3. For eacht>0, suppose the number of guests arriving at a bank during the time interval[0,t)follows a Poisson(λt). a. Denote byXthe arrival time of the first guest. What is the distribution ofX? b. Denote byYthe arrival time of the second guest. What is the distribution ofY?

Answer:51

Step-by-step explanation:

For the given system of linear inequalities (53, 4) represents 53 batches of soap and 4 batches of lotion were produced.

An equation with a linear expression and a relational operator is referred to as a linear inequality. Regions in a coordinate plane or space that fulfil a linear inequality are defined by the inequality. A linear inequality in two dimensions defines a half-plane, which, depending on the inequality, is either above or below a line. A linear inequality in three dimensions defines a half-space that, depending on the inequality, is either above or below a plane. In optimization situations, when the objective is to determine the greatest or lowest value of a linear function under a set of constraints represented by linear inequalities, linear inequalities are frequently utilised.

The given system of inequalities is:

5x + 15y ≤ 325

20x + 35y ≤ 1200

Here, x is the number of batches of soap and y is the number of batches of lotion.

Thus, (53, 4) represents 53 batches of soap and 4 batches of lotion were produced.

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The numbers ordered from least to greatest are 0.721, 73/100, and 0.75.

0.75, 0.721, 73/100

we can convert the fraction 73/100 to a decimal by dividing 73 by 100, which gives us 0.73.

0.721 < 0.73 < 0.75

"Least" is a mathematical term used to refer to the smallest value in a given set of numbers or a range of values. It is the opposite of the term "greatest," which refers to the largest value in the set. To find the least value in a set of numbers, you can sort them in ascending order and select the first or smallest number. Alternatively, you can use mathematical formulas or functions such as the minimum function to determine the least value.

In algebra, finding the least common multiple (LCM) or least common denominator (LCD) involves identifying the smallest multiple or denominator that two or more numbers or expressions have in common. This is essential in simplifying and solving complex equations and expressions. In geometry, the least distance between two points is the straight line or path that connects them and is the shortest possible route between them. This concept is fundamental in navigation and optimization problems.

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False. A probability distribution for a discrete variable is not exclusive, collectively exhaustive list of numerical outcomes for that variable and the probability of occurrence associated with each outcome.

A probability distribution for a discrete variable is a list of all possible values that the variable can take on, along with the probability of each value occurring. The values must be collectively exhaustive (meaning they include all possible outcomes) and mutually exclusive (meaning that each outcome cannot occur at the same time as any other outcome). However, the numerical outcomes do not have to be exclusive, as they can have the same probability of occurring. For example, a coin toss has two possible outcomes (heads and tails) with equal probability, and a dice roll has six possible outcomes with equal probability. These probabilities can be represented using a probability distribution.

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17. The population of interest is U.S. adults (age 18 and over).
18. The sample being used is 1,012 randomly selected U.S. adults (age 18 and over).
19. The population parameter of interest is the percentage of U.S. adults (age 18 and over) who are dissatisfied with the quality of education students receive in kindergarten through grade 12. The correct notation for this parameter is p and the relevant statistic is 53%.
20. The interval estimate for the parameter of interest is 49% - 57%, which indicates that between 49% and 57% of U.S. adults (age 18 and over) are dissatisfied with the quality of education students receive in kindergarten through grade 12.

The probability of drawing a club, a red card, and the six of hearts in that order from a standard deck of 52 cards is  [tex]1/13,552.[/tex]

This is because the probability of drawing a club is 1/4, and the probability of drawing a red card is 1/2, and the probability of drawing the six of hearts is 1/52.
Since the cards are drawn with replacement, the total probability is the product of the individual probabilities, which is equal to [tex]1/4 * 1/2 * 1/52 = 1/13,552[/tex].
It is important to note that if the cards were not drawn with replacement, then the probability of drawing the three cards would be slightly different. The total probability would be equal to [tex]1/4 * 1/2 * 1/51 = 1/12,600.[/tex]
It is also important to note that since this is a probability question, the answer can be expressed as a decimal or percentage. In decimal form, the probability of drawing the three cards is 0.000074, and in percentage form, the probability of drawing the three cards is 0.0074%.

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The corresponding sides and angles of two polygons ABCD and ZYXW must be proportionate if they are identical.

