y-4=-3(x+2)


y= -3/2x+1


y-1=-3x


3x+y=1

To find the probability that the ratio of the shorter to the longer segment is less than 1/4 when a point is chosen randomly on a line segment of length 'l,' we can consider the following approach.

Let's denote the position of the chosen point by 'x' where 0 ≤ x ≤ l represents the distance from one end of the line segment.

The ratio of the shorter segment to the longer segment will be less than 1/4 if 'x' lies in the interval (0, l/5).

This is because any point within this interval will divide the line segment into two parts such that the shorter segment is less than 1/4 of the longer segment.

The length of the interval (0, l/5) is l/5, and the total length of the line segment is 'l.' Therefore, the probability of choosing a point within the interval (0, l/5) is given by (l/5) / l = 1/5.

Hence, the probability that the ratio of the shorter to the longer segment is less than 1/4 is 1/5 or 0.2.

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If the length of the confidence interval for the mean of a normal population is reduced by 1/3, the sample size needs to be increased.

When the population standard deviation is known, the formula for calculating the confidence interval for the mean is given by:

Confidence interval = mean ± (z * (σ/√n))

Where:

mean represents the sample mean

z is the z-score corresponding to the desired level of confidence

σ is the population standard deviation

n is the sample size

To reduce the length of the confidence interval, we need to decrease the value of (z * (σ/√n)).

Since the population standard deviation (σ) is known, the only way to decrease this value is by increasing the sample size (n).

By increasing the sample size, the standard error (σ/√n) decreases, resulting in a narrower confidence interval.

Therefore, the sample size needs to be increased to achieve a reduction in the length of the confidence interval.

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After calling EMS personnel, it is important to ensure the child's safety and comfort while waiting for help to arrive. Stabilize the injured arm in a comfortable position using a makeshift splint or sling, and offer reassurance to the child.

Once EMS personnel have been called, the immediate priority is to ensure the child's safety and provide comfort while waiting for professional medical assistance. Start by carefully assessing the situation and determining if there are any immediate dangers in the vicinity, such as moving traffic or other potential hazards. If necessary, gently move the child to a safer location, keeping in mind the importance of minimizing movement and preventing further injury.

Next, attend to the injured elbow. If the child is unable to move the arm and complains of pain, it is important to immobilize it to prevent further damage. Look for any obvious signs of deformity, swelling, or discoloration around the elbow area. Using materials available, such as a folded towel, a piece of clothing, or a scarf, create a makeshift splint or sling to stabilize the injured arm in a position that feels comfortable to the child. This will help support the elbow and prevent any unnecessary movement while waiting for professional medical assistance to arrive.

While providing care, it is crucial to offer reassurance and comfort to the child. Stay calm and speak in a soothing tone, explaining that help is on the way and that everything will be okay. Encourage the child to keep still and avoid using the injured arm until medical professionals can assess and provide appropriate treatment. Monitor the child's condition closely, paying attention to any changes in symptoms or signs of distress. Remember, the primary goal is to maintain the child's safety and minimize further harm until professional medical help arrives.

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The client's fracture is likely to be graded as a Gustilo-Anderson Type III fracture, indicating extensive soft tissue damage and contamination.

The Gustilo-Anderson classification system is used to assess the severity of open fractures. It takes into account the extent of soft tissue damage, contamination, and associated vascular injury. In this case, the client's fracture is described as having extensive soft tissue damage and being highly contaminated. These factors align with the characteristics of a Type III fracture. Type III fractures are considered severe and require immediate medical attention due to the significant soft tissue injury and potential complications. It is important for the healthcare team to carefully manage and treat this type of fracture to minimize the risk of infection and promote proper healing.

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20. the mean of the binomial distribution is 9 and the variance is 36/5.

22. Probability of getting 22 or fewer questions correct: ≈ 0.1630

23. Probability of getting five or more questions correct: ≈ 0.9999

24. Probability of getting between 9 and 18 questions correct (inclusive): ≈ 0.7031

What is probability?

Probability is a measure or quantification of the likelihood of an event occurring. It is a mathematical concept used to describe uncertainty and randomness.

To solve these problems, we need to consider the binomial distribution with parameters n and p, where n is the number of trials and p is the probability of success.

In this case, the student has 45 trials (questions) and the probability of success (guessing correctly) on each question is 1/5 since there are 5 choices for each question. So, we have n = 45 and p = 1/5.

22. To estimate the probability that the student fails the exam (gets 22 or fewer questions correct), we need to find the cumulative probability from 0 to 22 using the binomial distribution.

