Suppose that gas costs Big Ray $2.00/gallon and that he pays an attendant $100/day. Let C(x)
represent the total daily cost as a function of the price of the gas. Find the formula for C(x)

(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

Learn more about line tangent: brainly.com/question/30162650

#SPJ11

Ben can plot the residuals, create a histogram and Q-Q plot, or use statistical tests such as the Shapiro-Wilk test.

To test for the normality of residuals in a multiple regression model, Ben can use several methods. Here are a few options:

Plot the residuals: Ben can create a scatter plot of the residuals against the predicted values. If the residuals are normally distributed, they should be evenly scattered around the zero line. If there is a pattern or if the residuals are skewed, this indicates non-normality.

Histogram and Q-Q plot: Ben can create a histogram of the residuals and compare it to a normal distribution. He can also create a Q-Q plot (quantile-quantile plot), which compares the quantiles of the residuals to the quantiles of a normal distribution. If the residuals are normally distributed, they should fall along the diagonal line in the Q-Q plot.

Statistical tests: Ben can use statistical tests to formally test for normality of residuals. One commonly used test is the Shapiro-Wilk test, which tests whether the residuals are drawn from a normal distribution. If the p-value is greater than 0.05, Ben can conclude that the residuals are normally distributed.

Learn more about Regression analysis

brainly.com/question/30011167

#SPJ11

The given system of equations is inconsistent and does not have a solution. After performing row operations on the augmented matrix, we obtained an inconsistent row with a non-zero constant term, indicating the impossibility of finding a solution.

To solve the system using matrices and row operations, we can represent the system in augmented matrix form:

\(\[ \left[ \begin{array}{rrr|r} -1 & 1 & 1 & -1 \\ -1 & 5 & -11 & -25 \\ 6 & -5 & -6 & -6 \end{array} \right] \]\)

We will perform row operations to transform the augmented matrix into row-echelon form. The goal is to create zeros below the diagonal entries in the first column. Using elementary row operations, we can achieve this:

1. Multiply Row 1 by -1 and add it to Row 2: This eliminates the x-term in Row 2.

2. Multiply Row 1 by -6 and add it to Row 3: This eliminates the x-term in Row 3.

After these operations, the augmented matrix becomes:

\(\[ \left[ \begin{array}{rrr|r} -1 & 1 & 1 & -1 \\ 0 & 4 & -12 & -24 \\ 0 & -11 & -12 & 0 \end{array} \right] \]\)

Next, we focus on the second column and perform row operations to create zeros below the diagonal entry:

3. Multiply Row 2 by (-11/4) and add it to Row 3: This eliminates the y-term in Row 3.

The augmented matrix now looks like this:

\(\[ \left[ \begin{array}{rrr|r} -1 & 1 & 1 & -1 \\ 0 & 4 & -12 & -24 \\ 0 & 0 & 0 & -11 \end{array} \right] \]\)

At this point, we can see that the third row corresponds to the equation 0x + 0y + 0z = -11, which is inconsistent since -11 is not equal to 0. Therefore, the system of equations is inconsistent, and there is no solution.

In summary, the given system of equations is inconsistent and does not have a solution.

To learn more about Augmented matrix, visit:

https://brainly.com/question/12994814

#SPJ11

Answer: 2 + x

Step-by-step explanation:

The mathematical procedure for decomposing a complex waveform into simpler waveforms is known as Fourier analysis. It allows for the identification of the individual frequency components that contribute to the overall pattern.

Fourier analysis, named after the French mathematician Jean-Baptiste Joseph Fourier, is a fundamental technique used in many fields, including signal processing, physics, and engineering. It is based on the concept that any complex waveform can be represented as a combination of simpler sinusoidal waveforms. These simpler waveforms are characterized by their frequency, amplitude, and phase.

The procedure involves decomposing a complex waveform into its constituent frequencies by applying the Fourier transform. The Fourier transform converts the waveform from the time domain to the frequency domain, revealing the underlying frequency components. By analyzing the resulting spectrum, which shows the amplitude and phase of each frequency component, one can determine the simpler waveforms that make up the original complex pattern.

Fourier analysis has numerous applications, such as analyzing sound waves, image processing, and data compression. It enables us to better understand and manipulate complex signals by breaking them down into their fundamental building blocks.

Learn more about fourier analysis here:

https://brainly.com/question/28385206

#SPJ11

To find the area of a triangle with the given vertices (2, 2), (5, 4), and (3, 8), we can use the formula for the area of a triangle using coordinates.

By applying this formula and performing the necessary calculations, we can determine the area of the triangle.

To find the area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3), we can use the formula:

Area = 0.5 * |(x1 * (y2 – y3) + x2 * (y3 – y1) + x3 * (y1 – y2))|

Substituting the coordinates of the given vertices into the formula, we get:

Area = 0.5 * |(2 * (4 – 8) + 5 * (8 – 2) + 3 * (2 – 4))|

Simplifying the expression inside the absolute value brackets, we have:

Area = 0.5 * |(-4 + 24 – 6)|

Area = 0.5 * |14|

Finally, we calculate the absolute value and multiply by 0.5 to get the area of the triangle:

Area = 0.5 * 14 = 7

Therefore, the area of the triangle with the given vertices is 7 square units.

Learn more about area of a triangle here : brainly.com/question/29156501

#SPJ11

Answer:

3  1/100

Step-by-step explanation:

Place the decimal number over a power of ten.

The differential equation dy/dx = 2ex - y is solved by integrating both sides, resulting in the solution y = 2ex + C, where C is the constant of integration

To solve the differential equation dy/dx = 2ex - y, we can use the method of separating variables.

Rearranging the equation, we have dy = (2ex - y)dx.

Next, we separate the variables by moving all terms involving y to one side and terms involving x to the other side. This gives us dy + y = 2exdx.

Now, we integrate both sides of the equation. The integral of dy + y with respect to y is simply y, and the integral of 2exdx with respect to x is 2ex + C, where C is the constant of integration.

Therefore, the solution to the differential equation is y = 2ex + C, where C represents the constant of integration..

Learn more about differential here:

https://brainly.com/question/32645495

#SPJ11

Answer:

Step-by-step explanation:

You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).

Writing the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -2 = 1/2(x -(-1)) . . . . . using given slope and point

  2y -4 = x +1 . . . . . . . . . . multiply by 2

  x -2y =  -5 . . . . . . . . . . . . add -1 -2y

Setting x=0 tells us the y-intercept is ...

  0 -2y = -5

  y = -5/-2 = 5/2

So, the y-intercept is (0, 5/2).

Setting y=0 tells us the x-intercept is ...

  x -2(0) = -5

  x = -5

So, the x-intercept is (-5, 0).

It will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...

  x -2y = -5

  x = -5 +2y = -5 +2(6) = 7

Another point on the line is (7, 6).

__

Additional comment

If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.

<95141404393>

The value of expression \(4^\frac{1}{3}\) × \(4^\frac{1}{5}\)  is \(4^\frac{8}{15}\).

Given,

In the question:

\(4^\frac{1}{3}\) × \(4^\frac{1}{5}\)

To solve the above given by using the product of powers property

and, Simplify the numeric expression.

The expression is as follows:

\(4^\frac{1}{3}\) × \(4^\frac{1}{5}\)

The property to be used is : \(x^a.x^b = x^a^+^b\)

This property is valid if the base is same. Here, base is x.

In this given problem, x = 4, a = 1/3 and b = 1/5.

And, plug the values of above property:

\(4^\frac{1}{3}\) × \(4^\frac{1}{5}\) = \(4^\frac{1}{3}^+^\frac{1}{5}\)

          =   \(4^\frac{5+3}{15}\)

           = \(4^\frac{8}{15}\)

Hence, The value of expression \(4^\frac{1}{3}\) × \(4^\frac{1}{5}\)  is \(4^\frac{8}{15}\).
Learn more about Powers Property at:

https://brainly.com/question/28747844

#SPJ1

The area between two negative scores can be found by taking the absolute difference between the two scores.

The area between two negative scores can be found by taking the absolute difference between the two scores. This is because the absolute difference gives us the distance between the two scores without considering their signs.

To calculate the area between two negative scores, follow these steps:

1. Identify the two negative scores.
2. Subtract the smaller negative score from the larger negative score.
3. Take the absolute value of the result to remove the negative sign.
4. The absolute difference between the two negative scores represents the area between them.

For example, let's say we have two negative scores, -5 and -10. To find the area between them, we subtract -5 from -10, resulting in -10 - (-5) = -10 + 5 = -15. Since we are interested in the distance, we take the absolute value of -15, which gives us 15. Therefore, the area between -5 and -10 is 15.

The absolute difference between two negative scores gives us the area between them. This approach is applicable whenever we want to find the distance or area between any two numbers, not just negative scores.

Know more about absolute difference here,
https://brainly.com/question/30241588

#SPJ11

Answer:

Part A: \(\frac{3}{5}\)

Part B: \(\frac{1}{2}\)

Step-by-step explanation:

We know that Alinn flipped a coin 20 times, and that 12 of those times resulted in heads. The other 8 times resulted in tails.

Part A wants us to find the experimental probability of the coin landing on heads. Experimental probability is the probability determined based on the experiments performed.

Part B wants us to find the theoretical probability of the coin landing on heads. Theoretical probability is determined based on the number of favorable outcomes over the number of possible outcomes.

Experimental probability is determined as # of times something occurred experimentally / total number of times.  

Since 12 of the 20 times that Alinn flipped the coin resulted in heads, this means that the experimental probability of Alinn flipping heads is \(\frac{12}{20}\), which simplifies down to \(\frac{3}{5}\).

Theoretical probability, as stated above, is the number of favorable outcomes / possible outcomes.

Our favorable outcome is flipping heads, and on a coin, there are two sides that a coin can land on: heads and tails. This means that there are two possible outcomes, and only one of them is favorable.

This means that our theoretical probability is \(\frac{1}{2}\).

By using the concept of depreciation, it can be calculated that

Value of x is 3.6%

What is depreciation?

Depreciation is the exponential decrease in the value of an asset or population or cost of an article at a certain rate over  a certain period of time.

Now opposite of depreciation is growth.

Growth is the exponential increase in the value of an asset or population or cost of an article at a certain rate over  a certain period of time.

Here concept of depreciation has been used

Number of deer in 2005 = 1480

Rate = x%

Time = 7 years

Number of deer after 7 years = 1141

\(1141 = 1480(1-\frac{x}{100})^7\\(1 - \frac{x}{100})^7 = \frac{1141}{1480}\\(1-\frac{x}{100}) = (\frac{1141}{1480})^{\frac{1}{7}}\\1 - \frac{x}{100} = 0.964\\\frac{x}{100} = 1 - 0.964\\\frac{x}{100} = 0.036\\x = 0.036 \times 100\\\)

x = 3.6 %

To learn more about depreciation, refer to the link-

https://brainly.com/question/25806993

#SPJ1

Answer: 1.247834e+15

Step-by-step explanation: Used Calculator

Answer:

x=15 y=22.5

Step-by-step explanation:

6x-5=85

6x=90

x=15

4y=90

y=22.5

4y makes a right angle so it is 90 degrees

Answer:

200

Step-by-step explanation:

6.6 divided by 3.3 is 2

10^-2 divided by 10^-4 is 10^2 or 100

2 times 100 is 200

As a result of answering the given question, we may state that  As a result, the variable f represents the total quantity of fish in the bucket expressions before Aisha feeds the dolphins as 20.

In mathematics, an expression is a set of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that expresses a quantity or value. Expressions might be simple, like "3 + 4", or complex, like "(3x2 - 2) / (x + 1)". They may also include functions such as "sin(x)" or "log(y)". Expressions can be evaluated by substituting values for the variables and carrying out the mathematical operations in the given order. For instance, if x = 2, the formula "3x + 5" is 3(2) + 5 = 11. In mathematics, expressions are widely used to explain real-world situations, build equations, and simplify complex mathematical issues.

We can use the equation to find the total quantity of fish in the bucket before Aisha feeds the dolphins:

f = 5 x 4

f denotes the total number of fish in the bucket.

Because there are 5 dolphins and each dolphin receives 4 fish, the total number of fish distributed to the dolphins is 5 times 4, or 20. As a result, the variable f represents the total quantity of fish in the bucket before Aisha feeds the dolphins as 20.

To know more about expressions visit :-

https://brainly.com/question/14083225

#SPJ1

Answer:

1. = 20

2.= 20

3.= 225

4.= 800

5.= 2

Step-by-step explanation:

Just do the RATE% of the BASE and you will get the PERCENTAGE. :)

1. The circumference of a donut is 11 inches.

2. There are 360 square inches in 2.5 square feet.

3. The length, width, and height of the new box should be 4 inches, 4 inches, and 2 inches.

4. The area of the bottom of the new box is 16 square inches.

5. The surface area of the new box is 48 square inches.

6. Yes, the new box does cost less than the original box.

1. The circumference of a donut is 11 inches. This is calculated by multiplying the diameter of 3.5 inches by pi (3.14).

2. There are 360 square inches in 2.5 square feet. This is calculated by multiplying 144 square inches by 2.5.

3. The length, width, and height of the new box should be 4 inches, 4 inches, and 2 inches. This is calculated by adding 1/2 inch to the diameter of the donut (3.5 inches) and the height of the donut (1.5 inches).

4. The area of the bottom of the new box is 16 square inches. This is calculated by multiplying the length (4 inches) by the width (4 inches). The length and width of the new box meet Dave's requirements because they are both 4 inches, which is 1/2 inch more than the diameter of the donut (3.5 inches).

5. The surface area of the new box is 48 square inches. This is calculated by multiplying the length (4 inches) by the width (4 inches) and multiplying that by the height (2 inches).

6. Yes, the new box does cost less than the original box. This is calculated by multiplying the cost of the original box ($15.00) by 25 (the number of boxes in the original order) and dividing that by 25 (the number of boxes in the new order). The cost of the new box is $12.00, which is less than the cost of the original box.

To learn more about diameter visit:

https://brainly.com/question/10907234

#SPJ4

Answer:

11.66

Step-by-step explanation:

I couldn't understand the question quite well but I think you are trying to say one - third of 45-10x

Abe jogs 1. 8 miles on Monday, 1. 3 miles on Tuesday, and 1. 2 miles on Wednesday.

Beth will jog 8.6 miles, if she jogs twice as far as Abe.

The answer provided below has been developed in a clear step by step manner.

Step: 1

Given that,

Abe jogs 1.8 miles on Monday, 1.3 miles on Tuesday and 1.2 miles on Wednesday.

So,

Total miles jog by Abe =1.8+1.3+1.2

Step: 2

Adding, we get,

Total miles jog by Abe = 4.3 miles

To find :-

The number of miles Beth jogged.

Step: 3

Since Beth jogs twice as far as Abe, we have,

Number of miles Beth jog = 2×4.3 miles = 8.6 miles

Since Abe jog 4.3 miles in total, Beth will jog (2* 4.3) miles

Hence the answer is, Beth will jog 8.6 miles, if she jogs twice as far as Abe.

To learn more about probability click here https://brainly.com/question/24756209

#SPJ4

Answer:

X is always 1+ bigger than Y

EX: if you have y as 9, X will be 10

Step-by-step explanation:

N = 9

The area of the triangle in the diagram is 1/2√(x₁² + y₁²) * √(x₂² + y₂²)

From the question, we have the following parameters that can be used in our computation:

The triangle

Where we have

Base = √(x₁² + y₁²)

Height = √(x₂² + y₂²)

The area of the triangle in the diagram is calculated as

Area = 1/2 * Base * height

So, we have

Area = 1/2√(x₁² + y₁²) * √(x₂² + y₂²)

Read more about area at

https://brainly.com/question/24487155

#SPJ1

By doing this, Pablo is likely trying to draw attention to the data on bottles, which may be of particular interest or importance in his analysis.

