The sum of two numbers is 38. The larger number is 12 more than the smaller number. What are the numbers?

you have n/3 = -12

to solve for n, multiply both sides by 3

n = -12 * 3 = -36

answer is A. -36

Answer:

Net income of Kaycie is $1,195

Step-by-step explanation:

We are given a monthly Income statement of September 2013.

First we count total income of Kaycie's

Income = Wages

Total Income = $2,700

Now we calculate total expenses

Kaycie's expenses are on food, rent clothing, transportation, medical and Insurance.

Expenses = Food+Rent+Clothing+Transportation+Medical+Insurance

Expenses=210+975+90+120+60+50

Total Expenses = $1,505

Net Income = Total Income - Total Expenses

Net Income = 2700 - 1505

Net Income = $1,195

Thus, Net income of Kaycie is $1,195.

Answer:

In so many words its "1,195"

Step-by-step explanation:

Final answer:

The correct O scale model train track spacing should be 1.17 inches. However, the actual O gauge spacing is 1.25 inches. The relative difference in the rail spacing is approximately 6.8%.

Explanation:

To solve for the correct O scale model train track spacing:

Convert the real train track gauge to inches: 4 feet x 12 inches/foot + 8 inches = 56 inches.

Divide the real gauge by the scale factor of 48 to find the model gauge: 56 inches / 48 = 1.1667 inches.

Round the result to the nearest hundredth of an inch: 1.17 inches.

Now to calculate the relative difference between O scale and the actual O gauge:

Determine the actual O gauge spacing: 1.25 inches.

Calculate the difference in spacing: 1.25 inches - 1.17 inches = 0.08 inches.

Find the relative difference by dividing the spacing difference by the O scale spacing and then multiply by 100 to get the percentage: (0.08 inches / 1.17 inches) x 100 = 6.8%.

Round the result to the nearest tenth of a percent: 6.8%.

Final answer:

To solve the equation 3/4x + 5/6 = 5x - 125/3 for x, you can start by getting rid of the fractions. Multiply every term in the equation by the least common multiple (LCM) of the denominators, which in this case is 12. Combine like terms and solve for x.

Explanation:

To solve the equation 3/4x + 5/6 = 5x - 125/3 for x, you can start by getting rid of the fractions. To do this, multiply every term in the equation by the least common multiple (LCM) of the denominators, which in this case is 12. This gives you:

9x + 10 = 60x - 500

Next, combine like terms by subtracting 9x from both sides of the equation:

10 = 51x - 500

Then, add 500 to both sides of the equation:

510 = 51x

Finally, divide both sides of the equation by 51 to solve for x:

x = 10

Answer:  Joseph's residual is 1.86 (option d).

Step-by-step explanation:

Hi, to answer this question we have to replace the variable "x" for Joseph’s age (23.5 months) in the equation given:

y = 63.80 + 0.61x.

y = 63.80 + 0.61 (23.5)

y = 63.80 + 14.335 = 78.135

Now, we subtract the amount obtained to Joseph's height ( 80 centimeters).

Mathematically speaking:

80 - 78.135 = 1.865  

So, Joseph’s residual is 1.86 (option d).

A normal distribution with a mean of 0 and a standard deviation of 1 called The Standard normal distribution or z - distribution.

A normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.

Given that a normal distribution with a mean of 0 and a standard deviation of 1

In the given condition, the normal distribution is called Standard normal distribution or z - distribution or Gaussian distribution.

Hence, the normal distribution with a mean of 0 and a standard deviation of 1 called Standard normal distribution or z - distribution or Gaussian distribution.

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Earth's radius is approximately 6,378.96 km.

To find the radius of Earth, we can use the information given in the question. We know that Earth's radius is approximately 261.4% of Mercury's radius, which is given as 2,440 km.

Let's set up an equation to solve for Earth's radius. Let x represent Earth's radius:

x = 261.4% * 2,440 km

Converting 261.4% to decimal form, we get 2.614. Multiplying this by 2,440 km, we find that Earth's radius is approximately 6,378.96 km.

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The planet Mercury is larger than the Moon, because the radius of Mercury is greater than the Moon.

Here,

Given that;

The planet Mercury has a diameter of 4,878 km.

And, The Moon has a radius of 1736.5 km.

We have to find the larger planet.

What is the relation between radius and diameter?

The radius is half or the diameter of the object.

Now,

The planet Mercury has a diameter of 4,878 km.