[tex]P(X \leq 22) = \sum(k=0\ to\ 22) [nCk * p^k * (1-p)^{(n-k)}][/tex], where nCk is the binomial coefficient.

Probability of getting 22 or fewer questions correct: ≈ 0.1630

23. To calculate the probability that the student gets five or more questions correct, we need to find the cumulative probability from 5 to 45 (the total number of questions).

[tex]P(X \geq 5) = \sum(k=5\ to\ 45) [nCk * p^k * (1-p)^{(n-k)}].[/tex]

Probability of getting five or more questions correct: ≈ 0.9999

24. To calculate the probability that the student gets between 9 and 18 questions correct (both inclusively), we need to find the cumulative probability from 9 to 18.

[tex]P(9 \leq X \leq 18) = \sum(k=9\ to\ 18) [nCk * p^k * (1-p)^{(n-k)}].[/tex]

Probability of getting between 9 and 18 questions correct (inclusive): ≈ 0.7031

Now, let's calculate the mean and variance of the binomial distribution.

The mean of a binomial distribution is given by μ = n * p.

So, the mean is μ = 45 * (1/5) = 9.

The variance of a binomial distribution is given by [tex]\sigma^2 = n * p * (1 - p).[/tex]

So, the variance is [tex]\sigma^2 = 45 * (1/5) * (1 - 1/5) = 36/5.[/tex]

Therefore, the mean of the binomial distribution is 9 and the variance is 36/5.

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To meet your retirement goal of spending $43,000/ year for 17 years, with an interest rate 6%/ year need to save $8,870.71 each year until retirement .

Amount spend = $43,000

Time period = 17 years

Annual interest rate = 6%

To determine how much you must save each year until retirement to meet your retirement goal,

Use the concept of present value (PV) and the formula for annuity payments.

The present value represents the current value of a future sum of money, taking into account the time value of money and the interest rate.

The retirement goal is to have $43,000 per year for 17 years, starting in 34 years, and the interest rate is 6% per year.

Calculate the annual savings required.

Let us break down the calculation step-by-step,

Calculate the present value (PV) of the retirement goal,

PV = Annual amount × [tex][1 - (1 + interest rate)^{(-number of years)}][/tex] / interest rate

⇒ PV = $43,000 ×  [tex][1 - (1 + 0.06)^{(-17)}][/tex] / 0.06

Calculate the present value of the annual savings needed until retirement,

PV = Annual savings ×  [tex][(1 - (1 + interest rate)^{(-number of years)})[/tex]/ interest rate]

Rearranging the formula to solve for the annual savings,

Annual savings = PV × interest rate / [tex][1 - (1 + interest rate)^{(-number of years)}][/tex]

⇒Annual savings = PV × 0.06 / [tex][1 - (1 + 0.06)^{(-34)}][/tex]

Now, let us calculate the annual savings required,

⇒PV = $43,000 × [tex][1 - (1 + 0.06)^{(-17)}][/tex] / 0.06

⇒PV ≈ $43,000 × [1 - 0.337916] / 0.06

⇒PV ≈ $43,000 × 0.662084 / 0.06

⇒PV ≈ $471,500

Annual savings = $471,500 × 0.06 / [tex][1 - (1 + 0.06)^{(-34)}][/tex]

⇒Annual savings ≈ $471,500 × 0.06 / 0.282171

⇒Annual savings ≈ $8,870.71

Therefore, need to save approximately $8,870.71 each year until retirement to meet your retirement goal of spending $43,000 per year for 17 years, assuming an interest rate of 6% per year.

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The correct statement regarding the hypothesis test is given as follows:

Because the P-value is less than α = 0.05, there is convincing evidence of a difference in the distribution of service ratings among all customers who dine at this restaurant during peak and off-peak hours.

The decision regarding the null hypothesis depends on if the p-value is less or more than the significance level:

The significance level for this problem is given as follows:

α = 0.05.

The p-value for this problem is given as follows:

Between 0.005 and 0.01.

As the p-value is less than the significance level, there is enough evidence of a difference, hence the first option is the correct option.

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Answer:

33) The elements of A U B are

c) ( 21,23,24,25,27,29,30)

34) this question answer is

a)(21,27)

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The percentage of youths surveyed that prefer reading electronic books is 54%

The percentage of a number represents a portion or fraction of that number expressed as a percentage. It is often used to describe a proportion or relative value.

