Sam is putting a patio around his pool. If he wants the patio to have a 10 foot width from the edge
of the pool. The pool has dimensions of 8ft by 12 ft, what is the area of his new patio?
sq ft

First-order partial derivatives: df/dx = sin(y^3), df/dy = 3xy^2 * cos(y^3)

Second-order partial derivatives: d²f/dx² = 0, d²f/dy² = 6xy * cos(y^3) - 9x^2y^4 * sin(y^3)

To find the first and second order partial derivatives of the function f(x, y) = x * sin(y^3), we will differentiate with respect to each variable separately. Let's start with the first-order partial derivatives:

Partial derivative with respect to x (df/dx):

Differentiating f(x, y) with respect to x treats y as a constant, so the derivative of x is 1, and sin(y^3) remains unchanged. Therefore, we have:

df/dx = sin(y^3)

Partial derivative with respect to y (df/dy):

Differentiating f(x, y) with respect to y treats x as a constant. The derivative of sin(y^3) is cos(y^3) multiplied by the derivative of the inner function y^3 with respect to y, which is 3y^2. Thus, we have:

df/dy = 3xy^2 * cos(y^3)

Now let's find the second-order partial derivatives:

Second partial derivative with respect to x (d²f/dx²):

Differentiating df/dx (sin(y^3)) with respect to x again yields 0 since sin(y^3) does not contain x. Therefore, we have:

d²f/dx² = 0

Second partial derivative with respect to y (d²f/dy²):

To find the second partial derivative with respect to y, we differentiate df/dy (3xy^2 * cos(y^3)) with respect to y. The derivative of 3xy^2 * cos(y^3) with respect to y involves applying the product rule and the chain rule. After the calculations, we get:

d²f/dy² = 6xy * cos(y^3) - 9x^2y^4 * sin(y^3)

These are the first and second order partial derivatives of the function f(x, y) = x * sin(y^3):

df/dx = sin(y^3)

df/dy = 3xy^2 * cos(y^3)

d²f/dx² = 0

d²f/dy² = 6xy * cos(y^3) - 9x^2y^4 * sin(y^3)

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Answer:

x = 14 inches

Step-by-step explanation:

The area of a square piece of paper is 200 square inches.

We need to find the point on the number line below represents the measurement closest to the side length of the piece of wrapping paper​. It is shown in the attached figure.

Area of a square = x², x is the side length

\(x=\sqrt{A} \\\\x=\sqrt{200} \\\\x=14.142\ \text{inches}\)

or

x = 14 inches

So, the side length of the square is 14 inches. It is shown in point A.

Answer:

Here is your answer . Hope this helps you.

Answer:

\(\boxed {\boxed {\sf \sqrt{218} \ or \ 14.76}}\)

Step-by-step explanation:

The formula for calculating the distance between 2 points is:

\(d= \sqrt{(x_2-x_1)^2 +(y_2-y_1)^2\)

In this formula, (x₁, y₁) and (x₂, y₂) are the 2 points. The 2 points we are given are (-4, 6) and (3, -7). If we match the value with the corresponding variable we see that:

Substitute the values into the formula.

\(d= \sqrt{(3 - -4)^2 + (-7-6)^2\)

Solve inside the parentheses.

\(d=\sqrt {(7)^2 + (-13)^2\)

Solve the exponents.

\(d= \sqrt{ (49)+(169)\)

Add.

\(d= \sqrt{218}\)

\(d=14.76482306\)

If we round to the nearest hundredth place, the 4 in the thousandth place tells us to leave the 6.

\(d \approx 14.76\)

The distance between the points (-4, 6) and (3, -7) is √218 or approximately 14.76.

Answer:

x = 0

Step-by-step explanation:

Lets make an equation.

x + 1 + (-1) = 0

=> x + 0 = 0

=> x = 0

Kind request:

Please give me brainliest :)

The set of parametric equations representing the skater's jump is:

x = 52t

y = 5 + 16t²

We have,

Let's denote the time as t.