With straight sides around its perimeter, a polygon is really a circular, two-dimensional, flat of planar structure. Its sides are straight with no bends. Another term for a polygon's sides is its edges. The points at which two sides of a polygon converge are known as its vertices (or corners). These are numerous examples of polygonal geometry.

A closed polygon is a form with more than three sides. A quadrilateral is a 4-sided polygonal shape. A quadrilateral is any closed 4-sided form, however there are six particular quadrilaterals with distinctive characteristics that give them their own names.

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Among the given factors, global competition does not contribute to the quest for quality. The correct answer is Option A.

In today's business environment, quality has become an important factor that can make or break a company's success. A successful firm must focus on the quality of the products and services they offer, as this can help them maintain their competitive advantage and ensure customer loyalty.

Quality is important for a variety of reasons, including customer satisfaction, reduced costs, increased productivity, and increased revenue. When firms focus on quality, they can provide better products and services to their customers, which can lead to increased customer loyalty and repeat business. This can help firms build a strong reputation in the market and maintain a competitive advantage.

Global competition has made it necessary for firms to focus on quality to maintain their competitive advantage. When firms face global competition, they need to ensure that their products and services are of high quality to compete effectively in the global market. High-quality products and services can help firms differentiate themselves from their competitors and gain a competitive advantage. This can help firms increase their market share and revenue.

Several factors contribute to the quest for quality. These include:

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The equation of the tangent line at x = 16 is therefore :y - 2 = (1/64)(x - 16)Simplifying, we get :y = (1/64)x + 1Using this equation, we can estimate the value of 12^1/4:y = (1/64)(12) + 1 = 49/32Therefore, the estimate for 12^1/4 using linear approximation is 49/32.

approximation is an approach used to estimate the value of a function at a point near a known point by using the linear equation tangent to the function at that point.

This technique is commonly used in physics, engineering, economics, and other fields where mathematical models are used to describe real-world phenomena.

To estimate 12^1/4 using linear approximation, we first need to find the equation of the tangent line at the point of interest, which is x = 16 (since 16^4 = 2^16 = 65536).

Then, we can use the equation of the tangent line to estimate the value of the function at a nearby point, which in this case is x = 12.

We can find the equation of the tangent line using the derivative of the function :f(x) =[tex]x^1/4f'(x) = (1/4)x^-3/4At x = 16:f(16)[/tex] = 2f'(16) = (1/4)(16)^-3/4 = 1/64

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Step-by-step explanation:

The formula to solve for the area of a circle is given by,

A

=

1

4

π

d

2

where

d

is the diameter.

Substituting the given, we have

A

=

1

4

×

3.14

×

(

3

ft

)

2

=

1

4

×

3.14

×

9

ft

2

A

=

7.065

ft

2

Next, solve for the circumference.

The formula for the circumference of a circle is written as,

C

=

π

d

where

d

is the diameter.

Substituting the given, we have

C

=

3.14

×

3

ft

C

=

9.42

ft

Hence, the

Area

=

7.065

ft

2

and the

Circumference

=

9.42

ft

.

Answer:

A = 19.625 ft²

C = 15.7 ft

Step-by-step explanation:

The equation for the area of a circle is πr², where r is the radius.

The radius is half of the diameter, so the radius here is 2.5.

Plug the radius into the equation and substitute 3.14 for π:

A  = 3.14 x 2.5²

2.5² = 2.5 x 2.5 = 6.25

A = 3.14 x 6.25 = 19.625

Area = 19.625 ft²

The equation for the circumference of a circle is 2πr.

Plug the radius into the equation and substitute 3.14 for π:

C = 2 x 3.14 x 2.5

C = 15.7

Circumference = 15.7 feet.

The alternative hypothesis in this case is that the variance of the population is significantly greater than 0.003. Therefore, the correct answer is option A, S^2>0.003.

The variance is a term used in statistics that refers to how far the numbers in a data set are spread out. A set of numbers with a large variance has a wide distribution, while a set with a small variance has a narrow distribution.

The formula for the variance is as follows:S² = ∑(X - μ)² / Nwhere:∑ = the sum ofX = each individual data pointμ = the population meanN = the number of data points in the population. The null hypothesis in this case would be that the variance of the population is not significantly different from 0.003. The alternative hypothesis, on the other hand, is that the variance is significantly greater than 0.003. This is what option A suggests.