To calculate the percentage of a number, you can use the following formula:

Percentage = (Part / Whole) * 100

To determine the percentage of youths that prefer electronic books is;

youths (electronic books) = number of electronic books(youth) / total number of youths.

youths (electronic books) = 40/(40 + 34) * 100

youths (electronic books) = 40/74 * 100

youths (electronic books) = 0.54 * 100

youths (electronic books) = 54%

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The correct answer is option c. 16.8%, which means that I can have an expected return of 16.8%.Let us go through the solution to know how option c. is the correct one.

The expected return of the portfolio can be calculated by weighing the expected returns of each investment based on their respective percentages in the portfolio.

In this case, with 40 percent invested in an investment with an expected return of 12 percent and 60 percent invested in an investment with an expected return of 20 percent, we can calculate the expected return of the portfolio as follows:

Expected Return of Portfolio = (Weight of Investment 1 * Expected Return of Investment 1) + (Weight of Investment 2 * Expected Return of Investment 2)

= (0.40 * 0.12) + (0.60 * 0.20)

= 0.048 + 0.120

= 0.168

Therefore, the expected return of the portfolio is 16.8%. Hence, the correct answer is option c. 16.8%.

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The correct equation that can be used to find the value of x is option 3.To find the correct equation that can be used to find the value of x in the given figure, we need to analyze the angle measurements provided.

In the figure:

∠1 is given as (4x)º

∠2 is given as (5x + 10)º

∠ABC is given as 110º

We know that the sum of the interior angles of a triangle is always 180º. Therefore, the equation that can be used to find the value of x is:

∠1 + ∠2 + ∠ABC = 180º

Substituting the given angle measurements:

(4x)º + (5x + 10)º + 110º = 180º

Simplifying the equation:

9x + 120º = 180º

To find the correct option, we need to check which equation matches the simplified equation 9x + 120º = 180º.

Looking at the given options:

1.4x = 5x + 10

2.4x = 110

3.5x + 10 = 110

4.4x + 5x + 10 = 110

Comparing the options to the simplified equation, we can see that Option 3: 5x + 10 = 110 matches the equation 9x + 120º = 180º.

Therefore, Option 3: 5x + 10 = 110 is the correct equation that can be used to find the value of x.

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The interquartile range (IQR) is the range of values that resides in the middle of the scores. The interquartile range (IQR) contains the second (Q2) and third quartiles (Q3), or the middle half of where data set. Whereas the range is the difference between the maximum and minimum values in a data set, the interquartile range gives the range of the "middle half" of a data set option b) The interquartile range (IQR) covers the middle 50 percent of a data set and is the difference between the third quartile (Q3) and the first quartile (Q1).

b) From the above definition of IQR, the interquartile range covers the middle 50 percent of a data set which is the difference between the third quartile and the first quartile. Therefore, this is the correct option.

The interquartile range (IQR) is a measure of statistical dispersion that represents the range of values within the middle 50% of a data set. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). The IQR provides valuable information about the spread of the data, specifically the range of values where the central bulk of the data lies.

Option a) is incorrect because the median is indeed the middle value of a data set, which corresponds to the 50th percentile, and it is not synonymous with the IQR.

Option c) is incorrect because the IQR is indeed resistant to outliers to some extent, similar to the median. The quartiles (Q1 and Q3) used to calculate the IQR are less affected by extreme values compared to the mean. Therefore, the IQR provides a measure of spread that is less influenced by outliers.

Option d) is incorrect because the mean is the To  value of a data set and is not directly related to the interquartile range.

In summary, option b) accurately describes the interquartile range as the difference between the third quartile and the first quartile, representing the middle 50% of a data set.

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The problem states that the intensity of a sound wave with a frequency of [tex]550 Hz is 7.0x10^-5 W/m^2[/tex]at a distance of 3 meters from the speaker. The task is to determine the intensity of the sound wave at a distance of 12 meters from the speaker.

The intensity of a sound wave decreases as the distance from the source increases. This relationship follows the inverse square law, which states that the intensity is inversely proportional to the square of the distance from the source.

To calculate the intensity at a distance of 12 meters, we can use the inverse square law equation:

[tex]I2 = I1 * (d1^2 / d2^2)[/tex]

I1 is the initial intensity [tex](7.0x10^-5 W/m^2)[/tex]

d1 is the initial distance (3 meters)

d2 is the final distance (12 meters)

I2 is the final intensity (what we need to find)

Plugging in the values into the equation:

[tex]I2 = (7.0x10^-5 W/m^2) * (3^2 / 12^2)[/tex]

[tex]= (7.0x10^-5 W/m^2) * (9 / 144)= 4.375x10^-6 W/m^2[/tex]

Therefore, the intensity of the sound wave at a distance of 12 meters from the speaker is approximately [tex]4.375x10^-6 W/m^2.[/tex]

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Poor road conditions, a slippery surface, or the undertow of the ocean are examples of the following type of factors that may cause injury are  human behavior, awareness, and response

Let's consider poor road conditions as an example. When roads are in a state of disrepair, they may contain potholes, loose gravel, or uneven surfaces. To evaluate the risk of injury, we can assign a probability value to the occurrence of an injury given the presence of poor road conditions. This probability could be denoted as P(injury|poor road conditions).

Similarly, a slippery surface, such as a wet floor or icy pavement, can also increase the chances of injury. By assigning a probability value to the event of injury given a slippery surface, we can express it as P(injury|slippery surface).

Lastly, the undertow of the ocean refers to a strong current beneath the water's surface that can pull swimmers away from the shore. To analyze the risk of injury in this scenario, we can again assign a probability value to the event of injury given the presence of an undertow, represented as P(injury|undertow).

To further understand the overall risk, we can consider the joint probability of multiple factors occurring simultaneously. For example, if both poor road conditions and a slippery surface are present, we can calculate the joint probability of injury as P(injury| poor road conditions and slippery surface).

This joint probability provides insight into the combined impact of these factors on the likelihood of injury.

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Your father invested $7,000.00 in the municipal bond account and $18,000.00 in the mutual fund account.

Total investment amount = $25,000

Interest earned from the municipal bond account = 3% of X

Interest earned from the mutual fund account = 9% of Y

Total interest earned for the year = $1830.00

We can set up a system of equations based on the given information

Equation 1: X + Y = $25,000 (Total investment amount)

Equation 2: 0.03X + 0.09Y = $1830.00 (Total interest earned)

To solve this system of equations, we can use the substitution or elimination method.

Using the substitution method, we can isolate one variable from Equation 1 and substitute it into Equation 2:

From Equation 1, we have X = $25,000 - Y

Substituting X in Equation 2

0.03($25,000 - Y) + 0.09Y = $1830.00

$750 - 0.03Y + 0.09Y = $1830.00

0.06Y = $1830.00 - $750

0.06Y = $1080.00

Y = $1080.00 / 0.06

Y = $18,000.00

Substituting Y back into Equation 1:

X + $18,000.00 = $25,000.00

X = $25,000.00 - $18,000.00

X = $7,000.00

Therefore, your father invested $7,000.00 in the municipal bond account and $18,000.00 in the mutual fund account.

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The rule of thumb for determining the basic pattern of a culture that involves understanding surface and deep cultures is known as the iceberg principle.

The iceberg principle is a rule of thumb used in cultural analysis to understand the basic pattern of a culture. It suggests that culture can be likened to an iceberg, where only a small portion is visible above the surface while the majority remains hidden beneath. The surface culture refers to the visible aspects of a culture, such as language, clothing, food, and visible behaviors. These elements are easily observed and often represent the superficial aspects of a culture.

On the other hand, deep culture refers to the underlying values, beliefs, norms, and interest that are not readily apparent but shape the behavior and actions of individuals within a culture. Deep culture encompasses aspects such as worldview, attitudes, social structures, and implicit cultural rules.

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The energy required to raise an iron atom in a solid from its vibrational ground state to its vibrational first excited state can be calculated using the formula for the energy of a harmonic oscillator.

In this case, the interatomic spring stiffness of iron is given as 48 N/m. To calculate the energy required, we need to determine the displacement (x) from the vibrational ground state to the vibrational first excited state.

The energy difference between the two states corresponds to the potential energy stored in the spring. The vibrational ground state is when the atom is at its equilibrium position, and the vibrational first excited state is when the atom is displaced from the equilibrium position.

To find the displacement, we can consider the fact that the displacement for the first excited state is typically smaller than the equilibrium position. Let's assume a small displacement of x meters.

Plugging the values into the energy (E) required to raise an iron atom from its vibrational ground state to its vibrational first excited state is calculated as follows:

E = [tex](1/2) * (48 N/m) * (x^2)[/tex]

Since the specific displacement (x) is not provided in the question, we cannot calculate the precise energy value.

