Suppose f(x,y) = (x - y)(1 - xy) Find the local maxima of f
Find the local minima of f
Find the saddle point of f

i. Vectors u and w are orthogonal.

ii. The two vectors orthogonal to v = √(2, -3) are u = (3, 2) and w = (-2, 3).

iii. The two unit vectors orthogonal to 7 are u = (1, -1) / √2 and w = (1, 1) / √2.

i. To show that vectors u = (a, b) and w = (-b, a) are orthogonal, we need to demonstrate that their dot product is zero.

The dot product of u and w is given by:

u · w = (a, b) · (-b, a) = a*(-b) + b*a = -ab + ab = 0

ii. To find two vectors orthogonal to vector v = √(2, -3), we can use the result from part i.

Let's denote the two orthogonal vectors as u and w.

We know that u = (a, b) is orthogonal to v, which means:

u · v = (a, b) · (2, -3) = 2a + (-3b) = 0

Simplifying the equation:

2a - 3b = 0

We can choose any values for a and solve for b. For example, let's set a = 3:

2(3) - 3b = 0

6 - 3b = 0

-3b = -6

b = 2

Therefore, one vector orthogonal to v is u = (3, 2).

To find the second orthogonal vector, we can use the result from part i:

w = (-b, a) = (-2, 3)

iii. To find two unit vectors orthogonal to 7, we need to consider the dot product between the vectors and 7, and set it equal to zero.

Let's denote the two orthogonal unit vectors as u and w.

We know that u · 7 = (a, b) · 7 = 7a + 7b = 0

Dividing by 7:

a + b = 0

We can choose any values for a and solve for b. Let's set a = 1:

1 + b = 0

b = -1

Therefore, one unit vector orthogonal to 7 is u = (1, -1) / √2.

To find the second unit vector, we can use the result from part i:

w = (-b, a) = (1, 1) / √2

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Answer: 2/12 (1/6 simplified)

Step-by-step explanation:

5+4+3=12

2 marbles of the same color

2/12

2/2=1

12/2=6

Answer:

>

Step-by-step explanation:

5 × 10^2 = 500

so 590 is greater than or > 5 × 10^2 or 500

The equation represents the total cost of turkey and amount is y= 3.25x.

We have,

The turkey costs $3. 25 per pound.

let x be the amount in pounds and y be the total cost in dollar.

Then, the relation between x and y

Total cost = 3.25 (amount in  poind)

y = 3.25 x

Thus, the required equation is y= 3.25x.

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Answer:

83.61551571

Step-by-step explanation:

hope this helps :)

1. Chicken became the key product that drove the creation of the Interstate Highway System, which led to the dominance of American trucks in the US truck market.

2. A party may want to impose a tariff to protect domestic industries from foreign competition or to generate revenue for the government.

3. A party is usually trying to protect domestic industries, but a tariff on automobiles would hurt both domestic consumers who would pay higher prices and foreign producers who would face reduced demand.

4. Competition encourages innovation by providing incentives for companies to improve their products and services to stay ahead of their rivals; American trucks stayed the same because they faced little competition due to protectionist policies.

5. Foreign companies tried to get around American-imposed tariffs on automobiles by establishing factories in the US, forming joint ventures with American companies, or exporting through third countries.

6. The methods used to get around tariffs can be efficient in the short term, but they may not be sustainable or desirable in the long term as they can lead to trade imbalances and undermine the competitiveness of domestic industries.

7. Tariffs can be used as a bargaining chip to negotiate better trade deals, but they should be imposed judiciously and only as a last resort to avoid damaging the economy and harming consumers.

1. In the podcast, chicken is cited as the reason why American trucks dominate the truck market in the United States.

This is because in the 1960s, the government imposed regulations on the trucking industry that limited the amount of weight a truck could carry.

To get around these regulations, the industry started using smaller trucks to transport goods, which were often not strong enough to handle the weight.

However, they found that if they put chicken on the back of the trucks, the weight of the cargo would distribute more evenly and the smaller trucks could handle the load.

This led to the development of the modern pickup truck, which is now a staple of the American automobile market.

2. Parties may want to impose tariffs for various reasons, such as to protect domestic industries and jobs from foreign competition, to raise revenue for the government, or to level the playing field in international trade.

Two specific reasons for imposing tariffs could be to protect national security interests or to address unfair trade practices by other countries.

3. Tariffs are usually imposed to protect domestic industries and jobs, and the parties that are being protected are typically the producers of the goods or services in question.