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Given a normal distribution is observed from the number of points per game for a certain basketball player. The mean for this distribution is 20 points and the standard deviation is 3 points.Using the empirical rule for normal distributions, the probability that in a randomly selected game the player scored less than 26 points is required .Empirical Rule: For a normal distribution with a mean µ and a standard deviation σ, the probability of an observation being within k standard deviations of the mean is approximately:•

68% of the observations fall within one standard deviation of the mean.• 95% of the observations fall within two standard deviations of the mean.• 99.7% of the observations fall within three standard deviations of the mean.Here, the mean is 20 points and the standard deviation is 3 points. We need to find the probability of getting less than 26 points.z-score = (x - µ) / σ = (26 - 20) / 3 = 2σ = 2According to the empirical rule, 95% of observations fall within 2 standard deviations of the mean.So, the probability that the player scored less than 26 points is 95%.Therefore, the final answer is 95% rounded to one decimal place. Answer: 95%.

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The probability of reaching into the box and randomly drawing a chip number that is smaller than 212 is 0.9378

First, we should find the total number of chips in the box. The box contains 225 chips numbered from 1 to 225. Therefore, the probability of reaching into the box and randomly drawing a chip number that is smaller than 212 is 211/225.

The probability can be expressed as a simplified fraction or a decimal rounded to four decimal places. The probability is rounded to four decimal places is 0.9378.

The probability of drawing a chip number that is smaller than 212 from the box is 211/225 or 0.9378 (rounded to four decimal places).

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Given that he is from the Dominican Republic, the likelihood that the chosen player is a pitcher is roughly 0.053.

The study of arbitrary events or experiments falls under the purview of probability, a subfield of mathematics. A value between 0 (impossible) and 1 is used to estimate the possibility or chance of an event occurring (certain). Several disciplines, including science, engineering, economics, finance, and more, utilise the idea of probability. It is frequently determined by dividing the number of positive events by the total number of outcomes that could occur.

given

(a) To find P, we can utilize the complement rule (T&D). The addition to T&D is the possibility that the chosen player is a pitcher or a Dominican. We thus have:

The equation P(T&D) = 1 - P(T'UD') = 1 - P(T') - P(D') + P(T'D')

P(T), P(D), and P(TD) are all provided as 0.42, 0.105, and 0.056 respectively. As a result, we may determine the complements' probabilities:

P(T') = 1 - P(T) = 1 - 0.42 = 0.58 P(D') = 1 - P(D) = 1 - 0.105 = 0.895 P(T'D') = P(TD)' = 1 - (P(T) + P(D) - P(TD)) = 1 - (0.471 + 0.42 + 0.105 - 0.056)

By replacing these values, we obtain:

P(T&D) = 1 - 0.58 - 0.895 + 0.471 = 0.046

As a result, there is a 0.046 percent chance that the chosen player is a non-pitcher from outside the Dominican Republic.

(b) In order to determine the likelihood that the chosen player is a pitcher given that he is from the Dominican Republic, we must first determine P(P|D). Bayes' Theorem may be applied:

P(P|D) equals P(D|P)P(P)/P (D)

P(D) = 0.105 and P(TD) = 0.056 are the values provided. Therefore,

P(P) is defined as P(TD') / P(D') = 0.056 / 0.895 0.0626.

P(D|P) is equal to P(T|D) / P(P) = 0.056 / 0.0626 0.895.

By replacing these values, we obtain:

P(P|D) = (0.895)(0.0626) / 0.105 ≈ 0.053

Given that he is from the Dominican Republic, the likelihood that the chosen player is a pitcher is roughly 0.053.

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The complete question is :-   Of all major league baseball players on 2008 Opening Day rosters:

42% are pitchers (call this event T)

10.5% are from the Dominican Republic (call this event D)

5.6% are pitchers from the Dominican Republic

A player is selected at random.

(a) Find P(T&D), the probability that that the selected player is a non-pitcher who is not from the Dominican.

(b) Given the information that the selected player is from the Dominican Republic, what is the probability that he is a pitcher?

(c) Given the information that the selected player is a non-pitcher, what is the probability that he is not Dominican?

Answer:

-

(x + is what you are looking for is the answer

The statement that is not true of the test data approach in a test of a computerized accounting system is B) Test data should consist of data related to all controls prevalent in the organization.

This statement is incorrect because the test data approach aims to test specific controls that the auditor wishes to rely on rather than all controls prevalent in the organization. The test data approach involves the creation of a set of test transactions that are processed by the client's computer program under the auditor's control.