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Answer:

a. Effectué.

b. La médiatrice (d) est la droite qui coupe le segment [MN] en son milieu et qui est perpendiculaire à ce segment. Pour la tracer, on trace un cercle centré

Many psychologists consider the distinguishing feature of adolescent thought to be the ability to think in terms of abstract concepts or hypothetical situations.

These cognitive abilities play a crucial role in adolescent development, facilitating problem-solving, decision-making, and the exploration of identity and future possibilities.

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Answer:

5

Step-by-step explanation:

45/9 equals 5 so the whole number would be 5

Calculators bought to help individuals complete their personal federal income tax forms is not a business product.

A business product refers to goods or services that are purchased by businesses or organizations to be used in their operations or to produce other goods and services. It excludes products intended for personal use or consumption.

In the given options, calculators bought to help individuals complete their personal federal income tax forms stands out as not being a business product. Calculators purchased for personal use, even if they are used for a specific task related to taxes, are not considered business products because they are intended for personal use rather than for business operations or production.

On the other hand, paper, pens, and tape to be used in an office, chips to be integrated into components for personal computers, marketing consulting services to aid a company in marketing a new product, and oil to be refined into fuel are all examples of business products.

Therefore, calculators bought for personal use is the option that does not represent a business product in the given choices.

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The volume of the rectangular prism is 96 cubic yards

A prism is a three-dimensional geometric shape that has two congruent parallel bases connected by rectangular or parallelogram-shaped faces. A rectangular prism is a specific type of prism where the bases are rectangles and the lateral faces are also rectangles.

To find the volume of a rectangular prism, we multiply the length, width, and height. In this case, the rectangular prism has a square base with a length of 4 yards and a height of 6 yards. Since the base is a square, its length is equal to its width. Therefore, the width of the base is also 4 yards.

The volume of the rectangular prism is calculated as follows: Volume = Length × Width × Height

= 4 yards × 4 yards × 6 yards

= 16 yards² × 6 yards

= 96 yards³

Hence, the volume of the rectangular prism is 96 cubic yards. The explanation shows that we multiplied the dimensions to obtain the volume, taking into account the properties of the square base and the given height.

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The eigenvalues of matrix A, which represents the building's dynamics, determine the frequencies of oscillation. The building's safety from a period-2 earthquake depends on the eigenvalues of A.

If the matrix K is multiplied by 10, making the building stiffer, the eigenvalues and frequencies will change. To put the building in the danger zone, the matrix K would need to be multiplied by a factor that significantly increases the eigenvalues.

To find the matrices M, K, and A, we need more information regarding the building's properties, such as the mass of each floor and the proportionality constants between floors. Without these values, it's not possible to provide accurate calculations for eigenvalues, frequencies, and periods of oscillation. However, I can explain the general concepts.

Matrix M represents the mass distribution in the building, while matrix K represents the stiffness. Matrix A is obtained by taking the inverse of M and multiplying it by K. The eigenvalues of A represent the natural frequencies of oscillation for the building. The frequencies can be calculated from the eigenvalues using the equation f = sqrt(λ/2π), where f is the frequency and λ is the eigenvalue.

The building's safety from a period-2 earthquake depends on the natural frequencies. If the earthquake's frequency matches one of the building's natural frequencies, resonance can occur, potentially causing significant damage. If the building's natural frequencies are well-separated from the earthquake's frequency range, it will likely be safe.

If the matrix K is multiplied by 10, the building becomes stiffer. This would lead to changes in the eigenvalues and consequently the frequencies of oscillation. The exact effect depends on the specific values of the proportionality constants.

To put the building in the danger zone, the matrix K would need to be multiplied by a factor that significantly increases the eigenvalues. This would require a substantial increase in stiffness, potentially beyond realistic limits, to make the building susceptible to dangerous resonance with seismic activity.

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The number of turns it will take for the gears to be back in their initial position would be 4 turns of the 18-teeth gear and 3 turns of the 24-teeth gear.

In order to ascertain the quantity of turns requisite to revert to the original state, it is imperative to ascertain the least common multiple (LCM) of the two numerical values. This is because the LCM is indicative of the number of teeth that both gears would mandatorily need to rotate, thus aligning themselves in the same manner as their original orientation.

The least common multiple of 24 and 18 is 72.

This means that the 24 - teeth gear would need to turn:

= 72 / 24

= 3 times

For the 18 teeth :

= 72 / 18

= 4 times

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The maximizing value of x is approximately 2.

What is the maximum value of x that maximizes the utility function [tex]U(x, y) = \sqrt{x} y,[/tex] given the budget constraint 10x + 9y ≤ 35?

