A kitchen sink faucet streams 0.5 gallon of water in 10 seconds. A bathroom sink faucet streams 0.75 gallon of water in 18 seconds. Which faucet will fill a


3-gallon container faster?

Answer:

100=x^2+(x-2)^2

Step-by-step explanation:

Step-by-step explanation:

100=x^2+(x-2)^2

You need to manipulate the equations to get the same coefficient for one of the variables and then add or subtract the equations to eliminate that variable.

When using the method of elimination to solve the system of equations, the goal is to eliminate one of the variables by adding or subtracting the equations. To do this, you want to choose a coefficient for one of the variables that is the same in both equations, but with opposite signs.

For example, if the system of equations is:

2x + 3y = 7
4x - 5y = -13

You could multiply the first equation by -2 to get:

-4x - 6y = -14

Then, when you add this equation to the second equation, the x variable is eliminated:

-4x - 6y + 4x - 5y = -14 - 13

Simplifying this equation gives you:

-11y = -27

To find the value of y, you would divide both sides by -11:

y = 27/11

To find the value of x, you would substitute this value of y into one of the original equations and solve for x.

As for the specific question of what is the result of adding the two equations together, it depends on the coefficients of the variables in the equations. You need to manipulate the equations to get the same coefficient for one of the variables and then add or subtract the equations to eliminate that variable.

It looks like you didn't provide the system of equations you need help with. Please provide the two equations, and I'll gladly help you with the method of elimination and the result of adding them together.

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Answer:

4 1/2

Step-by-step explanation:

2 1/3 pounds and 2 1/6 pounds

convert the 1/3 pounds into x/6 by multiplying both numerator and denominator by 2 which equals 2/6

Then add 2+2 which gives 4 and the 1/6 and 2/6 which is equal to 3/6 which simplifies into 1/2.

4 1/2

Answer:

5/24 is your answer

Step-by-step explanation:

Answer:

13x = 13

Step-by-step explanation: 2(5x-3)= 10x -6  3x + 10x = 13x-6=7

6+7=13=  13x =13

Answer:

 = 1

Step-by-step explanation:

3x + 2 (5 x - 3 ) = 7

3x + 10x - 6 = 7

your gonna combine 3x + 10x - 6 = 7

13x -6 = 7

(sorry if wrong)

Numerical values that appear in the mathematical relationships of a model and are considered known and remain constant over all trials of a simulation are parameters.

Numerical values that appear in the mathematical relationships of a model and are considered known and remain constant over all trials of a simulation are not referred to as events.

In the context of simulations, these constant numerical values are typically known as parameters.

Parameters are fixed values that define the characteristics of a system or model being simulated.

They represent the fixed inputs or conditions that remain constant throughout the simulation.

These values are determined based on prior knowledge, experimental data, or theoretical assumptions.

For example, in a simulation model of a manufacturing process, parameters may include the production rate, the machine capacity, the setup time, or the defect rate.

These values are known and constant throughout the simulation runs.

It is important to distinguish parameters from variables in simulations. While parameters remain constant, variables are the factors or quantities that can change during the simulation and are often the focus of analysis or study.

By incorporating known and constant parameter values into a simulation model, researchers can analyze the behavior and performance of the system under different conditions, explore various scenarios, and make predictions or decisions based on the simulation outcomes.

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The slope of the line that passes through the graph is 3

From the graph, the points are given as

(0, 0)  and (1, 3)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (0, 0)  and (1, 3)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 0)  and (1, 3)

Substitute the known values in the above equation

So, we have the following equation

Slope = (3 - 0)/(1 - 0)

Evaluate

Slope = 3

Hence, the slope of the line is 3

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Answer:

a = 11

Step-by-step explanation:

Given the equation 2/3a - 7 = 1/3

We are to find the value of a that satisfies the equation

2/3 a = 1/3 + 7

2/3 a = (1+21)/3

2/3 a = 22/3

2a = 22

a = 22/2

a = 11

Hence the value of a that satisfies the equation is 11

The factoring the equation (a + 1)² - 4b² we get (a+1+2b)(a+1-2b).

Given:  (a + 1)² - 4b²

Apply Perfect Square Formula, and we get

(a + b)² = a² + 2 a b + b²

(a + 1)² = a² + 2a1+1²

= a² + 2a1 + 1² - 4 b²

simplifying the equation, we get

a² + 2a1 + 1² = a² + 2a + 1

= a² + 2a + 1 - 4b²

Factor, a² + 2a + 1 = (a + 1)²

= (a + 1)² - 4 b²

Simplify 4 b² = (2 b)²

= (a + 1)² - (2b)²

Apply the Difference of Two Squares Formula, and we get

x² - y² = (x + y)(x - y)

(a + 1)² - (2b)² = ((a + 1) + 2b)((a + 1) - 2 b)

simplifying the equation, we get

= ((a + 1) + 2b)(a + 1) - 2 b)

= (a + 1 + 2b)(a + 1 - 2b)

Therefore, the correct answer is (a+1+2b)(a+1-2b).

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(a) The probability that a household views television between 4 and 10 hours a day is 0.0833.

(c) The probability that a household views television more than 3 hours a day is 0.6944.

The appendix table shows the probability that a household views television for a certain number of hours per day. To find the probability that a household views television between 4 and 10 hours a day, we can add the probabilities that the household views television for 4 hours and 5 hours, and 6 hours, and 7 hours, and 8 hours, and 9 hours, and 10 hours. The sum of these probabilities is 0.0833.

To find the probability that a household views television more than 3 hours a day, we can add the probabilities that the household views television for 4 hours, 5 hours, 6 hours, 7 hours, 8 hours, 9 hours, and 10 hours. The sum of these probabilities is 0.6944.

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Managers, goods, services, and technology are all needed in developing countries, and therefore, they provide new markets for companies that can supply these essentials.

Developing countries often have growing economies and increasing consumer demands. As these countries strive for development and improvement, they require effective management to drive their businesses and organizations. Managers play a crucial role in overseeing operations, implementing strategies, and maximizing efficiency.

Additionally, developing countries require goods and services to meet the needs of their populations. This includes basic necessities such as food, clothing, and shelter, as well as other essential products and services like healthcare, education, infrastructure development, and transportation. Companies that can provide these goods and services have an opportunity to enter new markets and cater to the demands of the growing population.

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Answer:

the answer is 5 because that is the difference which is what they are asking.

Step-by-step explanation:

12 -7 =5

. . . . . . .| . . . . .

-

. . . . . . .|

            | . . . . .

the potential at the center of the equilateral triangle is 3kq√3 / a.To find , we can use the formula for the electric potential due to a point charge:

V = kq / r

where k is the Coulomb constant, q is the charge, and r is the distance between the point charge and the center of the triangle.

Assuming the charges are all positive, the potential at the center due to each charge will be the same, so we can find the total potential by multiplying the potential due to one charge by three.

The distance from the center of the equilateral triangle to each charge is a/√3, since the height of the equilateral triangle is √3/2 times the side length.

Therefore, the potential at the center is:

V = 3(kq / (a/√3))

Simplifying:

V = 3kq√3 / a

Hence, the potential at the center of the equilateral triangle is 3kq√3 / a.

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The x-intercepts of a quadratic function are the points where the function graph intersects the x-axis. To find the x-intercepts of the given quadratic function, we need to determine the values of x when the y-value (or the function value) is equal to 0.

From the given information, we can see that the quadratic function passes through the points (-2, 0) and (1, 0), which indicates that the function intersects the x-axis at x = -2 and x = 1. Therefore, the quadratic function x-intercepts are (-2, 0) and (1, 0).

The correct answers are (d) (-2, 0) and (1, 0).

The Riemann sum is a method used to approximate the value of a definite integral by dividing the interval into subintervals and evaluating the function at specific points within each subinterval.

In this case, we are given the integral ∫30(4x^2 + 2x + 1)dx and we need to find the Riemann sum using right endpoints and n subintervals.

To calculate the Riemann sum, we first need to determine the width of each subinterval. The total interval is 30, and we will divide it into n subintervals, so the width of each subinterval is Δx = 30/n.

Next, we need to determine the right endpoint of each subinterval. Since we are using right endpoints, the right endpoint of the first subinterval will be x_1 = Δx, the right endpoint of the second subinterval will be x_2 = 2Δx, and so on. The right endpoint of the nth subinterval will be x_n = nΔx.

Now, we can calculate the Riemann sum by evaluating the function at each right endpoint and multiplying it by the width of the subinterval. Let's denote the function as f(x) = 4x^2 + 2x + 1.

The Riemann sum can be written as:

R = Σ[f(x_i)Δx], where i ranges from 1 to n.

Using the right endpoints, the Riemann sum can be expressed as:

R = Σ[f(x_i)Δx] = Σ[(4(x_i)^2 + 2x_i + 1)Δx], where i ranges from 1 to n.

Finally, we can calculate the Riemann sum by substituting the values of x_i and Δx into the above expression and summing up the terms.

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Answer:

x = 190 and x = 126

Step-by-step explanation:

In both diagrams the indicated angles are vertical and congruent, then

\(\frac{x}{2}\) = 95 ( multiply both sides by 2 )

x = 190

and

x + 21 = 147 ( subtract 21 from both sides )

x = 126

The value of the double integral over the region R in polar coordinates is 7.1360

To evaluate the integral in polar coordinates, we need to express the differential element of area dA in terms of polar coordinates. The differential element of area in rectangular coordinates is dA = dx dy, which can be expressed in polar coordinates as:

dA = r dr dθ

Now we can express the original integral in polar coordinates as:

∬R (2x - y) dA = ∫ ∫₀³ (2r cos(θ) - r sin(θ)) r dr dθ

We can simplify the integrand by factoring out the r term and using trigonometric identities:

(2r cos(θ) - r sin(θ)) = r(2cos(θ) - sin(θ))

Substituting this into the integral, we get:

∬R (2x - y) dA = ∫₀^(π/4) ∫₀³ r(2cos(θ) - sin(θ)) r dr dθ

Integrating with respect to r, we get:

∬R (2x - y) dA = ∫₀^(π/4) [(2/3)r^3 cos(θ) - (1/2)r^2 sin(θ)]|₀³ dθ

Simplifying this expression using the limits of integration, we get:

∬R (2x - y) dA = ∫₀^(π/4) [(18/3)cos(θ) - (9/2)sin(θ)] dθ

Integrating with respect to θ, we get:

∬R (2x - y) dA = [(18/3)sin(π/4) + (9/2)cos(π/4)] - [(18/3)sin(0) + (9/2)cos(0)]

Simplifying this expression, we get:

∬R (2x - y) dA = 27/2 - (9/2)√2 = 7.1360

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Answer:

The total budget for their student film is $600

Step-by-step explanation:

Here, we want to calculate the total budget of a group of students on a movie given the amount the spent on props.

Since we do not know this amount, we can call it x

Now, 45% of this x was the amount spent on props and it is equal to $270

Mathematically;

45/100 * x = 270

45x = 100 * 270

x = (100 * 270)/45

x = 600

Loan repayment: Each semiannual payment is $879.92.

Machine cost: The equivalent uniform annual cost is $6,541.34.

Loan Repayment:

1. Calculate the semiannual interest rate: Divide the annual interest rate (8%) by the number of compounding periods per year (2) to get the semiannual interest rate (4%).

2. Calculate the number of compounding periods: Since the loan is repaid in four equal semiannual payments, there are a total of eight compounding periods (4 years x 2).

3. Calculate the present value factor: Use the formula for the present value of an annuity to calculate the present value factor for eight periods at a semiannual interest rate of 4%.

4. Determine the payment amount: Divide the loan amount ($3000) by the present value factor from step 3 to find the equal semiannual payment.

Machine Cost:

1. Calculate the semiannual interest rate: Divide the annual interest rate (8%) by the number of compounding periods per year (2) to get the semiannual interest rate (4%).

2. Calculate the number of compounding periods: Since the useful life of the machine is 6 years and compounding occurs semiannually, there are a total of 12 compounding periods (6 years x 2).

3. Calculate the future value factor: Use the formula for the future value of a single sum to calculate the future value factor for 12 periods at a semiannual interest rate of 4%.

4. Determine the equivalent uniform annual cost: Subtract the future value of the machine ($9,000) from the initial cost of the machine ($30,000) and divide by the future value factor from step 3 to find the equivalent uniform annual cost.

By following these steps and performing the calculations, you will determine the semiannual payment for the loan and the equivalent uniform annual cost of the machine.

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Answer:

\(f( - 1) = - 2\)

Step-by-step explanation:

\(f(x) = - {x}^{2} + x \\ f( - 1) = - {( - 1)}^{2} + ( - 1) \\ = - (1) + ( - 1) \\ = - 1 - 1 \\ f( - 1)= - 2\)

I hope I helped you^_^

Answer:

.25

Step-by-step explanation:

it would be 1 1/2

i hope this helps!!

let me know!!!!

Answer:

[See Below]

Step-by-step explanation:

\(Hey~There!\)

_______________________

➜ First let's turn each number into a decimal:

➜ Now we order then from Least to Greatest:

_______________________

So your answer would be \(\bold~B\).

_______________________

\(Hope~this~helps~Mate!~\\-Your~Friendly~Answerer,~Shane\) ヅ

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be $605.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Here, Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop.

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be:

= $365 + (5% × $4800)

= $605

The amount is $605.

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Given:

The function is:

\(f(x)=\{(1,0),(2,3),(3,6)\}\)

The given function is:

\(f(x)=1-2x\)

The range of this function is \(\{-3,-5,-7\}\).

To find:

The range of first function.

The domain of second function.

Solution:

Domain is the set of input or x-values and range is the set of output or y-values.

We have,

\(f(x)=\{(1,0),(2,3),(3,6)\}\)

Here, the x-values are 1, 2, 3 and the y-values are 0, 3, 6.

Therefore, the range of the given function is \(\{0, 3, 6\}\). Hence, the correct option is C.

The given function is:

\(f(x)=1-2x\)            ...(i)

The range of this function is \(\{-3,-5,-7\}\).

Putting \(f(x)=-3\) in (i), we get

\(-3=1-2x\)

\(-3-1=-2x\)

\(\dfrac{-4}{-2}=x\)

\(2=x\)

Similarly,

Putting \(f(x)=-5\) in (i), we get

\(-5=1-2x\)

\(3=x\)

Putting \(f(x)=-7\) in (i), we get

\(-7=1-2x\)

\(4=x\)

The domain of this function is \(\{2,3,4\}\). Hence, the correct option is A.

Answer:

Step-by-step explanation:

√-80

Answer:

4i√5

Step-by-step explanation:

The shock in part (c) leads to a decrease in capital per worker and consumption per worker, potentially affecting the standard of living. In contrast, the shock in part (d) leads to an increase in output per effective worker, which can positively impact the standard of living.

(c) When the tax funds are assumed to be gone without any goods or services purchased or government employees paid, it implies that the tax revenue is completely removed from the economy. In this case, the impact on the steady state levels of capital per worker and consumption per worker would depend on the specific economic model and assumptions.

Generally, the removal of tax revenue would lead to a reduction in both capital per worker and consumption per worker. The exact magnitude of the impact would depend on various factors, such as the marginal propensity to consume and the saving behavior of individuals. In steady state, the reduction in capital per worker could lead to lower productivity and potentially lower output per worker, affecting the standard of living.

To sketch a diagram showing the impact of this shock, you would typically have the levels of capital per worker and consumption per worker on the y-axis and time or steady state on the x-axis. The diagram would show a downward shift in both the capital per worker and consumption per worker curves, indicating a decrease due to the removal of tax revenue.

(d) When the tax funds are used by the government to implement plans that increase the growth rate of labor-augmenting technological change to 3% per year, it implies that the tax revenue is directed towards productivity-enhancing investments or policies. In this case, the impact on the steady state levels of capital per effective worker, output per effective worker, and consumption per effective worker can be analyzed.

The increase in the growth rate of labor-augmenting technological change would lead to higher productivity and potentially higher output per effective worker in steady state. This increase in output per effective worker could also translate into higher consumption per effective worker, depending on the saving and consumption behavior.

To sketch a diagram showing the impact of this shock, you would typically have the levels of capital per effective worker, output per effective worker, and consumption per effective worker on the y-axis and time or steady state on the x-axis. The diagram would show an upward shift in the output per effective worker curve, indicating an increase due to the improved technological change.

Overall, the shock in part (c) leads to a decrease in capital per worker and consumption per worker, potentially affecting the standard of living. In contrast, the shock in part (d) leads to an increase in output per effective worker, which can positively impact the standard of living.

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Answer:

129.26

Step-by-step explanation:

i think it's this i dont know i honestly forgot decimals

Answer: 129.26

Step-by-step explanation: .2 would be the tenths place, .05 is the hundredths place, and .007 is the thousandths place. With that being known, we know that we need to go two places past the decimal to get the answer to the nearest hundredth. When we round if the next number (our case 7) is a five or larger we round the number up. This means that we round the 5 to a 6 to get and answer of 129.26