The results of the test data are used to determine whether the application and general controls are functioning properly. By using this approach, the auditor can gain assurance that the system is functioning as intended and identify any control weaknesses that need to be addressed.

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The cost of each nachos is $2.50 and the cost of each water bottle is $1.50.

What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let x be the cost of each water bottle and y be the cost of each nachos.

Two bottled water and an order of cheese nachos costs $5.50.

So, 2x+y=5.50 -------(I)

Three bottled water and two orders of cheese nachos costs $9.50​

3x+2y=9.50 -------(II)

Multiply equation (I) by 2, we get

4x+2y=11 -------(III)

Subtract equation (II) from equation (III), we get

4x+2y-(3x+2y)=11-9.50

x=$1.50

Substitute x=1.50 in equation (I), we get

2(1.50)+y=5.50

y=$2.50

Therefore, the cost of each nachos is $2.50.

The coordinate matrix LFE of L relative to the ordered bases E and F is given by:

LFE=12,3,0,12,3,0,0

LFE =

[[5, 1, 3, 3],

[0, 0, 3, 0],

[0, 0, 0, 0]]

This matrix can be obtained by computing the entries of LFE in terms of the components of L with respect to the basis E and then expressing those components with respect to the basis F. The elements of LFE are computed as follows:

LFE[1,1] = L(e1) = = 5 + 1 + 3 + 3 = 12

LFE[1,2] = L(e2) =  = 0 + 0 + 3 + 0 = 3

LFE[1,3] = L(e3) =  = 0 + 0 + 0 + 0 = 0

LFE[2,1] = L(f1) =  = 5 + 1 + 3 + 3 = 12

LFE[2,2] = L(f2) = = 0 + 0 + 3 + 0 = 3

LFE[2,3] = L(f3) = = 0 + 0 + 0 + 0 = 0

LFE[3,1] = L(f4) =  = 0 + 0 + 0 + 0 = 0

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The probabilities of exactly two students choosing Duke, NC State, and Hogwarts-NC are approximately 0.008, 0.008, and 0.327, respectively.

Let X be the number of students who choose UNC, and Y be the number of students who choose Duke. Then X follows a binomial distribution with n = 5 and p = 0.6, and Y follows a binomial distribution with n = 5 and p = 0.1.

(a) The event a 2 UNC corresponds to choosing exactly 2 out of 5 students to attend UNC. This can be written as:

A UNC = {X = 2}

The indicator random variable for a 2 UNC is

UNC = 1, if X = 2 , 0, otherwise

(b) Similarly, the events  a 2 Duke, a 2 NCS, and a 2 Hogwards-NC correspond to choosing exactly 2 out of 5 students to attend Duke, NC State, and Hogwarts-NC, respectively. These can be written as:

A 2 Duke = {Y = 2}

A 2 NCS = {Z = 2}, where Z is the number of students who choose NC State

A 2 HCS = {W = 2}, where W is the number of students who choose Hogwarts-NC

The indicator random variables for these events are:

2 DUKE= 1, if Y = 2 , 0, otherwise

2 NCS = 1, if Z = 2 , 0, otherwise

2 HNC = 1, if W = 2 , 0, otherwise

(c) To find the probability that at least two students choose UNC, we can use the complement rule:

P(at least 2 students choose UNC) = 1 - P(less than 2 students choose UNC)

= 1 - P(X = 0) - P(X = 1)

= 1 - (0.4)⁵ - 5(0.6)(0.4)⁴

≈ 0.848

(d) To find the probability that exactly 2 students choose UNC and 2 students choose Duke, we can use the joint probability:

P(2 students choose UNC and 2 students choose Duke) = P(X = 2)P(Y = 2)

= (0.6)²(0.4)³(0.1)²(0.9)³

≈ 0.0003456

For five graduating high school students from five different high schools in NC who have all been accepted to four colleges (UNC, Duke, NC State, and Hogwarts-NC), the probability that exactly two out of the five students choose UNC is approximately 0.259. Similarly, the probabilities of exactly two students choosing Duke, NC State, and Hogwarts-NC are approximately 0.008, 0.008, and 0.327, respectively.

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Answer:

Let's call the tens digit of the two-digit number "t" and the units digit "u".