Horizontal motion:

The skateboarder's horizontal velocity remains constant throughout the jump, so the horizontal position (x) can be represented as:

x = vt

where v is the horizontal velocity, which in this case is 52 ft/s.

Vertical motion:

The vertical position (y) can be determined using the equations of motion under constant acceleration.

The skateboarder experiences acceleration due to gravity (g) acting downward.

The initial vertical position is 5 ft, and the initial vertical velocity is

0 ft/s.

Using the equation of motion:

\(y = y_0 + vy_0t + 0.5gt^2\)

Substituting the given values:

y = 5 + 0t + 0.5(32)t²

y = 5 + 16t²

Thus,

The set of parametric equations representing the skater's jump is:

x = 52t

y = 5 + 16t²

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Answer:

2x=5 > -14

Step-by-step explanation:

6(x - 2) -3 ≥ -4 ( -3 + 9) +10​
6x-12-3 > 12-36+10
6x-15 > -36+22
6x-15 > -14
6x=15 > -14
3    3        
2x=5 > -14

|x-5| + 7 = 13 is equal to x= -11 and x = 1.

\(|x-5|+7=13\)

Subtract 7 from both sides

\(|x-5|+7-7=13-7\)

Simplify

\(|x-5|=6\)

Apply absolute rule: If \($|u|=a, a > 0$\) then \($u=a$\) or \($u=-a$\) \($x-5=-6$\) or \($x-5=6$\)

\($$x-5=-6 \text { or } x-5=6$$\)

\($$x=-1 \text { or } x=11$$\)

Making something simpler is making it less intricate or crowded. When you describe a complex mathematical idea to a youngster in words they can easily comprehend, you are simplifying. When you eliminate many of the tasks that were keeping you occupied and stressed out, you have simplified.

Making something simpler refers to making it simpler to accomplish or comprehend. Therefore, when we reduce or simplify a fraction, we aim for maximum simplicity. In order to do this, we divide both the numerator and the denominator by the biggest integer that can be divided precisely into both numbers.

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Answer:

LOL

Step-by-step explanation:

To determine if a function crosses the horizontal asymptote, analyse the behavior of the function as it approaches the asymptote and on either side of it.

1. Identify the horizontal asymptote of the function. The horizontal asymptote is a horizontal line that the function approaches as the independent variable (usually denoted as x) goes to positive or negative infinity. It is often denoted by a horizontal line y = a, where "a" is a constant.

2. Examine the behavior of the function as x approaches positive infinity. Evaluate the limit of the function as x goes to positive infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. However, if the limit does not equal the asymptote, move to the next step.

3. Examine the behavior of the function as x approaches negative infinity. Evaluate the limit of the function as x goes to negative infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. If the limit does not equal the asymptote, proceed to the next step.

4. Investigate the behavior of the function around critical points or points where the function changes its behavior. These points may include the x-intercepts or vertical asymptotes. Determine if the function crosses the asymptote around these points by analyzing the behavior of the function in their vicinity.

If, at any point in this process, the function crosses the horizontal asymptote, then it does not have a true horizontal asymptote. However, if the function approaches the asymptote and does not cross it at any point, then it has a horizontal asymptote.

It's important to note that some functions may have multiple horizontal asymptotes or no horizontal asymptote at all. The steps outlined above are a general guideline, but the specific behavior of the function needs to be analyzed to make a conclusive determination.

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Answer:

43 & 53

Step-by-step explanation:

Answer:

D=5g/ml

Step-by-step explanation:

D=M/V

D=55/11

Step-by-step explanation:

x varies directly as y

x=ky

12=4k

k=12/4

k=3

Answer: √58 or about 7.6

Step-by-step explanation:

use the distance formula: √((x1 - x2)² + (y1 - y2)²)

√((3 - 0)² + (7 - 0)²)

√((3)² + (7)²)

√(9 + 49)

√58

hope this helps!

Answer:

about 7.6

Step-by-step explanation:

right on edge 2021

Answer:

  1/5

Step-by-step explanation:

  1/3 of 3/5 is 1/5

The amount of flour you need is 1/5 cup.

Answer:

\(12x + 31 > 11 \\ 12x > 11 - 31 \\ 12x > - 20 \\ x > - \frac{20}{12} \\ \\ x > - \frac{5}{3} \)

When identifying the parts of a packaged data model that apply to your organization, you should first start with understanding your Organization's specific needs and requirements.

This involves the following steps:

1. Assess your organization's business processes and goals, which helps in identifying key areas where data modeling can enhance decision-making and performance.

2. Analyze existing data sources and systems to understand the current data landscape, including its structure, relationships, and data quality.

3. Identify the critical data elements that align with your organization's needs, such as customer information, sales data, or financial data. These elements form the foundation of your data model.

4. Determine the relevant industry-standard data models or frameworks that can serve as a starting point for your organization's data model. This may include industry-specific models or general models applicable to a variety of businesses.

5. Evaluate the suitability of the selected packaged data model for your organization by comparing its features, flexibility, and scalability with your specific requirements.

6. Customize the chosen data model to fit your organization's unique processes, data structures, and business rules, ensuring that it accurately represents your data environment.

7. Implement and maintain the data model, regularly updating it to reflect changes in your organization's processes, data sources, or business objectives.

By following these steps, you will effectively identify and apply the parts of a packaged data model that best suit your organization's needs, enabling improved decision-making and performance.

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Answer:

.15¢

Step-by-step explanation:

1.20$ total divided by 8 and its .15¢

Let's start by setting up some equations based on the given information.
Let's call the width of the rectangle "w" and the length "l". We know that:
l = 2w - m  (since the length is "m less than twice its width")

When we add "m" to the width, we get a square with an area of:
(w + m)^2 =
We can set up another equation based on the fact that the area of the original rectangle is:
A = lw =
Now, we can use the information we have to solve for the dimensions of the original rectangle. We can start by simplifying the equation for the area of the square:
(w + m)^2 =
w^2 + 2wm + m^2 =
Now we can substitute our expression for "l" in terms of "w" and "m":
w(2w - m) =
Expanding this out gives us:
2w^2 - wm =
We can substitute this expression for "lw" in our equation for the area of the square:
2w^2 - wm =
w^2 + 2wm + m^2 =
Now we can simplify this equation by expanding out the square on the left side:
2w^2 - wm =
w^2 + 2wm + m^2 =
2w^2 - wm =
w^2 + 2wm + m^2 =
w^2 + wm + m^2 =
Now we can solve for "m" by subtracting the first equation from the second:
3wm + m^2 =
Subtracting "w^2" from both sides gives us:
wm + m^2 =
Now we can solve for "m" using the quadratic formula:
m =
We can use this value for "m" to solve for the dimensions of the original rectangle. Substituting into our equation for "l" in terms of "w" and "m", we get:
l = 2w - m =
And substituting into our equation for the area of the rectangle, we get:
A = lw =
So the dimensions of the original rectangle are:
Width: w =
Length: l =

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The probability that if a malpractice suit is filed, it originated in hospital 1 = P(B1|A) =

To solve this problem we will use Baye's theorem which states

P(B1 |A) = P(A/B1)P(B1) / P(A|B1)P(B1) + P(A|B2)P(B2) + P(A|B3)P(B3)       (1)

where P(A|B) is the probability of event A occurring given that event B has already taken place.

Probability of hospital 1 having the case = P(B1) = 50

Probability of hospital 2 having the case = P(B2) = 30

Probability of hospital 3 having the case = P(B3) = 20

Probability of case resulting in malpractice in hospital 1= P(A/B1) =0.001

Probability of case resulting in malpractice in hospital 2= P(A/B2) =0.005

Probability of case resulting in malpractice in hospital 3= P(A/B3) =0.008

The probability that if a malpractice suit is filed, it originated in hospital 1 = P(B1|A)

Using equation (1)

P(B1|A) = (0.001)(50) / (0.001)(50) + (0.005)(30) + (0.008)(20)

          = 0.05 / ( 0.05 + 0.15 + 0.16 )

          = 0.05 / 0.36

          = 0.138

Problem based on Bayes's theorem

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In general, observational studies are more problematic than randomized controlled trials because they can produce spurious relationships.

Observational studies rely on the natural variation in exposures and outcomes that occur in the population, without any intervention or manipulation by the researcher.

This can lead to confounding variables, which are factors that are associated with both the exposure and the outcome and can produce a false association between them.

Randomized controlled trials, on the other hand, assign participants to different exposure groups at random, which reduces the risk of confounding and allows for a more accurate assessment of causality.

Therefore, researchers must be cautious when interpreting observational studies and consider the potential for spurious relationships.

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Answer:

y=3x-2

Step-by-step explanation:

y-y1=m(x-x1)

y-13=3(x-5)

y=3x-15+13

y=3x-2

The length of the arc opposite a central angle that measures 46 degrees is 2.72 cm.

What is circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

in a circle of radius 3.4 cm

central angle that measures 46 degrees

length of arc = (46/360) * 2π*3.4

=2.72cm

Hence the length of the arc opposite a central angle that measures 46 degrees is 2.72 cm

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The confidence interval for the proportion of adults who identify chocolate pie as their favorite pie can be calculated using the following formula:
Confidence Interval = Sample Proportion ± Margin of Error

First, we need to calculate the sample proportion. In this case, the sample proportion is equal to the percentage of respondents who chose chocolate pie, which is 48%.

Sample Proportion = 48% = 0.48

Next, we need to calculate the margin of error. The margin of error depends on the confidence level and the sample size. In this case, the confidence level is 90%, which corresponds to a z-score of 1.645 (obtained from a z-table). The sample size is 22.

Margin of Error = z * sqrt((Sample Proportion * (1 - Sample Proportion)) / Sample Size)
                = 1.645 * sqrt((0.48 * (1 - 0.48)) / 22)
                = 0.229

Now we can calculate the confidence interval.
Confidence Interval = Sample Proportion ± Margin of Error
                          = 0.48 ± 0.229
                          = (0.251, 0.709)

The confidence interval for the proportion of adults who identify chocolate pie as their favorite pie is (0.251, 0.709) at a 90% confidence level.

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Answer:

B

Step-by-step explanation:

i believe the answer is B because C and D don't make sense in the context of the problem

Answer:

Step-by-step explanation:

Use tigonometry to find the value of d

Answer:

497 m (nearest whole number)

Step-by-step explanation:

As the problem has been modeled as a right triangle, we can use the sine trigonometric ratio to find the distance d.

Sine trigonometric ratio

   \(\sf \sin(\theta)=\dfrac{O}{H}\)

where:

From inspection of the given diagram:

Substitute the values into the formula and solve for d:

\(\implies \sf \sin(38^{\circ})=\dfrac{306}{H}\)

\(\implies \sf H=\dfrac{306}{\sin(38^{\circ})}\)

\(\implies \sf H=497.0263891...\)

Therefore, the distance d between the helicopter and the landing pad is 497 m (nearest whole number).

Answer:

V = 1072.3 cm³

Step-by-step explanation:

Volume of a hemisphere = \(\frac{2}{3} \pi r^3\) [Because it's half of a sphere's volume]

V = \(\frac{2}{3} (3.14)(8)^3\)

V = \(\frac{2}{3} (3.14)(512)\)

V = \(\frac{3216.99}{3}\)

V = 1072.3 cm³

Answer:

40%      

I looked it up

Answer:

0.45%

Step-by-step explanation:

Answer: Let the number = x

5x+10 = 120

Or, 5x = 120 - 10

Or, 5x = 110

Or, x = 110/5

Or, x = 2

Step-by-step explanation:

The fractional equivalent of the repeating decimal 0.2 is 2/9

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

Repeating decimal = 0.2

Represent properly

So, we have

Repeating decimal = 0.2222

Express as fraction

So, we have

Fraction = 2/(10 - n)

In this case

n = 1

So, we have

Fraction = 2/(10 - 1)

Evaluate

Fraction = 2/9

Hence, the fractional equivalent is 2/9

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