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QUESTION 3 [30 Marks] (a) An experiment involves tossing two dice and observing the total of the upturned faces. Find: (i) The sample space S for the experiment. (3) (ii) Let X be a discrete random va

Answer:

I think it's 5(9)+20

Step-by-step explanation:

5(9+4) can be expanded to get 5(9)+5(4). And 5(4)=20

Answer:

The answer is D

Step-by-step explanation:

Answer:

51.7661748226 degrees; 38.2338251774 degrees

Step-by-step explanation:

First, draw a diagram to illustrate this situation. Looking at angle A, Eric's height, 1.65 m, corresponds to OPPOSITE, and Eric's shadow, 1.30 m, corresponds to ADJACENT. Using SOH CAH TOA, the equation is:

tan(A) = 1.65/1.30

A = arctan(1.65/1.30)

A = 51.7661748226 deg

Looking at angle B, 1.65 m is ADJACENT and 1.30 m is OPPOSITE. Therefore, the equation is:

tan(B) = 1.30/1.65

B = arctan(1.30/1.65)

B = 38.2338251774 deg

the function y = f(x) that satisfies the given conditions is y = 2x^3 - x^2 - 5x + C2, where C2 is a constant that can take any real value.

First, integrate y' with respect to x to find the first derivative y:

∫(y') dx = ∫(12x - 2) dx

y = 6x^2 - 2x + C1

Next, integrate y with respect to x to find the function f(x):

∫y dx = ∫(6x^2 - 2x + C1) dx

f(x) = 2x^3 - x^2 + C1x + C2

To determine the specific values of C1 and C2, we use the given condition that the line y = -x + 5 is tangent to the graph at x = 1.

Since the tangent line has the same slope as the function f(x) at x = 1, we can equate their derivatives:

f'(1) = -1

Taking the derivative of f(x), we have:

f'(x) = 6x^2 - 2x + C1

Substituting x = 1 and equating f'(1) to -1, we can solve for C1:

6(1)^2 - 2(1) + C1 = -1

6 - 2 + C1 = -1

C1 = -5

Now we have the values of C1 and C2. Plugging them back into the equation for f(x), we obtain the final function:

f(x) = 2x^3 - x^2 - 5x + C2

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Answer:

A. 18x - 3y = 6

Step-by-step explanation:

By taking 3 common from the terms 18x and 3y we get,

3 (6x-3y) = 6

or, 6x - y = 6/3

or, 6x - y = 2

And,

The equation becomes,

y = 6x - 2

The equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

By taking 3 commons from the terms 18x and 3y we get,

3 (6x-3y) = 6

6x - y = 6/3

6x - y = 2

The equation becomes,

y = 6x - 2

Therefore, the equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

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According to the output analysis, the model presented above is of Discrete-event simulation (DES) type.

What is Discrete-event simulation (DES)?

Discrete-event simulation (DES) is indeed a type of computer-based simulation where events occur at specific points in time. In DES, a system's behavior is modeled by specifying the sequence of events that occur during the system's lifespan.

In a discrete-event simulation, the state of the system changes only when events occur, rather than continuously evolving over time. Events represent significant occurrences or activities within the system, such as customer arrivals, service completions, or resource allocations. Each event is associated with a specific time or occurrence point, and the simulation progresses by processing events in chronological order.

DES is particularly useful for modeling complex systems where the timing of events and their interactions play a crucial role. It allows for capturing the dynamic nature of the system, simulating the flow of entities (such as customers, vehicles, or messages) through the system, and observing the effects of event sequencing and resource allocation on system performance.

By simulating the system and observing the events and their consequences, DES enables analysts to evaluate different scenarios, study the impact of various parameters, and optimize system design or operation. It provides insights into system performance measures, such as throughput, waiting times, resource utilization, or customer satisfaction.

Overall, discrete-event simulation is a powerful technique for modeling and analyzing complex systems with discrete changes, events, and interactions over time.

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The model above is known as a discrete-event simulation model according to the output analysis.

A discrete event simulation is a type of computer-based modeling where a series of discrete events in a system are simulated.

In such models, the system under consideration evolves through a series of discrete events that are instantaneous.

For example, in the retail establishment model, each customer arriving at the store would be considered a separate, discrete event.

The simulation would model the sequence of events that occur between the time the store opens at 9 am and when the last customer leaves before closing time at 5 pm.

The objective of the simulation would be to estimate some measure of the quality of customer service during this time period.

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Answer:

There is no significant evidence to conclude that the mean waiting time is less than 3.8 minutes

Step-by-step explanation:

H0 : μ = 3.8

H1 : μ < 3.8

Test statistic :

(x - μ) ÷ s/sqrt(n)

(3.7 - 3.8) ÷ 0.6/sqrt(60)

Test statistic = - 1.29

The Pvalue from test statistic :

P(z < -1.29) = 0.0985

Reject Null if

Pvalue < α

0.0986 > 0.01 ; Hence, we fail to reject the null ;

There is no significant evidence to conclude that the mean waiting time is less than 3.8 minutes

Answer:

Step-by-step explanation:

1. 4/1

2. 5/1

3. 1/8

4. 2/3

5. 3/4

6. 4/12 = 1/3, 8/12 = 2/3

7. 2/5, 3/5

Answer:

EF = 6

Step-by-step explanation:

(whole secant) x (external part) =  (whole secant) x (external part)

(4+2x) * 4 = (5+x) * 5

Distribute

16+8x = 25+5x

Subtract 5x

16+3x = 25

Subtract 16

3x = 25-16

3x = 9

Divide by 3

x = 9/3

x=3

We want EF

EF = 2x = 2*3 = 6

Answer:

x=19

Step-by-step explanation:

The perimeter of the right triangle is

P=9+12+15 =36

The perimeter of the left triangle is

P =x-7+ x-7+ x-7 = 3x-21

Set them equal

36 = 3x-21

Add 21 to each side

36+21 = 3x-21+21

57 = 3x

Divide each side by 3

57/3 = 3x/3

19 =x

Answer:

\(x=19\)

Step-by-step explanation:

The perimeter of a shape is the sum of all of its side lengths. Therefore, the perimeter of the first triangle is \(x-7+x-7+x-7=3x-21\) and the perimeter of the second triangle is \(9+15+12=36\).

We are given that the perimeters of the triangles are equal, so \(3x-21\) equals \(36\). As an equation, that would be \(3x-21=36\). Solving for \(x\), we get:

\(3x-21=36\)

\(3x=57\) (Add \(21\) to both sides of the equation to isolate \(x\))

\(x=19\) (Divide both sides of the equation by \(3\) to get rid of \(x\)'s coefficient)

Hope this helps!

After carrying out the above operations, the result is 2a²√(35a)

First, we can combine the square roots by using the product rule:

√(2a) * √(14a³) * √5a = √(2a * 14a³ * 5a)

Next, we can simplify the expression inside the square root by using the rule for multiplying exponents:

2a * 14a³ * 5a = 140a⁵

So we have:

√(2a) * √(14a³) * √5a = √(140a⁵)

To remove perfect squares from inside the square root, we can factor out any perfect squares from under the radical:

√(140a⁵) = √(2² * 5 * 7 * a² * a² * a) * √(a)

= 2a₂√(35a)

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Full Question:

Although part of your question is missing, you might be referring to this full question: See attached image.

Simplify. Multiply and remove all perfect squares from inside the square roots. Assume √(2a) * √(14a³) * √5a =?

Answer:

Step-by-step explanation:

hhh

Answer:

Quadrilateral ABCD is not congruent to quadrilateral KLMN. Quadrilateral ABCD cannot be mapped onto quadrilateral KLMN through a series of rotations, reflections or translations.

Step-by-step explanation:

For the two quadrilaterals to be congruent they must be the same size. By comparing the length of AD in quadrilateral ABCD, and KN in quadrilateral KLMN, you will get 4 units and 6 units respectively. That suggests that it is impossible to map line AD onto line KN (and vice versa) through any rotation, reflection or translation.

The same approach applies if you try to map line BC onto line LM. They would not be the same length (or size), and therefore the quadrilaterals are not congruent.

Step-by-step explanation:

3x - 5 = 2x - 25

3x - 2x = -25 + 5

x = -20

The value of x from the given figure is 42°.

The given angles are (3x-5)° and (2x-25)°.

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

from the given figure,

y+(2x-25)°=180° (Adjacent angles adds up to 180°)

⇒ y=180°-2x+25°

⇒ y=205°-2x

Here, (3x-5)°=y (Corresponding angles are congruent)

⇒ (3x-5)°=205°-2x

⇒ 3x+2x=205+5

⇒ 5x=210

⇒ x=42°

Hence, the value of x from the given figure is 42°.