From the problem statement, we know that:

t = u - 5 (the tens digit is 5 less than the units digit)

10t + u = 3(t + u) + 5 (the number is five more than three times the sum of its digits)

We can use the first equation to substitute for t in the second equation:

10(u - 5) + u = 3((u - 5) + u) + 5

Simplifying and solving for u, we get:

10u - 50 + u = 6u - 9

Simplifying further, we get:

5u = 41

Therefore, u = 8.2

Since u must be a whole number, we round up to 9. Then, we can use the first equation to find that t = u - 5 = 4.

So the two-digit number is 49 (with t=4 and u=9).

We can check if it satisfies the second equation:

10t + u = 10(4) + 9 = 49

3(t + u) + 5 = 3(4 + 9) + 5 = 46

49 is indeed five more than three times the sum of its digits (4 + 9), so our solution is correct.

Therefore, the two-digit number is 49.

The tens digit is 3 and the unit digit is 8. So, the number is 38.

Important information:

Let x be the tens digit and y be the unit digit.

The tens digit is 5 less than the unit digit.

[tex]x=y-5[/tex]          ...(i)

The number itself is five more than three times the sum of its digits.

[tex]10x+y=3(x+y)+5[/tex]

[tex]10x+y=3x-3y=5[/tex]

[tex]7x-2y=5[/tex]          ...(ii)

Using (i) and (ii), we get

[tex]7(y-5)-2y=5[/tex]

[tex]7y-35-2y=5[/tex]

[tex]5y=40[/tex]

[tex]y=8[/tex]

Substitute this value in (i).

[tex]x=8-5[/tex]

[tex]x=3[/tex]

Therefore, the number is 38.

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The perimeter of the triangle AABC is 19.27 m.

In order to solve this we first have to create a triangle rectangle, check the image attached to understand it better, and with that we use law of sines in order to calculate the other sides of the triangle:

As you can see we know that the hypothenuse is 8 m, and we have both angles, so for the angle that is opposed to the 50º angle we will use [tex]8cos(50)=5.1423 \ m[/tex].

For the side that is opposed to the 40º angle we will use [tex]8cos(40):6.1283m[/tex]

SO to calculate the perimeter we just add the three sides:

[tex]5.1423 + 6.1283 + 8= 19.27[/tex]

Therefore, The perimeter of the triangle AABC is 19.27 m.

Let's assume that the measure of angle BAC is less than or equal to the measure of angle ABC.

Since AB = AC, then angles BAC and BCA are also equal. Let's denote the measure of angle BAC as x, then the measure of angle ABC and angle BCA is also x.

According to the triangle inequality theorem, the sum of any two sides of a triangle must be greater than the third side. In our case, we have:

AB + BC > AC

AB + 24 > AC

2AB + BC > 2AC

2AB + 24 > 2AC

2AB > 2AC - 24

AB > AC - 12

Since AB = AC, then AC - 12 < AB = AC, which means AC < AC + 12. This is a contradiction, and therefore our assumption that the measure of angle BAC is less than or equal to the measure of angle ABC is false.

Therefore, we can conclude that Angle BAC > Angle ABC.

a) A greedy algorithm is an approach to problem-solving that makes the locally optimal choice at each step with the hope of finding a globally optimal solution.

This means that at each step, the algorithm chooses the best available option without considering the future consequences of that decision.

(b) An example of a greedy algorithm that produces an optimal solution is the activity selection problem.

Given a set of activities with their start and end times, the goal is to select the maximum number of non-overlapping activities. The greedy algorithm sorts the activities by their end times and selects the first non-overlapping activity.

It then repeats this process with the remaining non-overlapping activities until all activities have been selected. This algorithm produces an optimal solution because selecting the activity with the earliest end time leaves the maximum amount of time available for the remaining activities.

(c) An example of a greedy algorithm that does not always produce an optimal solution is the knapsack problem.

Given a set of items with their weights and values, the goal is to maximize the value of items that can be carried in a knapsack of a given weight capacity. The greedy algorithm selects items based on their value-to-weight ratio until the knapsack is full.

However, this algorithm can fail to produce an optimal solution if there are items with high value but large weight, which cannot fit in the knapsack after the algorithm selects several low-value items with small weight. In such cases, a more sophisticated algorithm is required to find the optimal solution.