However, tariffs can also harm consumers who may have to pay higher prices for imported goods or may have fewer choices in the marketplace. For example, if a tariff is imposed on automobiles, domestic car manufacturers may benefit, but consumers may have to pay more for cars, and foreign automakers may lose market share.

4. Competition encourages innovation by creating incentives for companies to improve their products or services to gain a competitive advantage.

In the case of American trucks, the lack of competition may have contributed to their lack of innovation over the years. Since they dominated the market, there was little pressure to improve or innovate, and as a result, they have largely stayed the same.

However, the rise of foreign competition in recent years has led American truck manufacturers to invest more in innovation to stay competitive.

5. Foreign companies have tried to get around American-imposed tariffs on automobiles in various ways, such as by moving production to countries not subject to the tariffs, by exporting parts and assembling them in the United States, or by lobbying the government for exemptions or tariff reductions.

6. The methods used by foreign companies to get around tariffs may not be efficient for the economy as a whole because they can lead to higher costs and inefficiencies in the supply chain.

However, they may be necessary for individual companies to remain competitive in the short term.

Ultimately, a more efficient solution would be to address the root causes of the trade imbalances that lead to tariffs in the first place.

7. A tariff can be used as a bargaining chip by threatening to impose tariffs on imports from a country unless they make concessions in trade negotiations.

While this can be an effective strategy in certain situations, it can also lead to a trade war and harm both economies.

In general, tariffs should be used sparingly and as a last resort, and efforts should be made to address underlying trade issues through diplomacy and negotiation.

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Answer:

x=25°, y=18°

Step-by-step explanation:

Solved! Here is the explanation. As we have supplementary angles, we have a total of 180° of angles. Angle BXD is a right angle, so 2x+40°=90°. 2x=50°, and then we have x=25°. Now, to figure out y, we have to look at angle BXA. In this case, 5y=90°. y=18°. So, x=25° and y=18°. Hope this explanation helps!

Answer:

5.6023 × 10^-5

Step-by-step explanation:

Let me know if you need an explanation.

Answer:

0.00005602

Step-by-step explanation:

0.00005602

(hope this helps can i plz have brainlist :D hehe)

Answer:

like an echo in the forest

yeahhhhh life goes on

Answer:

Step-by-step explanation:

4 - 12x

So option C is the correct answer

The value of the integral [*(4F(X) 4f(x) - 3g(x))dx is 6.

Given, f(x) dx = 5 and 2 f²f(x) dx = -3, we can solve for f(x) and get f(x) = -1/2. Similarly, we are given g(x) dx = -1 and [*9(x) dx [*g(x) dx = 2, which gives us 9g(x) = -2. Solving for g(x), we get g(x) = -2/9.  

Now, we can substitute the values of f(x) and g(x) in the integral [*(4F(X) 4f(x) - 3g(x))dx to get [*(4F(X) 4(-1/2) - 3(-2/9))dx. Simplifying this, we get [*(4F(X) + 8/3)dx.

Further, using the given integral f(x) dx = 5, we can find F(x) by integrating both sides with respect to x. Thus, F(x) = 5x + C, where C is the constant of integration.

Substituting the value of F(x) in the integral [*(4F(X) + 8/3)dx, we get [*(4(5x + C) + 8/3)dx = [*(20x + 4 + 8/3)dx = [*(20x + 20/3)dx.

Integrating this, we get the value of the integral as 10x^2 + (20/3)x + K, where K is the constant of integration.

Since we don't have any boundary conditions or limits of integration given, we can't find the exact value of K. However, we do know that [*9(x) dx [*g(x) dx = 2, which means the integral [*(4F(X) 4f(x) - 3g(x))dx evaluates to 2.

Therefore, 10x^2 + (20/3)x + K = 2. Solving for K, we get K = -20/3. Substituting this value, we can finally conclude that the value of the integral [*(4F(X) 4f(x) - 3g(x))dx is 6.

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A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.

To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:

Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.

Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.

Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

Given:

Population mean (μ) = 93 minutes

Sample mean (\(\bar x\)) = 86.8 minutes

Sample standard deviation (s) = 14.6 minutes

Sample size (n) = 18

Significance level (α) = 0.10

Calculating the test statistic:

t = (86.8 - 93) / (14.6 / sqrt(18))

t = -6.2 / (14.6 / 4.24264)

t ≈ -2.677

The degrees of freedom for this test is n - 1 = 18 - 1 = 17.

Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.

Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.

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Gastronomy is a way of promoting understanding among different cultures, and of bringing people and traditions closer together.

The practise of choosing, preparing, presenting, and consuming exquisite cuisine. The foundation of gastronomy lies in the connections between food, culture, and tradition. Gastronomy has emerged through time as a more potent cultural force than language or other influences among the peoples of the world.

Molecular gastronomy is a relatively recent branch of science that studies the physical and chemical changes that take place during cooking. Molecular cuisine is the name of the new culinary movement based on this emerging discipline.

Nowadays, the world may be broken down into separate gastronomic zones, where different cuisines are popular and similar cooking techniques are used. Throughout much of Southeast Asia, rice is the main food. The abundant and creative use of spices to give meals an extra flavour is what makes Indian and Indonesian cuisine unique. The prevalent ingredient in Mediterranean recipes is olive oil.

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Complete question:

How can gastronomy help us live harmoniously?

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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A polynomial function of degree n has at most n real zeros and at most n - 1 turning points.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

A polynomial function

Now,

Because of the Fundamental Theorem of Algebra states that a polynomial function of degree n has exactly n complex roots (or zeros), some of which may be repeated or non-real. The number of real roots is equal to or less than the number of complex roots.

A turning point is a point where the graph of the polynomial function changes direction from increasing to decreasing or vice versa. The number of turning points is equal to or less than one less than the degree of the polynomial function. This is because each turning point corresponds to a change in the sign of the first derivative of the function, and the first derivative is a polynomial function of degree n - 1.

Therefore, by the function the answer will be n - 1.

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A) The stated the null and alternative hypotheses are defined as

H₀ : μItalian = μSeafood = μsteakhouse

Hₐ : Not all the population means are equal. So, correct answer is option (a).

B) The value of the test statistic is equals to the 6.70. The p-value is equals to the 0.0056.

C) Conclusion : The null hypothesis H0 is rejected, so there is sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.

We have a consumer reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains. The above table data show the meal prices ($) obtained for the 24 restaurants sampled ( 8 seafood restaurants, 8 Italian restaurants, and 8 steakhouses). So, sample size , n = 24

Significance level = 0.05

A) For Hypothesis testing, the null and alternative hypothesis are defined as

H₀ : μItalian = μSeafood = μsteakhouse

Hₐ : Not all the population means are equal. So, correct answer is option (a).

B) We have more than two groups for analysis so we use ANOVA test to compare the means among three or more groups. Using the Excel the above second table is made which represents the mean, standard deviations and standard error for data. It also contains ANOVA table. So,

Mean value of Italian = 17

Mean value of Seafood = 19

Mean value of steakhouse = 24

Uding all the above details or Excel command, The value of the F test- statistic value = 6.70

Using the distribution table, the p-value for test-static value 6.70 is 0.0056.

C)Now, we see P-value = 0.0056 < 0.05, which implies the null hypothesis is rejected. Thus, There is sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.

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Complete question:

You may need to use the appropriate technology to answer this question. The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains. † One of the variables in the study is meal price, the average amount paid per person for dinner and drinks, minus the tip. Suppose a reporter for a local newspaper thought that it would be of interest to her readers to conduct a similar study for restaurants located in her city. The reporter selected a sample of 8 seafood restaurants, 8 Italian restaurants, and 8 steakhouses. The following data show the meal prices ($) obtained for the 24 restaurants sampled.

Italian Seafood Steakhouse

$12 $17 $23

13 18 18

16 18 24

16 27 25

18 23 21

19 15 23

18 20 28

24 14 30

Use α = 0. 05 to test whether there is a significant difference among the mean meal price for the three types of restaurants. State the null and alternative hypotheses.

a) H0: μItalian = μSeafood = μSteakhouse

Ha: Not all the population means are equal.

b)H0: μItalian ≠ μSeafood ≠ μSteakhouse

Ha: μItalian = μSeafood = μSteakhouse

c) H0: At least two of the population means are equal.

Ha: At least two of the population means are different.

d)H0: Not all the population means are equal.

Ha: μItalian = μSeafood = μSteakhouse

e) H0: μItalian = μSeafood = μSteakhouse

Ha: μItalian ≠ μSeafood ≠ μSteakhouse

B) Find the value of the test statistic. (Round your answer to two decimal places. )

test statistic=___

Find the p-value. (Round your answer to four decimal places. )p-value =____

V)What is your conclusion?

a)Do not reject H0. There is not sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.

b)Reject H0. There is sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.

c)Do not reject H0. There is sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.

d)Reject H0. There is not sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants

Each angle on a square road sign measures 90 degrees.

