Solve for x: 2 + 3x = 10x - 5

Answer:

(- 1, 4 ) makes both equations true

Step-by-step explanation:

substitute the x- coordinate of each point into the right side of both equations and if value obtained is equal to the left side, that is the y- coordinate of the point, then it makes the equation true.

(- 1, 4 )

y = x + 5 = - 1 + 5 = 4 ← true

y = 2x + 6 = 2(- 1) + 6 = - 2 + 6 = 4 ← true

(2, 3 )

y = x + 5 = 2 + 5 = 7 ≠ 3 ← false

y = 2x + 6 = 2(2) + 6 = 4 + 6 = 10 ≠ 3 ← false

(2, - 3 )

we know from the previous part for x = 2 that y = 7 , 10 ≠ - 3

similarly

(2, - 2 )

we know when x = 2 that y = 2 and y = 10 ≠ - 2

then the ordered pair that makes both equations true is (- 1, 4 )

The expected value of the random variable is 5.37, the variance of the random variable is 0.8531 and the standard deviation of the random variable is 0.9236.

Given that,

The number of days it takes for packages to arrive from an online shop, together with the probability that it will happen, are provided in the table below.

The table is

Number of days           Probability

A-3                                    0.01

B-4                                    0.14

C-5                                    0.46

D-6                                    0.25

E-7                                     0.14

We have to find the expected value of the random variable, the variance of the random variable and the standard deviation of the random variable.

We know that,

The random variable's predicted value is now shown.

Expected value = summation (x ×P(x))

= 3×0.01+4×0.14+5×0.46+6×0.25+7×0.14

= 5.37

Now the variance of the random variable

Variance =summation ((x - mean)² ×P(x))

= (3-5.37)² × 0.01 + (4-5.37)² × 0.14 + (5-5.37)² × 0.46 + (6-5.37)² × 0.25 + (7-5.37)² × 0.14

= 0.8531

The random variable's standard deviation is now available.

σ  = √(0.8531)

= 0.9236

Therefore, the expected value of the random variable is 5.37, the variance of the random variable is 0.8531 and the standard deviation of the random variable is 0.9236.

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Answer:

47/53 or 0.88 or 88%

Step-by-step explanation:

Answer:

– Practicing is key. ...

2 – The formula sheet is your best friend. ...

3 – Understand what your calculator can do. ...

4 – Understanding the derivations of certain formulas. ...

5 – Understand your mistakes and close up any knowledge gaps. ...

6 – Practice on example questions in your textbook.

Answer:

so I'm guessing you're solving for x

because angle 2 is the vertical angle to angle 3 so this means that they are congruent

4x-26=3x+4

4x-3x=4+26

x=30

Using the provided table as a foundation, the sample median is a fair approximation. The reason is that the sample median is not biassed towards any one value because 50% of the sample medians are 17 or higher and 50% are lower.

A procedure or function called an estimator is used to estimate a specific quantity using data from observations.

The estimator generates an estimate as a result of using the observed data as input. If the expected value of an estimator matches the actual value of the parameter being estimated, the estimator is said to be impartial.

To put it another way, an estimator is impartial if it generates parameter estimates that are generally accurate. The estimator is considered to be biassed if the expected value of the estimator differs from the parameter's true value.

Thus, the anticipated discrepancy between an estimator and the true parameter is known as bias.

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We have that because the central angle is 90°, the sector represents 1/4 of a circle with a radius of 10 yd.

So, length of the safety rail is given by:

Where:

r = 10 yd

pi = 3.14

Substitute, we have:

The Answer is 15.7 yd

Next, area of the deck is given by:

Substitute the values:

The answer is 78.5 yd^2

Answer:

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Answer:

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Answer:

y = 12x + 8

Step-by-step explanation:

56 - 8 = 48

48/12 is possible therefore its 1

Answer:

A is correct.

Step-by-step explanation:

Reasoning: I can confirm the answer above is correct. I'm not gonna lie saying something like "cuz I am right" so yeah. <3

Answer:

8 feet

Step-by-step explanation:

there's 12 inches in 1 foot so 12 x 8 = 96

1/2 miles in each 1/8 hour is a rate of 4 miles per hour. Therefore, option D is the correct answer.

A) Given that, 1/2 mile in each 1/4 hour

Rate = 1/2 ÷ 1/4

= 2 miles per hour

B) Given that, 1/5 miles in each 1/10 hour

Rate = 1/5 ÷ 1/10

= 2 miles per hour

C) Given that, 1/2 miles in each 1/6 hour

Rate = 1/2 ÷ 1/6

= 3 miles per hour

D) 1/2 miles in each 1/8 hour

Rate = 1/2 ÷ 1/8

= 4 miles per hour

Therefore, option D is the correct answer.

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Answer:

f^-1 (x) =7 − 21x

Step-by-step explanation:

Hope this helps!

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The volume of the given cylinder is 400π cubic millimeter.

Given that, a cylinder has a radius of 5 mm and a height of 8 mm.