Hence, The radius of Mercury = 4,878/2 = 2,439 km

And,  The radius of the Moon = 1736.5 km

Clearly, 2,439 > 1,736.5

So, The planet Mercury is larger than the Moon, because the radius of Mercury is greater than the Moon.

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Answer:

TFT

Step-by-step explanation:

Since the company’s profits drop by $1,500 per month for every increase of $450 per year in the worker’s average pay, the slope of the graph of the equation is -40.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]

Based on the information provided, we can logically deduce that the rise and run are as follows;

Rise = 12 × -1500 = 18,000 units (its negative because the profit drops)

Run = 450 units.

By substituting the given data into the formula for the slope of a line, we have the following:

Slope (m) = rise/run

Slope (m) = -18000/450

Slope (m) = -40.

Love them or hate them, they do be spitting straight facts

The Laplace transform of  f(t) is [tex]\( \frac{4}{s}e^{-4s} \)[/tex].

Sure, let's find the Laplace transform of the piecewise function [tex]\( f(t) = \begin{cases} 0, & 0 \leq t < 4 \\ t - 4, & t \geq 4 \end{cases} \).[/tex]

Define the function for all ( t ):

[tex]\[ f(t) = \begin{cases} 0, & 0 \leq t < 4 \\ t - 4, & t \geq 4 \end{cases} = (t - 4)u(t-4) \][/tex]

where  u(t) is the unit step function.

Use the definition of the Laplace transform:

[tex]\[ \mathcal{L}\{f(t)\} = \int_0^\infty f(t)e^{-st} dt \][/tex]

Break the integral into two parts based on the piecewise definition of  f(t) :

[tex]\[ \mathcal{L}\{f(t)\} = \int_0^4 0 \cdot e^{-st} dt + \int_4^\infty (t - 4)e^{-st} dt \][/tex]

Solve each integral separately:

[tex]\[ \int_0^4 0 \cdot e^{-st} dt = 0 \][/tex]

[tex]\[ \int_4^\infty (t - 4)e^{-st} dt = \int_4^\infty te^{-st} dt - 4\int_4^\infty e^{-st} dt \][/tex]

Integrate:

[tex]\[ = \left[ -\frac{1}{s}te^{-st} \right]_4^\infty - \left[ -\frac{4}{s}e^{-st} \right]_4^\infty \][/tex]

[tex]\[ = \left(0 - \left(-\frac{4}{s}e^{-4s}\right)\right) - \left(0 - \left(-\frac{4}{s}e^{-4s}\right)\right) \][/tex]

[tex]\[ = \frac{4}{s}e^{-4s} \][/tex]

Combine the results:

[tex]\[ \mathcal{L}\{f(t)\} = \frac{4}{s}e^{-4s} \][/tex]

So, the Laplace transform of  f(t) is [tex]\( \frac{4}{s}e^{-4s} \)[/tex].

The Laplace transform of the given piecewise function f(t) is found using the Heaviside step function and shifting theorem, yielding[tex]\[ \mathcal{L}\{f(t)\} = \frac{6}{s^4} \][/tex]

To find the Laplace transform of the function f(t), we'll break it down into two parts: one for  t < 4  and another for [tex]\( t \geq 4 \).[/tex]

For  t < 4 ,  f(t) = 0 , so its Laplace transform is simply 0.

For [tex]\( t \geq 4 \), \( f(t) = (t - 4)^3 \)[/tex]. We'll use the property of the Laplace transform that states [tex]\( \mathcal{L}\{t^n\} = \frac{n!}{s^{n+1}} \). So, for \( f(t) = (t - 4)^3 \)[/tex], we get:

[tex]\[ \mathcal{L}\{(t - 4)^3\} = \frac{3!}{s^{3+1}} \\\[ = \frac{6}{s^4} \][/tex]

Now, we can combine both parts:

[tex]\[ \mathcal{L}\{f(t)\} = 0 \quad \text{for } t < 4 \\\[ \mathcal{L}\{f(t)\} = \frac{6}{s^4} \quad \text{for } t \geq 4 \\\text{Therefore, the Laplace transform of}\; \( f(t) \) is:\[ \mathcal{L}\{f(t)\} = \frac{6}{s^4} \][/tex]

3x + 50 = 6x -10

add 10 to each side

3x +60 = 6x

subtract 3x from each side

60 = 3x

x = 60/3 = 20

x = 20