A square is a quadrilateral with four equal sides and four right angles. In a square, all angles are congruent, meaning they have the same measure. Since a square has four angles, each angle is equal to the total sum of the interior angles of a square divided by four.
The total sum of the interior angles of a square can be calculated using the formula (n - 2) * 180 degrees, where n is the number of sides. For a square, n = 4, so the total sum of the interior angles is (4 - 2) * 180 = 2 * 180 = 360 degrees.
To find the measure of each angle, we divide the total sum of the interior angles by the number of angles, which is 4 in the case of a square:
360 degrees / 4 angles = 90 degrees.
Therefore, each angle on a square road sign measures 90 degrees.

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The sum is 3. So the correct option is (D) A+B=3.

The initial value problem is given by z³y" = 2y with the initial conditions y(1) = 3 and y'(1) = -2. We need to find the value of A + B, where y(2) is the solution.

To solve the given initial value problem, we can use the method of integrating factors. First, let's rewrite the equation in standard form:

y" - (2/z³)y = 0

Now, we assume a solution of the form y = z^m, where m is a constant. Differentiating twice, we get:

y" = m(m-1)z^(m-2)

Substituting these derivatives into the differential equation, we have:

m(m-1)z^(m-2) - (2/z³)z^m = 0

Simplifying the equation, we find:

m(m-1) - 2z^(m-5) = 0

Since this equation should hold for all z, the coefficient of each power of z must be zero. Therefore, we have two cases:

Case 1: m(m-1) = 0

This implies m = 0 or m = 1. Hence, we have the solutions y₁ = z^0 = 1 and y₂ = z¹ = z.

Case 2: -2z^(m-5) = 0

This equation holds only when m - 5 ≤ 0, which gives m ≤ 5. Thus, we have the solutions y₃ = z², y₄ = z³, y₅ = z⁴, and y₆ = z⁵.

The general solution is given by the linear combination of these solutions:

y(z) = c₁ + c₂z + c₃z² + c₄z³ + c₅z⁴ + c₆z⁵

To find the particular solution that satisfies the initial conditions, we substitute y(1) = 3 and y'(1) = -2 into the equation and solve for the coefficients c₁, c₂, c₃, c₄, c₅, and c₆.

After calculating, we find that y(z) = 1 + 4z - 2z² + 4z³ - 2z⁴ + z⁵.

Now, we can find y(2) by substituting z = 2 into the solution:

y(2) = 1 + 4(2) - 2(2)² + 4(2)³ - 2(2)⁴ + (2)⁵ = 1 + 8 - 8 + 32 - 32 + 32 = 33

Therefore, the sum A + B is 3 + 0 = 3 which concludes that the correct option is D

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Answer:

202 meters

Step-by-step explanation:

a) The area of triangle PQR is:

Area = √(6)/2

b) The equation of the plane that contains P, Q, and R is:

x + y + 2z = 2

a) For the area of the triangle PQR, we can use the formula:

Area = 1/2 |PQ x PR|

where PQ and PR are the vectors from P to Q and R, respectively, and x denotes the cross product.

So, we have:

PQ = <1-0, -1-0, 2-1> = <1, -1, 1>

PR = <-1-0, 1-0, 1-1> = <-1, 1, 0>

Taking the cross product:

PQ x PR = <1, -1, 1> x <-1, 1, 0> = <-1, -1, -2>

Taking the magnitude:

|PQ x PR| = √((-1)² + (-1)² + (-2)²) = √(6)

So, the area of triangle PQR is:

Area = 1/2 × √(6) = √(6)/2

b) To find the equation of the plane that contains P, Q, and R, we can use the point-normal form of the equation:

n · (r - P) = 0

where n is the normal vector of the plane (which is perpendicular to the plane), r is any point on the plane, and · denotes the dot product.

To find the normal vector, we can take the cross product of PQ and PR:

n = PQ x PR = <-1, -1, -2>

Now, we can use any of the three points to find the equation of the plane. Let's use P:

n · (r - P) = 0

Substituting n and P:

<-1, -1, -2> · (r - <0, 0, 1>) = 0

Expanding the dot product:

-1(r_x - 0) - 1(r_y - 0) - 2(r_z - 1) = 0

Simplifying:

-r_x - r_y - 2r_z + 2 = 0

So, the equation of the plane that contains P, Q, and R is:

x + y + 2z = 2

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The final elevation of the AUV is \(-31 \frac{5}{12}\) feet.