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The approximate circumference of spaceship Earth is 160m

The formula for calculating the volume of a sphere is given as;

V = 4/3 πr³

Given that;

Now, substitute the values

65417 = 1. 3 ×3.14r³

Multiply the values

65417 = 4. 082r³

Make r the subject

r³ = 16025. 722

Find the cube root

r = 25. 2m

The circumference is expressed as;

Circumference = 2πr

Substitute the values, we have;

Circumference = 2× 3.14 × 25.2

Circumference = 160 m

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Answer:

4(h+3) = 20

Step-by-step explanation:

Para empesar, disculpa si mi español no es perfecto, pero igual me encataria a ayudarte.

Pues, se sabe que estas temporadas de practica vienen en groupitos de horas a la ves. Dijo que cada dia, ella practica por alguans horas, las cuales suman a 20 en total. Como la problema nos dice que ella practica 4 veces a la semana, tienemos 4 de estos groupitos de horas. Por eso, la respuesa es 4(h+3) = 20, porque ella va por estas 4 temporadas de practicar 3 horas en la manana y quien sabe cuantos en la tarde. Addicionalmente, este"quien sabe" numero de horas se representa con h.

The limit of the expression is 7.

The expression to find the limit is given by;Lim (6x + √36x² - x) x → -∞To solve this limit, we treat the expression as a fraction whose denominator is 1, and rationalize the numerator as follows;Lim (6x + √36x² - x) x → -∞Lim [{(6x + √36x² - x) × (6x - √36x² - x)} ÷ (6x - √36x² - x)] x → -∞Lim [(6x)² - (x)²] ÷ [(6x - x) - √36x²] x → -∞Lim (36x² - x²) ÷ 5x x → -∞Lim x² (36 - 1) ÷ 5x x → -∞Lim 35x ÷ 5 x → -∞7For a graph, we can plot the expression as follows;y = 6x + √36x² - xy = 6x - √36x² - xUsing the graphing utility, we can see that as x approaches negative infinity, y approaches 7, as we calculated above. Thus, the limit of the expression is 7.

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Answer:

Give a brainliest answer

The rate of change of an edge of the cube is approximately 0.048 m/min when the volume is exactly 27 cubic meters.

To find the rate of change of an edge of the cube, given that the volume decreases at a rate of 4 cubic meters per minute when the volume is exactly 27 cubic meters, follow the solution below:Let the length of the edge of the original cube be L.Let the volume of the original cube be V, such that V = L³.The rate of change of volume is given as -4 m³/min; the negative sign is used to indicate a decrease in volume, and this is obtained when the derivative of the volume with respect to time is multiplied by the negative sign.Let V₀ be the original volume of the cube, and V₁ be the volume after t minutes. Thus, V₁ = V₀ - 4t m³. We are told that V₁ = 27 m³, hence:V₀ - 4t = 27 ⇒ V₀ = 27 + 4t m³Substituting V₀ in terms of t into the expression V = L³, we have:L³ = 27 + 4tTaking the derivative of both sides with respect to t, we have:3L²(dL/dt) = 4 ⇒ dL/dt = 4/(3L²)Substituting L from the expression L³ = 27 + 4t, we have:L = (27 + 4t)^(1/3)Therefore, the rate of change of an edge of the cube is given by the derivative of L with respect to t:dL/dt = 4/(3L²) = 4/(3(27 + 4t)^2/3) ≈ 0.048 m/min (to 3 decimal places)Answer: The rate of change of an edge of the cube is approximately 0.048 m/min when the volume is exactly 27 cubic meters.

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Answer:

<abc

Step-by-step explanation:

Leo has 38 toy troops as there aren't enough for him to line them up four by four.

The equal symbol (=) is frequently used to separate the expressions in equations. The left-hand side (LHS) and right-hand side (RHS) of the equation, respectively, are the formulas on either side of the equal sign. If you replace the variable(s) in both expressions with the same value, they will have the same value, as indicated by the equal symbol, which denotes that the two sides are equivalent.

given

We'll name Leo's collection of toy soldiers "x" the amount.

Finally, we know that the remainder is 3 when x is split by 5. Thus, x Plus 2 must be a multiple of 5.

Using this knowledge, we can construct the following system of equations:

x = 4n (where n is a positive number) (where n is a positive integer)

x + 1 = 7m (where m is a positive number) (where m is a positive integer)

x + 2 = 5p (where p is a positive number) (where p is a positive integer)

Testing different values of x that meet these two requirements reveals that x = 38 is the only answer that also resolves the second problem.

Leo has 38 toy troops as there aren't enough for him to line them up four by four.

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