The maximum value of x, rounded to one decimal place, that maximizes the utility function is approximately 2.0. This value is obtained by solving the optimization problem using Lagrange multipliers and considering the budget constraint.

To maximize the utility function subject to the budget constraint 10x + 9y ≤ 35, we can use the method of Lagrange multipliers. We want to maximize the function U(x, y) subject to the constraint 10x + 9y ≤ 35.

The Lagrange function is defined as [tex]U(x, y,\lambda) = \sqrt{x} y+\lambda(35-10x-9y),[/tex], where λ is the Lagrange multiplier.

To find the maximum, we need to find the values of x, y, and λ that satisfy the following equations:

[tex]1.\frac{\delta L}{\delta x }= 0\\\\2.\frac{\delta L}{\delta y}= 0\\[/tex]

3.Constraint equation: 10x + 9y = 35

Taking partial derivatives and setting them equal to zero:

[tex]1.\frac{\delta L}{\delta x }= \frac{1}{2}\sqrt{y}+ \lambda(-10) = 0\\\\2.\frac{\delta L}{\delta y }= \frac{1}{2}\sqrt{x} +\lambda(-9) = 0[/tex]

Solving these equations, we get:

[tex]\sqrt{y }= 5\lambda\\\\\sqrt{x} = 4.5\lambda[/tex]

Squaring both equations:

[tex]y = 25\lambda^2\\\\x = 20.25\lambda^2[/tex]

Substituting these values into the constraint equation:

[tex]10x + 9y = 10(20.25\lambda^2) + 9(25\lambda^2)\\ = 350\lambda^2[/tex]

Setting this equal to 35:

[tex]350\lambda^2 = 35[/tex]

Simplifying, we find:

[tex]\lambda^2 = 0.1[/tex]

Taking the square root of both sides:

[tex]\lambda = \pm\sqrt{0.1}[/tex]

Since λ must be positive, we take [tex]\lambda= \sqrt{0.1 }= 0.3162.[/tex]

Substituting this value into[tex]x = 20.25{\lambda}^2[/tex], we get:

[tex]x = 20.25(0.3162)^2= 2.03[/tex]

Therefore, rounding to one decimal place, the maximizing value of x is approximately 2.

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The list of numbers ordered from least value to greatest value are :

[tex]\frac{18}{5}[/tex] , 3.71, [tex]\frac{57}{15}[/tex], [tex]\sqrt{17}[/tex] .

How can we determine the missing number in a list of numbers ordered from least to greatest?

By examining the given list of numbers and identifying the pattern or logic behind their order, we can determine the range within which the missing number should fall. Subsequently, we can evaluate the given answer choices and select the option that fits within the determined range and maintains the order of the numbers from least to greatest.

To determine which number could be the missing number, we can examine the given list of numbers and look for a pattern or logic based on their order.

The list of numbers provided is: [tex]\frac{18}{5}[/tex], 3.71, [missing number], [tex]\sqrt{17}[/tex]

We can observe that the missing number should fall between 3.71 and [tex]\sqrt{17}[/tex].

Now, let's evaluate the given answer choices:

A) 4.5:

This number is greater than [tex]\sqrt{17}[/tex], so it cannot be the missing number.

B) 3.8%:

This is a percentage and does not fit into the numerical pattern of the other numbers. It cannot be the missing number.

C) [tex]\frac{57}{15}[/tex]:

This fraction is greater than 3.71 and falls between 3.71 and [tex]\sqrt{17}[/tex]. It is a valid possibility for the missing number.

D) (3.9)²:

This is equal to 15.21, which is greater than [tex]\sqrt{17}[/tex]. It cannot be the missing number.

Based on the options provided, the missing number could be C) [tex]\frac{57}{15}[/tex], as it falls within the range of the given numbers and maintains the order from least to greatest.  

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We can see here that the volume of such solid is: 1/12m³.

Volume refers to the amount of space occupied by an object or substance. It is a physical quantity that describes the three-dimensional size of an object or the capacity of a container.

We can actually deduce here that the area of the base of the solid is (1/2)(1)(1) = 0.5 square meters.

The side length of each square cross section is equal to the height of the solid at that point.  Let h be the height of the solid.  The volume of each square cross section is

(h/2)² = h²/4 cubic meters.

The solution is given below.

[tex]\int\limits^1_0 {\frac{h^{2} }{4} } \, dh = \frac{h^{3} }{12} |^{1} _{0} = \frac{1}{12} =\frac{1}{12} m^{3}[/tex]

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