Given that, AUV is at an elevation of -8.25 ft. It dives down \(6\frac{2}{3}\) ft to collect a specimen. Then the AUV dives another \(15\frac{3}{4}\) ft.

The angle of elevation in math is "the angle formed between the horizontal line and the line of sight when an observer looks upwards is known as an angle of elevation".

Here, the mixed fraction can be written in improper fraction

\(6\frac{2}{3} = \frac{20}{3}\) and \(15\frac{3}{4}=\frac{63}{4}\)

Now, 8.25 = 825/100 = 33/4

The final elevation = -33/4-20/3-63/4

= -99/4 - 20/3

= -297/12 -80/12

= - 377/12

= \(-31 \frac{5}{12}\)

Therefore, the final elevation of the AUV is \(-31 \frac{5}{12}\) feet.

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Answer:

Yes it is absolutely right.

Answer:

Its B

Step-by-step explanation:

Hey queen the answer is 16.5 inch!!

Answer:

x plus 1

Step-by-step explanation:

Answer:

x+1

Step-by-step explanation:

if you simplify the equation, you will get x+1

first, you take the parentheses away.  The equation becomes

3x-2x-4+5

then you combine like terms

x+1

The total area of the figure in this problem is given as follows:

41.3 ft².

The area of the composite figure is given by the sum of the areas of all the parts that compose the figure.

The figure in this problem is composed as follows:

Then the area of the triangle is given as follows:

At = 0.5 x 6 x 3 = 9 ft².

The area of the semicircle is given as follows:

Ac = π x 3² = 28.3 ft².

The area of the square is given as follows:

As = 2² = 4 ft².

Then the total area of the figure is given as follows:

9 + 28.3 + 4 = 41.3 ft².

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Answer:

False

Step-by-step explanation:

Answer: B

Solution: Because the line is a dotted line. so print (-3, -1) and (3, 3) , (0, 0) are not the solution, so , answer is (0, 5) choice B.

Answer:

C

Step-by-step explanation:

first way: (easier way)

Plot the points out, points in the blue region are solutions. points on the dotted line are not solutions since it is a dashed line.

(0,5 is in the blue region)

second way:

find the equation of the in-equality:

the line that divides solutions and non-solutions passes through 3,3 and -3,-1

y=mx+b

m=change in y/change in x = (-1-3)/(-3-3) = 2/3

y=2/3x+b

plug x=3, y=3 (from the point "3,3")

3=2/3*3+b

3=2+b

b=1

y=2/3x+1 is the solution of the line.

the in-equality is

y(?)2/3x+1

plug in -5,5, which is a solution (looking at the graph)

5>-7/3

so use >, and not <

y>2/3x+1 is the equation of the in-equality, now just plug the answer choices in to see that

x=0,y=5 is a solution

Equation that relates D = 0.5 + 20x + 0.5v

Initial distance covered d1 = 0.5km

If she rode a bicycle for x hours at an average speed of 20 kilometers per hour, then her distance during this period is:

Speed = Distance/Time

Speed is defined as the rate that an object travels through space; it is the distance traveled in a certain amount of time. A familiar example from our daily lives can be seen when we drive to work or school. Our speed is measured by how fast or slowly we drive. Our car is said to have a speed of 60 miles per hour (mph) if it will travel a distance of 60 miles in exactly 1 hour.

Distance d2 = speed × time

d2 = 20x

If she ran for 0.5 hour at an average speed of v kilometers per hour, her distance this time will be;

Distance d3 = 0.5v

If her total distance is D, then;

D = d1+d2+d3

D = 0.5 + 20x + 0.5v

Hence an equation that relates D, x, and v is D = 0.5 + 20x + 0.5v

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M(8)<M(4) means that 8th drive was less expensive than 4th drive.

M(n) denotes Aiden's fee (in dollars) for his n^th drive on a certain day.

The reason for the m(8) is that the model fee for this is nth driver for a certain  day.  this implies M (8) < M (4)

M(8) is Aiden's fee for his 8th drive;

M(4) is Aiden's fee for his 4th drive

In conclusion, Aiden's fee for his 8th drive is greater than his drive for the 4th drive

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Answer:its D

Step-by-step explanation: