B2] is the strain-displacement matrix for the second sub-element. The strain-displacement matrix for the second sub-element can be obtained by replacing ξ with ξ2 = 2ξ/L - 1 in the strain-displacement matrix derived above. Therefore,[B2] = [3ξ2 + 3, 4 + 8ξ2, ξ2 + 1][E]The stiffness matrix for the whole element is obtained by combining the stiffness matrices for the two sub-elements. Therefore, k = k1 + k2In matrix form, the stiffness matrix is given by: k = [(EIL^-3)(7/3L  2/3L; 2/3L  4/3L)]The above equation represents the stiffness matrix for the beam element with an additional node in the center (higher-order element).

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Answer:

The equation is: 20 + 4.5h = 11 + 5.75h

The total cost of the services will be equal at 7.83 or 8 hours.

Step-by-step explanation:

This equation is correct because it shows that these two scenarios equal the same amount of money when there is a certain amount of hours, or "h."

Here is how we solve the equation;

20 + 4.5h = 11 + 5.75h <-----Here is the original equation.

Service A                                                        Service B

1. 20 - 20 + 4.5h                         =               11 - 20 + 5.75h

2.4.5h - 5.75h =  -1.15h                             -9 + 5.75h/5.75 =

3. -1.15h/-1.15 = h                                              9/-1.15 = 7.83

                  h = 7.83 or 8 hours when rounded to the nearest hour

Hope this helps! :)

Answer:

0

Step-by-step explanation:

2(n - 1) + 4n = 2 ( 3n - 1 )

2n - 2 + 4n = 6n - 2

6n - 2 = 6n - 2

6n - 6n = -2 + 2

0 = 0

Answer:

894

Step-by-step explanation:

Just divide the number by 7

Answer:

y=7

Step-by-step explanation:

x=3

Answer:

C \(\sqrt{5}\)

Step-by-step explanation:

Use pythagorean theorem.

\(x^{2}\) +\(\sqrt{7} ^{2}\) = (2\(\sqrt{3}) ^{2}\)    

\(x^{2}\) + 7 = 12   Subtract 7 from both sides

\(x^{2}\) = 5           Take the square root of both sides to solve

x = \(\sqrt{5}\)

b1 = 4 1/4 in

b2= 3 3/4 in

h= 2 1/2 in

Area = 1/2h (b1+b2)

Replacing:

A = 1/2 *2 1/2 (4 1/4 + 3 3/4 )

A = 1/2 * 5/2 (7 4/4)

A = 5/4 (8 )

A = 40/4

A = 10 in2

Answer:

120

Step-by-step explanation:

36x94=2700+120+540+24

After doing the equitation the at rate of $15 per week.

How to do graph representation?

Graph representation is a way of visualizing data as a graph or chart. It is used to easily identify relationships between data points and to illustrate trends in the data. Graphs can be used to present data in a variety of ways, such as bar graphs, line graphs, pie charts, scatter plots and more. Graphs are especially useful when trying to compare two or more sets of data and to highlight any patterns or trends that may exist. Additionally, graphs are often used to represent numerical data in a more visually appealing way. By using graphs, it is easier to identify relationships, trends and outliers in the data. Graphs also help to make data easier to interpret and understand.

Carson owes = $110

At rate of $15 per week.

The graph representation will follows:

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The center of mass of the wire in the shape of the helix with parametric equations x = 5 sin(t), y = 5 cos(t), z = 2t, 0 ≤ t ≤ 2, with constant density k, is located at the point (0, 0, 2/3).

To find the center of mass, we need to calculate the average of the x, y, and z coordinates weighted by the density. The density is constant, denoted by k in this case.

First, we find the mass of the wire. Since the density is constant, we can treat it as a common factor and calculate the mass as the integral of the helix curve length. Integrating the length of the helix from 0 to 2 gives us the mass.

Next, we find the moments about the x, y, and z axes by integrating the respective coordinates multiplied by the density. Dividing the moments by the mass gives us the center of mass coordinates.

Upon evaluating the integrals and simplifying, we find that the center of mass of the wire is located at the point (0, 0, 2/3).

In summary, the center of mass of the wire in the shape of the helix is located at the point (0, 0, 2/3). This is determined by calculating the average of the coordinates weighted by the constant density, which gives us the point where the center of mass is located.

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By definition a parallelogram:

* Its opposite sides are equal in length

* Its opposite sides are parallel.

Since the figures ABCD and ABEC satisfy those properties, we can conclude that they are parallelograms

Answer:

1.25

Step-by-step explanation:4 pounds equal to 1 dollar so that means that each pound equals to 0.25 cents. SO, now you multiply 0.25 x 5= 1.25

A polygon is called non-convex if there are "dents" or indentations in it, where the internal angle is greater than 180 degrees.

In other words, a non-convex polygon is a polygon whose line segments intersect, creating an interior angle greater than 180 degrees. This is in contrast to a convex polygon, where all of the interior angles are less than 180 degrees and none of the line segments intersect.

Non-convex polygons can have a variety of shapes and sizes, and can be composed of any number of sides. However, they are generally more difficult to work with mathematically than convex polygons, and often require more advanced techniques to analyze and understand their properties.

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Answer :

1. Add 1 to both sides of the equation :

3t–1 =8

3t–1+1 =8+1

2. Add the numbers :

3t= 9

3. Divide both sides of the equation by the same term :

3t =9

3t/3 = 9/3

4. Simplify

• Cancel terms that are in both the numerator and denominator

• Divide the numbers

t =3

#Hope it helps!!

This number has to be read with its whole part first (twenty-three) and then its decimal part (one hundreth), so the complete sentence to read this number is twenty-three and one hundredth.

Answer: D. Twenty-three and one hundredth

a. The expected search path length in a skip list of size n is at most 1/p * log1/p (n) + O(1).

b. The expression 1/p * log1/p (n) is minimized when p = 1/2.

For a, To show this, we use the following observations:

The expected number of nodes in the i-th level of a skip list of size n is

The expected number of levels in a skip list of size n is

The expected number of nodes in a skip list of size n is therefore

Combining these observations, we get that the expected search path length in a skip list of size n is at most:

1/p * (n * (log1/p (n) + O(1)) * p)

= log1/p (n) + O(1)

For b, The expression 1/p * log1/p (n) is minimized when p = 1/2.

To see this, we can take the derivative of the expression with respect to p and set it to zero:

d/dp (1/p * log1/p (n)) = -log1/p (n) / p² + log(1/p) / p²

= (log(1/p) - log1/p (n)) / p²

Setting this to zero and solving for p, we get:

log(1/p) - log1/p (n) = 0

log(1/p) = log1/p (n)

1/p = \(n^{(1/p)\)

p = log(n) / log(log(n))

However, this value of p is not in the range (0, 1), so we need to choose the value of p that is closest to the optimal value of log(n) / log(log(n)) within the range (0, 1). It turns out that this value is p = 1/2, which gives the minimum expected search path length of approximately 1.4427 * log(n).

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 The total debt of the government at the end of year three is $7.2 billion.

Starting with a total debt of $5.5 billion, the government's deficits of $600 million in year one and $1.5 billion in year two contribute to an increase in the debt. However, in year three, the government runs a surplus of $400 million, which helps reduce the debt.

Thus, the total debt at the end of year three is calculated by adding the initial debt and deficits, and subtracting the surplus. In this case, the total debt at the end of year three is $7.2 billion.

Assuming the government runs a deficit of $200 million in year three, the calculation changes. With the initial debt of $5.5 billion, the deficits of $600 million in year one and $1.5 billion in year two, and the additional deficit of $200 million in year three, the total debt at the end of year three would be $7.8 billion. This demonstrates how the deficit amounts impact the overall debt accumulation.

If a government runs a budget deficit of $5 billion each year for ten years, resulting in a total deficit of $50 billion, followed by a surplus of $2 billion per year for five years, reducing the debt by $10 billion, and then maintaining a balanced budget for another ten years, the government debt would amount to $40 billion. The deficits over the initial ten years lead to a significant accumulation of debt, but the subsequent surpluses help mitigate the debt by reducing the deficit. Finally, the balanced budget in the later years ensures that there is no further increase in debt. Understanding the interplay between deficits, surpluses, and a balanced budget is crucial to grasp the long-term implications on government debt and fiscal stability.

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Randy can buy six gallons of gas for $18. He would pay $24 for 8 gallons of gas.

We can see that he pays three dollars per gallon by dividing the per gallon. 18 dollars/6 gallons equals 3 dollars, and 21 dollars/7 gallons equals 3 dollars. So, if he pays the same $3 per gallon rate, he will pay $24.

Fuel costs can be estimated using this calculator based on trip distance, vehicle fuel efficiency, and gas prices in various units. Gas prices fluctuate, but for most drivers, it is always a significant expense.

If you use mpg (miles per gallon), the total gas consumption formula is as follows: as an example The total amount of fuel required is 500 / 20 = 25 gallons if the distance is 500 miles and the consumption rate is 20 miles per gallon


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Answer:

With enough centrifugal force and outward thrust the rocket can exceed the pull of the vacuum no matter how strong it is.