The yellow highlight can make the data stand out more visually, making it easier for viewers to quickly identify and understand the information presented.

Data visualization tools can be useful in helping to communicate complex information in a clear and concise way. By using different colors, shapes, and visual elements, it is possible to highlight key data points and make patterns and trends more apparent.

This can be especially useful in business, scientific, and academic settings, where data analysis and communication are important skills.

To learn more about data click on,

https://brainly.com/question/28101060

#SPJ1

Answer:

1782 cm³

Step-by-step explanation:

First, you measure the volume of the cuboid as a whole which is length x breadth x height, 9 x 12 x 18 = 1944 cm³. Then measure the volume occupied by the space, 3 x 3 x 18 since the hole runs along the entire length = 162 cm³.

Then you subtract the volume occupied by the hole from the volume of the cuboid in total, 1944 - 162 = 1782 cm³

As a result, the horizontal component of velocity has a magnitude of 11.8 m/s\ while the vertical component of velocity has a value of 8.0 m/s.

The pace at which an item changes its position is described by a vector quantity called velocity. It is described as the rate at which displacement changes in relation to time The amount and direction of velocity are both present. Speed refers to the velocity's magnitude.

The football's velocity in this scenario is 32 miles per hour, or around 14.3 meters per second.

We can use trigonometry to determine the sizes of a velocity vector's horizontal and vertical components.

Vₓ = V cos (theta), where V is the magnitude of the velocity vector and theta is the angle that the velocity vector makes with the horizontal axis, gives the horizontal component of velocity.

Vy = V sin (theta), where V is the magnitude of the velocity vector and theta is the angle that the velocity vector makes with the horizontal axis, gives the vertical component of velocity.

In this instance, we are aware of the football's velocity, which is 32 miles per hour, or around 14.3 meters per second6. It makes a 34 degree 6 angle with the ground.

Therefore,

Vₓ= V cos (theta) * cos (34 degrees) = 14.3 m/s * 11.8 m/s

Vy = V sin (theta) * sin (34 degrees) = 14.3 m/s * 8.0 m/s

To know  more about velocity visit:

brainly.com/question/30559316

#SPJ1

The predicted total number of calories for a food containing 25 grams of fat is approximately 483.55. 

The equation for the least-squares regression line is:

z = 13.198x + 153.6

where ŷ= predicted value of y (total calories), x = value of the predictor variable (grams of fat), 13.198= slope of the line, and 153.6= y-intercept of the line.

To find the predicted total calories for a food with 25 grams of fat, simplify by substituting x = 25 into the equation.

z = 13.198x + 153.6

ŷ = 13.198(25) + 153.6

ŷ = 329.95 + 153.6

z = 483.55

Therefore, the predicted total number of calories for a food containing 25 grams of fat is approximately 483.55. 

learn more about the regression line

brainly.com/question/7656407

#SPJ4

Reports that describe how many customers shared positive comments about the gardening magazine on social media in the past year. Reports that compare past weather patterns to the number of people asking gardening questions to their social media. Reports that examine how a recent 50%-off sale affected the number of subscription purchases. Reports that predict the success of sales leads to secure future subscribers.

In order to find relevant information, support inferences, and help decision-making, data analysis is the process of analyzing, cleaning, manipulating, and modeling data. A data analyst examines data to find significant consumer insights and potential uses for the information. They also advise the company's management and other stakeholders of this information. Although it is recommended that data analysts have a basic understanding of statistics and mathematics, many of their tasks may be completed without it. However, data analysts often need to be familiar with statistics, linear algebra, and calculus.

To know more about data analyst,

https://brainly.com/question/28893491

#SPJ4