Find f(x) and g(x) so that the function can be described as y = f(g(x)).

y = 4/x^2+9

(4x + 5)(3x + 10) or 12x² + 55x +50

Forming the Expression for the Area of Rectangle

The formula for the area of a rectangle is given as,

Area, A = length × breadth

Here, the dimensions of the rectangle are given as,

length = (4x + 5)

breadth = (3x + 10)

∴ The equation for the area of the rectangle is,

A = (4x + 5)(3x + 10)

A = 12x² + 55x +50

Hence, 12x² + 55x +50 is the required expression.

Degree and Classification of the Expression

The highest power of a variable that is present in an expression is known as its degree.

Since the degree of the expression formed in part a is 2, it is classified to be a quadratic expression.

Closure Property For Polynomials

When the output is the same kind of object as the inputs, an expression is said to be closed. The expression obtained for the area of the rectangle is a combination of constants and variables closed under multiplication and addition.

Hence the expression formed in part a indicates at the closure property for polynomials.

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Answer:

87.5°

Step-by-step explanation:

So we know that the arc CD is 175°. This is the same thing as saying that the measure of the central angle, ∠CAD, is 175°. By the Inscribed angle theorem, we know that the measure of the inscribed angle, ∠DBC, is half of the measure of the central angle, ∠CAD. So:

m∠DBC = m∠CAD × 1/2

m∠DBC = 175/2

m∠DBC = 87.5

So the measure of ∠DBC would be 87.5°. Answer choice 2 would be correct.

I hope you find my answer and explanation to be helpful. Happy studying.

75% of the beads are green in color.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Chase ordered a set of beads

He received 4,000 beads in all.

3,000 of the beads were green.

We need to find the  percentage of the beads were green of 4000.

x/100×4000=3000

40x=3000

Divide both sides by 40

x=75%

Hence, 75% of the beads are green in color.

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Perimeter of Rectangle is 44m

A perimeter is a closed path that encompasses, encircles, or delineates a one-dimensional length or a two-dimensional shape.

According to the given information

Area of Rectangle = l × b

Area of Rectangle = 105 \(m^{2}\)

Length of one side = 7 m

Let the length of the adjacent side = b

Area of Rectangle given = 7 × b

                     105   = 7 × b

                       b    =  \(\frac{105}{7}\)

                       b   = 15 m

Perimeter of Rectangle given = 2( l + b )

                                        = 2 ( 7 + 15 )

                                        = 2 × 22

                                        = 44m

Perimeter of Rectangle is 44m

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Answer:

It would be the fourth one

Step-by-step explanation:

To find the linear approximation L(x) to y = f(x) near x = a for the function f(x) = 1, a = 5, we need to use the formula:

L(x) = f(a) + f'(a)(x - a)

Since f(x) = 1 for all values of x, we have f(a) = 1 for a = 5. To find f'(a), we take the derivative of f(x):

f'(x) = 0

Therefore, f'(a) = 0 for a = 5. Substituting these values into the formula, we get:

L(x) = 1 + 0(x - 5) = 1

So the linear approximation to y = f(x) near x = 5 is L(x) = 1.

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One method to introduce bias into data collection is through non-random sampling, specifically by using convenience sampling.

Convenience sampling introduces selection bias, which occurs when the sample is not representative of the population of interest. This can lead to inaccurate or misleading conclusions.

Convenience sampling involves selecting individuals who are readily available or easily accessible to participate in the study. This method introduces bias because the sample may not accurately represent the entire population. For example, if a researcher wants to study the eating habits of a particular city's population and only collects data from people who visit a specific restaurant, the sample will not be representative of the entire population.

This introduces selection bias as the sample is biased towards individuals who frequent that restaurant and may not reflect the eating habits of the broader population. Consequently, any conclusions drawn from this convenience sample would be limited and potentially misleading.


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True. The 3px, 3py, and 3pz orbitals are similar in shape but differ in their orientation or direction.

The p orbitals are one type of orbital that corresponds to the angular momentum number l = 1. These p orbitals are designated as 3px, 3py, and 3pz to indicate their orientations along the x, y, and z axes, respectively.

The p orbitals have a  shape with a node at the nucleus. They consist of two lobes of electron density, one on either side of the nucleus, separated by a region of zero electron density. The lobes are oriented along the designated axes. The 3px orbital points along the x-axis, the 3py orbital points along the y-axis, and the 3pz orbital points along the z-axis. Although they have different orientations, their shapes and sizes are the same.

So, while the 3px, 3py, and 3pz orbitals differ in their orientation in space, they share the same overall shape and size.

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Answer:

$2.40

Step-by-step explanation:

We know that the sales tax is 8% , we also know that we want to buy two t shirts that cost $15.00 each.

So first, look at what we are purchasing, two t-shirts costing 15.00 dollars each.

Since we are buying two, multiply $15 by 2,

==> $30.00 dollars

And since the sales tax is 8%, to find how much we will pay will mean to multiply the amount by the percent,

30 * 8%

==> $2.40 dollars

You will pay $2.40 dollars in tax

Answer: 170

Step-by-step explanation:

275-105

Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

Answer:

c

Step-by-step explanation:

As per duality theory, every original linear programming problem has an associated dual problem. The dual of the original linear programming problem is feasible and the optimal cost is infinite.

Let's consider a general linear programming problem in standard form that is infeasible. We aim to demonstrate that the dual of the original problem is feasible, and the optimal cost is infinite.

Linear programming (LP), or linear optimization, is a mathematical technique used to determine the optimal solution for a given mathematical model with linear relationships, typically involving maximizing profit or minimizing cost. LP falls under the broader category of optimization techniques.

As per duality theory, every original linear programming problem has an associated dual problem. Solving one problem provides information about the other problem, and vice versa. The dual problem is obtained by creating a new problem with one variable for each constraint in the original problem.

To show that the dual of the original problem is feasible and the optimal cost is infinite, we will follow these steps:

Derive the dual of the given linear programming problem.

Demonstrate the feasibility of the dual problem.

Establish that the optimal cost of the dual problem is infinite.

Step 1: Dual of the linear programming problem

The given problem is:

Minimize Z = c'x

subject to Ax = b, x >= 0

Here, x and c are column vectors of n variables, and A is an m x n matrix.

The dual problem for this is:

Maximize Z = b'y

subject to A'y <= c, y >= 0

In the dual problem, y is an m-dimensional column vector of dual variables.

Step 2: Feasibility of the dual problem

Since the primal problem is infeasible, it means that no feasible solution exists for it. Consequently, the primal problem has no optimal solution. By the principle of weak duality, the optimal solution of the dual problem must be less than or equal to the optimal solution of the primal problem. As the primal problem has no optimal solution, the dual problem must have an unbounded optimal solution. Therefore, the dual problem is feasible.

Step 3: The optimal cost of the dual problem is infinite

Since the primal problem has no optimal solution, the principle of weak duality states that the optimal solution of the dual problem must be less than or equal to the optimal solution of the primal problem. As the primal problem has no optimal solution, the dual problem must have an unbounded optimal solution. Consequently, the optimal cost of the dual problem is infinite.

In conclusion, we have shown that the dual of the original problem is feasible, and the optimal cost is infinite.

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The way that data sets can be used to compare two data

When attempting to compare two sets of data, there are numerous ways one can utilize visual representations to help recognize similarities and variances between the two. Here are some common examples:

Measures of center: Data displays such as box plots or histograms can be employed to quickly display measures of central tendency – like the mean, median, and mode – then contrast them amongst the two datasets.

Measures of variability: To compare two collections of data in terms of their measures of variability – including range, interquartile range, and standard deviation

Trends: Scatterplots or line graphs can be used to discern trends among the data and observe distinguishing characteristics between the two sets.

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Answer:

x = 3  x = 5

Step-by-step explanation:

(a)The optimal order quantity is  4609 units.

(b)The time between orders is  1.98 months.

To determine the optimal order quantity and the approximate time between orders, the Economic Order Quantity (EOQ) model. The EOQ model minimizes the total cost of inventory by balancing ordering costs and carrying costs.

Optimal Order Quantity:

The formula for the EOQ is given by:

EOQ = √[(2DS) / H]

Where:

D = Annual demand

S = Cost per order

H = Holding cost per unit per year

calculate the annual demand (D) using the 2020

sales numbers provided:

D = 651 + 808 + 514 + 174 + 435 + 426 + 687 + 582 + 662 + 1551 + 1295 + 1774

= 9559 units

To calculate the cost per order (S) and the holding cost per unit per year (H).

The cost per order (S) is given as $500.

The holding cost per unit per year (H)  calculated as follows:

H = Carrying cost percentage × Unit value

= 0.30 × $3

= $0.90

substitute these values into the EOQ formula:

EOQ = √[(2 × 9559 × $500) / $0.90]

= √[19118000 / $0.90]

≈ √21242222.22

≈ 4608.71

Approximate Time Between Orders:

To calculate the approximate time between orders, we'll divide the total number of working days in a year by the number of orders per year.

Assuming 360 days in a year and a lead time of 1 week (7 days) for shipping, we have:

Working days in a year = 360 - 7 = 353 days

Approximate time between orders = Working days in a year / Number of orders per year

= 353 / (9559 / 4609)

= 0.165 years

Converting this time to months:

Approximate time between orders (months) = 0.165 × 12

= 1.98 months

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An oblique asymptote occurs when the degree of the numerator is one more than the degree of the denominator. The numerator of the function is a polynomial of degree two and the denominator is a polynomial of degree one. The degree of the numerator is one greater than the degree of the denominator,

so the function has an oblique asymptote. The steps to find an oblique asymptote are as follows:Divide the numerator by the denominator using long division. Ignore any remainder. The quotient represents the equation of the oblique asymptote. 

\(\[ f(x)=\frac{7 x^{2}+3}{1-x}\]\)

By doing the long division, we get:

```
        7x - 8
     _________
1 - x | 7x² + 0x + 3
       -7x² + 7x
        ---------
            7x + 3
           -7x - 3
           -------
                 0
```

Therefore, the quotient is $7x-8$ which is the equation of the oblique asymptote of the function.

\(\[ f(x)=\frac{7 x^{2}+3}{1-x} \\\\)implies y=7x-8 \]Hence, the answer is not listed above. The correct answer would be:\(\[ f(x)=\frac{7 x^{2}+3}{1-x} \\).

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Answer:

84.5 square units.

Step-by-step explanation:

The formula to calculate the area of a trapezoid is:

Area = (base 1 + base 2) * height / 2

Using the measurements you provided, we can calculate the area of the trapezoid as follows:

Area = (12 + 14) * 6.5 / 2

Area = 26 * 6.5 / 2

Area = 169/2

Area = 84.5

Therefore, the area of the trapezoid is 84.5 square units.

Answer:

Step-by-step explanation:

132°

To send Kred to a Krew member, you can follow the steps provided by the Kred platform. These steps typically involve accessing your Kred account, selecting the desired recipient, specifying the amount of Kred to send, and confirming the transaction.

Sending Kred to a Krew member usually requires using the features and functionalities provided by the specific Kred platform or service. The process may vary depending on the platform, so it is recommended to refer to the official documentation or guidelines provided by the platform. Typically, you would need to log in to your Kred account, navigate to the appropriate section for sending Kred, select the intended recipient from the list of Krew members, enter the desired amount of Kred to send, review the transaction details, and confirm the transfer. The platform may also offer additional options or settings for customizing the transfer process.

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Answer:

25 buttons per package

Step-by-step explanation:

Answer:

I believe it is 25 buttons per package

Based on the information provided, we cannot definitively say whether the county rate is higher than the state rate. The reason for this is because the confidence intervals for both rates overlap.

Since these intervals overlap, there is a chance that the true rate for the county is lower than the true rate for the state, even though the point estimate (i.e. the reported rate) for the county is higher than the point estimate for the state.

To be more precise, we can use the margin of error for each estimate to calculate the range of values that could reasonably contain the true rate. For the county rate, the margin of error is (14.9-10.3)/2 = 2.3. For the state rate, the margin of error is (11.3-9.8)/2 = 0.75.

Therefore, the range of confidence intervals values that could reasonably contain the true rate for the county is (10.3-2.3, 10.3+2.3) = (8, 12.6), and the range of values that could reasonably contain the true rate for the state is (9.8-0.75, 9.8+0.75) = (9.05, 10.55).

As we can see, the two ranges of confidence intervals overlap, indicating that we cannot say with certainty that the county rate is higher than the state rate. We can only say that the county rate is higher than the state rate at the reported significance level (i.e. 95%), but there is still a chance that this result is due to chance or sampling variability.

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No, the mean time to spoil is not necessarily greater if the banana is hung from the ceiling.

This can only be determined by analyzing the data from the experiment with 15 bananas. If the sample mean is greater than 6.5 days, then the mean time to spoil is greater when the banana is hung from the ceiling. If the sample mean is less than or equal to 6.5 days, then the mean time to spoil is not necessarily greater when the banana is hung from the ceiling.

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In each scenario, the choice between mean and median as a representative measure of central tendency depends on the nature of the data and the specific context..

1. Scenario: Income distribution of a population

- If the income distribution is skewed or contains extreme values (outliers), the median would be a better representation of the central tendency. This is because the median is not influenced by outliers and provides a more robust estimate of the "typical" income level. However, if the income distribution is approximately symmetric without outliers, the mean can also be an appropriate measure.

2. Scenario: Exam scores in a class

- If the exam scores are normally distributed without significant outliers, the mean would be a suitable measure as it takes into account the value of each score. However, if there are extreme scores that deviate from the majority of the data, the median may be a better representation. This is especially true if the outliers are indicative of errors or exceptional circumstances.

3. Scenario: Housing prices in a city

- In this case, the median would be a more appropriate measure to represent the central tendency of housing prices. This is because the housing market often exhibits a skewed distribution with a few high-priced properties (outliers). The median, being the middle value when the data is sorted, is not influenced by these extreme values and provides a better understanding of the typical housing price in the city.

Ultimately, the choice between mean and median depends on the specific characteristics of the data and the objective of the analysis. It is important to consider the distribution, presence of outliers, and the context in which the data is being interpreted.

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Answer:

\(r = \sqrt{ {(6 - 2)}^{2} + {(1 - ( - 3))}^{2} } \)

\(r = \sqrt{ {4}^{2} + {4}^{2} } = \sqrt{16 + 16} = \sqrt{32} \)

So the equation of the circle is

\( {(x - 2)}^{2} + {(y + 3)}^{2} = 32\)