We know that, the volume of a cylinder is πr²h.

Here, volume = π×5²×8

= π×25×8

= 400π

Therefore, the volume of the given cylinder is 400π cubic millimeter.

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Answer:

4.8-46c+13x

Step-by-step explanation:

Answer:

Step-by-step explanation:

176 divided by 2 is 88 so 8 ft

When dealing with random walk data, Holt's method is preferred due to its ability to capture short-term fluctuations and changing trends without assuming a specific pattern.

A random walk is a time series where the future values are dependent on the previous values and exhibit a random or unpredictable behavior. In such cases, using methods like Moving Average, Holt-Winters, or Logistic Regression may not yield accurate results because they assume certain patterns or trends in the data.

Holt's method, also known as exponential smoothing, is particularly suitable for handling random walk data. It is a forecasting technique that takes into account both the level and the trend of the time series. This method assigns exponentially decreasing weights to past observations, giving more weight to recent data points. By incorporating a level and trend component, Holt's method can capture the short-term fluctuations and gradual changes in the data without assuming a specific pattern.

Unlike Moving Average or Holt-Winters, Holt's method does not rely on a fixed window of past observations, which can be limiting for random walk data. Instead, it adapts dynamically to the changing characteristics of the time series.

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Answer:

The answer would be C. An obtuse equilateral triangle :)

The line integral of xy dx + x^2 dy around the given rectangle is 0.

To evaluate the line integral ∮C (xy dx + x^2 dy) along the given rectangle C with vertices (0, 0), (5, 0), (5, 1), and (0, 1), we can break it down into four line integrals along each side of the rectangle and sum them up.

Along the bottom side:

Parametrize the line segment from (0, 0) to (5, 0) as r(t) = (t, 0), where t ranges from 0 to 5. The differential element along this line segment is dr = (dt, 0). Substituting these values into the line integral, we get:

∫[0,5] (t*0) dt = 0.

Along the right side:

Parametrize the line segment from (5, 0) to (5, 1) as r(t) = (5, t), where t ranges from 0 to 1. The differential element along this line segment is dr = (0, dt). Substituting these values into the line integral, we get:

∫[0,1] (5t0 + 25dt) = ∫[0,1] 25*dt = 25.

Along the top side:

Parametrize the line segment from (5, 1) to (0, 1) as r(t) = (5-t, 1), where t ranges from 0 to 5. The differential element along this line segment is dr = (-dt, 0). Substituting these values into the line integral, we get:

∫[0,5] ((5-t)*0 + (5-t)^2 * 0) dt = 0.

Along the left side:

Parametrize the line segment from (0, 1) to (0, 0) as r(t) = (0, 1-t), where t ranges from 0 to 1. The differential element along this line segment is dr = (0, -dt). Substituting these values into the line integral, we get:

∫[0,1] (0*(1-t) + 0) dt = 0.

Summing up all the line integrals, we have:

0 + 25 + 0 + 0 = 25.

Therefore, the line integral of xy dx + x^2 dy around the given rectangle is 25.

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The present worth (PW) of each project is calculated based on the given cash flows and the firm's minimum attractive rate of return (MARR) of 10% per year.

To calculate the PW of each project, we discount the cash flows at the MARR of 10% per year. The PW for each project is determined as follows:

Project 1: EOY 0: -\(10,000 + (5,125 / (1 + 0.10)^1) + (5,125 / (1 + 0.10)^2) + (5,125 / (1 + 0.10)^3) = $10,682.13\)

Project 2: EOY 0: -\(8,500 + (4,450 / (1 + 0.10)^1) + (4,450 / (1 + 0.10)^2) + (4,450 / (1 + 0.10)^3) = $9,202.79\)

Project 3: EOY 0: \(11,000 + (5,400 / (1 + 0.10)^1) + (5,400 / (1 + 0.10)^2) + (5,400 / (1 + 0.10)^3) = $9,834.71\)

The project with the highest PW is recommended. In this case, Project 1 has the highest PW of $10,682.13, so it would be the recommended project.

The IRR for each project can be determined by finding the discount rate that makes the PW equal to zero. Using the cash flows provided, the IRR for each project can be calculated using a trial-and-error approach or financial software. Let's assume the IRRs are as follows:

Project 1: IRR ≈ 17.5%

Project 2: IRR ≈ 15.3%

Project 3: IRR ≈ 13.8%

The project with the highest PW may differ from the project with the largest IRR due to the timing and magnitude of cash flows. The PW takes into account the timing of cash flows and discounts them to the present value. It represents the total value created by the project over its lifetime. On the other hand, the IRR considers the rate of return that equates the present value of cash inflows to the initial investment. It represents the project's internal rate of return.

Therefore, a project with a higher PW indicates higher overall value, while a project with a larger IRR implies a higher rate of return. These measures can lead to different rankings depending on the cash flow patterns and the MARR.

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Answer:

Pour calculer le temps nécessaire pour que la valeur de l'investissement atteigne $7,700, il faut résoudre l'équation suivante :

2^(t/15) = 7,700/3,500

En résolvant cette équation, on obtient :

t/15 = log2(7,700/3,500)

t = 15 * log2(7,700/3,500)

Le temps nécessaire pour que la valeur de l'investissement atteigne $7,700 est donc égal à environ 8,9 ans (arrondi au dixième de l'année le plus proche).

a) To graph the marginal utility of x, we need to find the derivative of the utility function with respect to x. Given that y=1, the utility function becomes U=x^(1/5). Taking the derivative of U with respect to x, we get dU/dx = (1/5)x^(-4/5). This represents the marginal utility of x.

When we graph the marginal utility of x, we put the marginal utility on the vertical axis and x on the horizontal axis. Since x^(-4/5) is positive for all positive values of x, the graph of the marginal utility of x will have a positive slope that decreases as x increases. The shape of the graph will resemble a downward-sloping curve that approaches zero as x approaches infinity.

b) The MRS (Marginal Rate of Substitution) for this consumer is the rate at which the consumer is willing to trade one good for another while keeping the total utility constant. In this case, the MRS is the negative ratio of the marginal utility of x to the marginal utility of y. Mathematically, MRS = -(dU/dx)/(dU/dy).

Since y is a constant and dU/dy = 0, the MRS simplifies to MRS = -(dU/dx)/0 = undefined. This means that the consumer is not willing to trade any amount of y for x, as the marginal utility of y is zero. The consumer only derives utility from x and does not value y in terms of marginal utility.

The graph of the marginal utility of x will have a positive slope that decreases as x increases. The MRS for this consumer is undefined, indicating that the consumer does not value y in terms of marginal utility.

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The greatest acceleration when the unbalanced force is applied will be experienced by the least weighted box ( i.e., the mass of 2 kg)

Acceleration: it is defined as rate of change of velocity with respect to time.

Unbalanced Force:  it means that the force applied in one direction is greatest than the force applied in the opposite direction.

Given that, F = 8n.

let us assume that the boxes are of 2kg, 4 kg, 6 kg and 8 kg.

According to the 2nd law of motion: the external unbalanced force is directly proportional to rate of change of momentum or Force is equal to the product of mass and acceleration.

                         F = m × a

                 ⇒     a = F/ m

where,  F is Force, m is mass and a is acceleration.

Now, acceleration of the box of 2kg = 8÷2 = 4 m/s²

         acceleration of the box of 4kg = 8÷ 4 = 2 m/m²

         acceleration of the box of 6 kg = 8÷ 6 = 1.34 m/s²

         acceleration of the box of 8kg = 8÷ 8 = 1 m/s²

∴ the box with mass of 2kg experience the greatest acceleration.

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Answer:

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Answer:

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Step-by-step explanation:

The derivative of f(x) = e^(cos(ln(2x+1))) is: f′(x) = e^(cos(ln(2x + 1))) * (-sin(ln(2x + 1)) * 2/(2x + 1))

To find the derivative of the function f(x) = e^(cos(ln(2x+1))), we can use the chain rule.

Let's break down the function step by step:

Step 1: Let u = cos(ln(2x + 1))

Step 2: Let y = e^u

Now, we can find the derivative of each step:

Step 1:

Using the chain rule, the derivative of u with respect to x is given by:

du/dx = -sin(ln(2x + 1)) * d(ln(2x + 1))/dx

To find d(ln(2x + 1))/dx, we differentiate ln(2x + 1) with respect to x using the chain rule:

d(ln(2x + 1))/dx = 1/(2x + 1) * d(2x + 1)/dx

                  = 1/(2x + 1) * 2

                  = 2/(2x + 1)

Substituting this back into du/dx:

du/dx = -sin(ln(2x + 1)) * 2/(2x + 1)

Step 2:

Using the chain rule, the derivative of y with respect to u is given by:

dy/du = e^u

Now, we can find the derivative of f(x) using the chain rule:

df(x)/dx = dy/du * du/dx

        = e^u * (-sin(ln(2x + 1)) * 2/(2x + 1))

Since u = cos(ln(2x + 1)), we substitute it back into the equation:

df(x)/dx = e^(cos(ln(2x + 1))) * (-sin(ln(2x + 1)) * 2/(2x + 1))

Therefore, the derivative of f(x) = e^(cos(ln(2x+1))) is:

f′(x) = e^(cos(ln(2x + 1))) * (-sin(ln(2x + 1)) * 2/(2x + 1))

Simplifying further, we have:

f′(x) = -2sin(ln(2x + 1)) * e^(cos(ln(2x + 1))) / (2x + 1)

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Let the number of day is expressed as d and number of workers as w.

So relation between number of workers and number of days is,

Substitute 72 for d and 5 for w in the equation to obtain the value of k.

The equation is,

Substitute 18 for w to determne the number of day.

So 20 days are required to build a house with 18 workers.

Answer is 20 days.