Step-by-step explanation:

The increase in the money supply that causes prices to rise and leads to inflation, loses purchasing power.

What is inflation?

Inflation refers to the persistent rise in the general prices of commodities in the economy over a period of time. If the prices of goods and services increase in an economy without an increase in income of people, it reduces the purchasing power of individuals.

This follows the law of demand which states that; the higher the price, the lower the quantity demanded; the lower the price, the higher the quantity demanded.

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Answer: 2.5.02

Step-by-step explanation:

There is about a 33.7% probability that a case of 48 cans will contain at least two cans with a defective ball.

To solve this problem, we can use the binomial distribution. Let's define "success" as getting a can with no defective ball and "failure" as getting a can with at least one defective ball.

The probability of success in one can is:

P(success) = 1 - P(failure) = 1 - 0.025 = 0.975

The probability of failure in one can is:

P(failure) = 0.025

Now, let's define X as the number of cans in a case of 48 that have at least one defective ball. We want to find the probability that X is greater than or equal to 2.

We can use the binomial distribution formula to calculate this probability:

P(X ≥ 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)

P(X = 0) = (0.975)^48 ≈ 0.223

P(X = 1) = 48C1 (0.975)^47 (0.025)^1 ≈ 0.44

where 48C1 is the number of ways to choose one can out of 48.

Therefore, the probability that a case of 48 cans will contain at least two cans with a defective ball is:

P(X ≥ 2) ≈ 1 - 0.223 - 0.44 ≈ 0.337

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The monthly mortgage payment will be approximately \(\$1,054.84\).

To find the monthly mortgage payment, we need to calculate the principal amount and the monthly interest rate.

Given:

- Home price: \(\$200,000\)

- Down payment: \(22\%\) of \(\$200,000\)

- Loan amount (principal): \(\$200,000 - (22\% of \$200,000)\)

- Mortgage term: 15 years

- Annual interest rate: \(2.75\%\)

Calculating the principal amount:

Down payment = \(22\% of \$200,000 = \$44,000\)

Principal = $200,000 - $44,000 = $156,000

Calculating the monthly interest rate:

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = \(2.75\% / 12 = 0.0022917\)

To find the monthly mortgage payment, we can use the formula for the monthly payment on an amortizing loan:

\(Monthly payment = (Principal * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Total number of months))\)

Total number of months = \(Mortgage term * 12 = 15 * 12 = 180\)

Calculating the monthly mortgage payment:

\(Monthly payment = (\$156,000 * 0.0022917) / (1 - (1 + 0.0022917)^(-180)) = \$1,054.84\)

Therefore, the monthly mortgage payment will be approximately \(\$1,054.84.\)

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To find the z-score for the amount spent yesterday by a customer which made a purchase of $32.25, we first need to calculate the standard deviation of the sampling distribution of the means.

We can use the formula:
Standard Deviation = standard deviation of population / square root of sample size
Since we don't know the sample size, we will assume that it is large enough (more than 30) and use the central limit theorem to estimate the standard deviation of the sampling distribution of the means.
The standard deviation of the sampling distribution of the means is:
Standard Deviation = 2.50 / sqrt(n)
Assuming n is large enough, we can estimate the standard deviation to be approximately:
Standard Deviation ≈ 2.50 / sqrt(30) ≈ 0.456
Now we can calculate the z-score using the formula:
z-score = (x - μ) / σ
Where:
x = $32.25 (amount spent by the customer)
μ = $28.50 (mean amount spent by a typical customer)
σ = 0.456 (estimated standard deviation of the sampling distribution of the means)
z-score = (32.25 - 28.50) / 0.456 ≈ 8.24
Therefore, the z-score for the amount spent yesterday by a customer which made a purchase of $32.25 is approximately 8.24. This suggests that the amount spent by this customer is quite unusual, as it is more than 8 standard deviations above the mean.

To calculate the z-score for a customer's purchase of $32.25 at a convenience store chain, where the mean amount spent by a typical customer is $28.50 and the standard deviation is $2.50, you can follow these steps:
1. Determine the mean (μ) and the standard deviation (σ). In this case, μ = $28.50 and σ = $2.50.
2. Identify the individual data point (x) for which you want to calculate the z-score. Here, x = $32.25.
3. Use the z-score formula: z = (x - μ) / σ.
4. Plug in the values: z = ($32.25 - $28.50) / $2.50 = $3.75 / $2.50 = 1.5.
So, the z-score for the amount spent yesterday by the customer who made a purchase of $32.25 is 1.5.

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