a square has an area of 15 feet squared. what are two ways of expressing its side length

I need to write that in form : x(a)+y(b)+z(c) where a,b and c are constants so, a=36, b=18(2y+4z), c=18x

Given expression is 36x1​2+92​xy+942​y2+181​xz+92​yz+36y2

Rearranging the given expression,

we have to group the terms having variables.

36x1​2+(92​xy+181​xz)+(942​y2+92​yz+36y2)⇒ 36x1​2+9(2xy+4yz+2y2)+18xz

(1) Comparing equation (1) with

x(a)+y(b)+z(c),

we get a=36, b=18(2y+4z), c=18x.

Answer: x(36)+y(18(2y+4z))+z(18x)

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Step-by-step explanation:

Base...from  - 7 to + 4 = 11 units

Height from  -4 to +5 = 9 units

Area of a traingle = 1/2  * base * height = 1/2 (11)(9) = 49.5   units^2

The open spaces in sculpture are called negative spaces.

In sculpture, negative space refers to the empty or void areas that exist between and around the solid forms or objects. It is the space that surrounds and defines the positive elements or shapes in a sculpture. Negative space plays a crucial role in creating balance, contrast, and harmony in sculptural compositions.

When an artist sculpts an object, they not only consider the physical mass and volume of the object itself but also pay attention to the spaces that are created as a result. These empty spaces are as important as the solid forms and contribute to the overall aesthetic and visual impact of the sculpture. By carefully manipulating the negative spaces, artists can enhance the perception of the positive elements and create a sense of depth, movement, and tension within the artwork.

In contrast, positive space refers to the solid or occupied areas in a sculpture, while the terms "literal" and "linear" do not specifically relate to the concept of open spaces in sculpture. Therefore, the correct answer is negative spaces.

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The correlation coefficient ρ for X and Y is ρ = -0.6675 in the given function.

The correlation coefficient is a statistical concept that aids in establishing a relationship between expected and actual values obtained through statistical experimentation. The calculated correlation coefficient's value explains why the difference between the predicted and actual values is so exact.

Correlation Coefficient value is always in the range of -1 to +1. A similar and identical relationship exists between the two variables if the correlation coefficient value is positive. Otherwise, it reveals how differently the two variables behave.

Pearson's correlation coefficient is calculated by taking the covariance of two variables and dividing it by the sum of their standard deviations. is typically used to represent it (rho).

The correlation coefficient is computed as,

\($ \rho & =\frac{{Cov}(X, Y)}{\sqrt{V(X)} \times \sqrt{V(Y)}}\)

\($=\frac{-0.0267}{\sqrt{0.04} \times \sqrt{0.04}}\)

= -0.6675

Thus, the correlation coefficient ρ for X and Y is ρ = -0.6675.

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Diego travelled x miles in the cab. To find out how far Diego travelled in the cab, we need to use the information given. We know that City Cabs charges a pickup fee of $ and $ per mile travelled.

Let's assume that Diego traveled x miles in the cab. The fare for the ride would be the pickup fee plus the cost per mile multiplied by the number of miles traveled. This can be represented as follows:

Fare = Pickup fee + (Cost per mile * Miles traveled)

Since we know that Diego's fare for the ride is $, we can set up the equation as:

$ = $ + ($ * x)

To solve for x, we can simplify the equation:

$ = $ + $x

$ - $ = $x

Divide both sides of the equation by $ to isolate x:

x = ($ - $) / $

Now, we can substitute the values given in the question to find the distance travelled:

x = ($ - $) / $

x = ($ - $) / $

x = ($ - $) / $

x = ($ - $) / $

Therefore, Diego travelled x miles in the cab.

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The surface area and weight of the cylinder is 45.1805 in² and 11.107 lbs respectively.

A cylinder is a three-dimensional geometric shape that has two parallel circular bases and a curved lateral surface connecting the bases. The bases are located at opposite ends of the cylinder, and they have the same diameter. The lateral surface is a rectangle that has been bent around the circumference of the circular bases.

The height of a cylinder is the distance between the two bases, and the diameter of the bases is the distance across the circle through its center. The volume of a cylinder can be calculated by multiplying the area of one of its bases by its height. The formula for the volume of a cylinder is:

V = πr²h

where r is the radius of the circular base and h is the height of the cylinder.

Cylinders are commonly used in many real-world applications, such as in the design of pipes, cans, and other containers. They are also commonly used in mathematics and physics, where they can serve as models for objects with cylindrical symmetry, such as pipes and wires.

In summary, a cylinder is a three-dimensional shape with two parallel circular bases and a curved lateral surface connecting the bases. The height of the cylinder is the distance between the bases, and its volume can be calculated using the formula V = πr²h. Cylinders are commonly used in real-world applications and in mathematics and physics.

The following formula can be used to determine the cylinder's volume:

V = π × r² × h = π × (d/2)² × h = π × (1.35²) × 7.45 = 42.63374 in³

The following formula can be used to get the cylinder's surface area:

A = 2πr² + 2πrh = 2π × r² + 2π × r × h = 2π × (1.35²) + 2π × 1.35 × 7.45 = 45.1805 in²

The cylinder's weight can be determined using the formula below:

W = d × V = 0.259 lbs/in³ × 42.63374 in³ = 11.107 lbs.

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Applying the triangle proportionality theorem, the length of AD that will make DE║AB is: AD = 60.

According to the triangle proportionality theorem, the equation or proportion we can create to find x is expressed as:

(2x - 4) / 5x = 3x / 8x

Cross multiply:

8x(2x - 4) = (3x)(5x)

16x² - 32x = 15x²

x² - 32x = 0

Solve to find x by factoring:

The equation x² - 32x = 0 can be solved by factoring:

x(x - 32) = 0

So either x = 0 or x - 32 = 0, meaning x = 32.

The solutions to the equation are x = 0 and x = 32.

Using x = 32:

AD = 2x - 4 = 2(32) - 4

AD = 60

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Answer:

Mark arrived at school at 9:45 A.M. or either 9:45 P.M.

Answer:

Christy got to school at 9:45am

Step-by-step explanation:

Answer:

2 ...................

Answer:

Step-by-step explanation:

c

The appropriate regression model depends on the stationarity properties of both the dependent and independent variables, as well as the error term. The researcher can use a standard OLS regression model with first-order differencing of both Y and X.

In the first scenario, both Y and X are I(0), which means they are stationary time series. In this case, the researcher can perform a standard linear regression analysis, as the stationary series would lead to a stable long-run relationship. The answer from this model will be reliable and less likely to suffer from spurious regressions. In the second scenario, Y is I(2) and X is I(0). This implies that Y is integrated of order 2 and X is stationary. In this case, the researcher should first difference Y twice to make it stationary before performing a regression analysis. However, this approach might not be ideal as the integration orders differ, which can lead to biased results.

In the third scenario, Y and X are both I(1) and the error term is I(0). This indicates that both Y and X are non-stationary time series, but their combination might be stationary. The researcher should employ a co-integration analysis, such as the Engle-Granger method or Johansen test, to identify if there is a stable long-run relationship between Y and X. If co-integration is found, then an error correction model can be used for more accurate predictions.

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a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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Answer:

Step-by-step explanation:

56.1,12.1,23.6

Answer:

\(f(-7) = \bold{125}\)

Step-by-step explanation:

Given:

\(f(x) = 2x^2 - 3x + 6\)

\(f(-7) = 2(-7)^2 -3(-7) +6 \\ f(-7) = 2(49) -3(-7) +6 \\ f(-7) = 98 +21 +6 \\ f(-7) = 125\)

Answer: \(f=125\)

Step-by-step explanation:

\(f=2\left(-7\right)^2-3\left(-7\right)+6\)

\(f=2\left(-7\right)^2+3\cdot \:7+6\)

\(f=7^2\cdot \:2+3\cdot \:7+6\)

\(f=7^2\cdot \:2+3\cdot \:7+6\)

\(f=98+27\)

\(f=125\)

Answer:

find the value of ×

× +23)

Step-by-step explanation:

(×+25)

(×+12)

The tank with the smallest surface area has dimensions of 6ft.

s = 12ft and h = 6ft.

A(s) = s² + 4 × (V ÷ s)

The rectangular tank has a capacity of 864 feet.

Let the square base's long sides be.

Let h represent the tank's height.

Let A represent the tank's whole area.

A = (Base Area) + (4 × Lateral Area)

Lateral Area = s × h

Lateral Area = s × (V ÷ s²)

Lateral Area = (V ÷ s)

Base Area = s²

Compared to the objective function,

A(s) = s² + 4 × (V ÷ s)

A(s) = s² + 4 × (864 ÷ s)

The area function's derivative,

A'(s) = 2s - (3456 ÷ s²)

The smallest surface area is now.

A'(s) = 0

2s - (3456 ÷ s²) = 0

2 × \(s^{3}\) = 3456

\(s^{3}\) = 3456

s = \(\sqrt[3]{3456}\)

s = 12ft

The volume is,

V = s² × h

864 = 12² × h

h = 6ft

As a result, the tank's height is 6 feet, and the square base's long sides measure 12 feet.

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The question is -

A rectangular tank with a square​ base, an open​ top, and a volume of 864 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. Let s be the length of one of the sides of the square base and let A be the surface area of the tank. Write the objective function.

Given

Annual profits of four years $8 million, $3 million, $2 million, and $9 million.

In the fifth year, it reported a loss of $7 million.

To find:

The mean annual profit.

Solution:

Formula for mean is:

\(\text{Mean}=\dfrac{\text{Sum of observations}}{\text{Number of observations}}\)

Annual profits are $8 million, $3 million, $2 million, $9 million and -$7 million. Here negative sign represent loss.

So, the mean annual profit is:

\(\text{Mean}=\dfrac{8+3+2+9+(-7)}{5}\)

\(\text{Mean}=\dfrac{22-7}{5}\)

\(\text{Mean}=\dfrac{15}{5}\)

\(\text{Mean}=3\)

Therefore, the  mean annual profit is $3 million.

Colin is one of the few individuals who would be categorized as being intellectually gifted, typically falling within the top 2-3% of the population.

Intellectual giftedness refers to individuals who demonstrate exceptional intellectual abilities and potential beyond what is considered typical for their age group. It is often assessed through various measures, such as IQ tests and academic achievements. The exact percentage of the population considered intellectually gifted can vary depending on the specific criteria and assessments used.

However, it is generally estimated that gifted individuals represent around 2-3% of the population or even less. These individuals often show advanced cognitive abilities, strong problem-solving skills, and a high capacity for learning and academic achievement.

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The probability of an earthquake in that magnitude range occurring in next 30 years is 3%.

The probability that the event will not occur for an exposure time of x years is:

\((1-\frac{1}{MRI} )^{x}\)

where, MRI = Mean Recurrence Interval = 1000

                x = Years = 30

Therefore, Probability of not occurring = \((1-\frac{1}{1000} )^{30}\)

                                                                 = \((\frac{999}{1000} )^{30}\)

                                                                 = \((0.999)^{30}\)

                                                                 = 0.97

Probability of occurring = 1 - 0.97

                                       = 0.3

Probability percent = 0.03 * 100

                                = 3 %

Hence, probability is 3%.

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This means that the central angle of the sector is \((2/5)(360)=144^{\circ}\)

Part i

\(\frac{144}{360} (\pi)(2)(7)=\frac{28\pi}{5} \text{ cm}\)

Part ii

\((\pi)(7^2) \frac{144}{360}=\frac{98\pi}{5} \text{ cm}^2\)

Answer:

63

Step-by-step explanation:

Answer:

4 cm : 3 m

Step-by-step explanation:

Answer:

121.36

Step-by-step explanation:

L times W times H

Step-by-step explanation:

8 x 3.7 x 4.1 = 121.36

length x width x height = volume

Answer:

36)12(37)0.67

Step-by-step explanation:

36)A=base×height

A=2×6

A=12

37)A=a+b/2h

A=2+6/12

A=8/12

A=0.67

Answer: 7

Step-by-step explanation: If they equal each other, then that must mean that the exponents equal. Therefore, we can draw out the conclusion that x+2=9, which is x=7

Answer:

$6.80

Step-by-step explanation:

1.79 x 3.8 = 6.802

So $6.80

The equation x² + y² = 1/cos²(θ) represents a circle centered at the origin with a radius of 1/cos(θ).

In a two-dimensional or three-dimensional plane, the cartesian form is useful for representing a point, a line, or a plane. The x, y, and z axes are correspondingly used to express the cartesian form with regard to the three-dimensional cartesian system.

To find a Cartesian equation for the curve described by the polar equation r²cos(2θ) = 1, we can use the conversion formulas:

x = r cos(θ)

y = r sin(θ)

Substituting these into the given equation, we have:

(x² + y²)cos(2θ) = 1

Expanding the cosine term using the double-angle formula, cos(2θ) = cos²(θ) - sin²(θ), we get:

(x² + y²)(cos²(θ) - sin²(θ)) = 1

Simplifying further, we have:

x²cos²(θ) + y²cos²(θ) - x²sin²(θ) - y²sin²(θ) = 1

Using the identity cos²(θ) + sin²(θ) = 1, we can substitute it in the equation:

x² + y² - x²sin²(θ) - y²sin²(θ) = 1

Rearranging terms, we obtain:

x²(1 - sin²(θ)) + y²(1 - sin²(θ)) = 1

Using the identity 1 - sin²(θ) = cos²(θ), we can simplify further:

x²cos²(θ) + y²cos²(θ) = 1

Finally, dividing both sides by cos²(θ), we get:

x² + y² = 1/cos²(θ)

The equation x² + y² = 1/cos²(θ) represents a circle centered at the origin with a radius of 1/cos(θ).

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If you were able to add the numbers 26 and 41 in your head, it is assumed that you would be doing this in your working memory.

A cognitive apparatus known as working memory has a finite capacity and can only temporarily store information. It is crucial for reasoning, decision-making, and behaviour direction. When working on a long-division problem, kids use their working memory abilities to retain the long-division steps. Other instances include keeping track of complicated instructions, taking notes in class, recalling an argument while someone else is speaking, or performing mental calculations. In contrast to long-term memory, which stores a large amount of knowledge over a lifetime, working memory is the little amount of information that may be kept in mind and used to carry out cognitive tasks. One of the most often used concepts in psychology is working memory.

Given,

If you were able to add the numbers 26 and 41 in your head, it is assumed that you would be doing this in your:

d) Working memory

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