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According to given equation a. Never true, b. Always true, c. Always true, d. Always true, e. Always true.

In mathematics, a function is a rule that assigns each element in one set, called the domain, to a unique element in another set, called the range. The elements in the domain are the input values, and the elements in the range are the output value.

a. x - 13 = x + 1

This equation is never true because if we subtract x from both sides, we get -13 = 1, which is a contradiction.

b. x + 12/1/2 = x - 21/1/2

This equation is always true because both sides simplify to x + 24 = x - 42. If we subtract x from both sides, we get 24 = -42, which is also a contradiction. Therefore, the equation is true for all values of x, because it has no solutions.

c. 2(x + 3) = 5x + 6 - 3x

This equation is always true. Simplifying both sides, we get 2x + 6 = 2x + 6, which is true for all values of x.

d. x - 3 = 2x - 3 - x

This equation is always true. Simplifying both sides, we get x - 3 = x - 3, which is true for all values of x.

e. 3(x - 5) = 2(x - 5) + x

This equation is true for all values of x. Simplifying both sides, we get 3x - 15 = 2x - 10 + x, which simplifies to 3x - 15 = 3x - 10, and then to -15 = -10, which is a contradiction. Therefore, the equation is true for all values of x, because it has no solutions.

Therefore, according to given equation a. Never true, b. Always true, c. Always true, d. Always true, e. Always true

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In the context of demand forecasting for a product with consistent year-round demand, the planner is tasked with experimenting with time series analysis.

By utilizing previous weekly data, the planner can make predictions regarding the demand pattern for the upcoming weeks or months.

Having access to data from several weeks is crucial for the planner to accurately forecast the demand and make informed decisions. The demand forecast plays a vital role in meeting the demand effectively and avoiding any losses resulting from excessive production.

Time series analysis enables the examination of trends, seasonality, and cycles within the data, providing valuable insights.

To forecast the demand pattern, the planner can employ various methods such as Simple Moving Average, Weighted Moving Average, and Exponential Smoothing.

Each method offers a different approach to analyzing the data pattern and generating accurate forecasts. The planner can select the most suitable method based on the specific characteristics of the data and aim to provide accurate forecasting results.

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Operation question

Week 1 2 3 4 5 6 7 8 9 10 11 12 Q1 A product has a consistent year round demand. You are the planner and have been tasked with experimenting with some time series analysis. Using this previous weekly data:

Week 1: 100 units

Week 2: 120 units

Week 3: 110 units

Week 4: 130 units

Week 5: 140 units

Week 6: 150 units

Week 7: 160 units

Week 8: 170 units

Week 9: 180 units

Week 10: 190 units

Week 11: 200 units

Week 12: 210 units

Q1: A product has a consistent year-round demand. You are the planner and have been tasked with experimenting with some time series analysis. Using this previous weekly data, you need to forecast the demand for the next quarter (Weeks 13 to 24) using a simple exponential smoothing method with a smoothing constant of 0.3.

A. Null hypothesis (H0): The proportion of algae in the water is less than or equal to 0.7.

Alternative hypothesis (H1): The proportion of algae in the water is greater than 0.7.

B. The appropriate test statistic in this case would be the z-test for proportions.

Assumptions for the z-test for proportions:

1. The sample is a simple random sample.

2. The sampling distribution of the sample proportion can be approximated by a normal distribution.

3. The samples are independent.

4. The sample size is large enough (np0 >= 10 and n(1-p0) >= 10, where n is the sample size and p0 is the hypothesized proportion).

c) The rejection region for this one-tailed test at an α level of 0.05 would be in the right tail of the distribution.

d) To compute the value of the test statistic, we need to calculate the standard error of the sample proportion and compare it to the critical value of the standard normal distribution at α = 0.05.

Let p-cap be the sample proportion (85/100 = 0.85), and n be the sample size (100).

Standard error (SE) = √((p-cap x (1 - p-cap)) / n)

SE = √((0.85 x 0.15) / 100) = 0.03887

z-score = (p-cap - p0) / SE

z-score = (0.85 - 0.7) / 0.03887 ≈ 3.854

Looking up the critical value for α = 0.05 in the standard normal distribution table, the critical z-value is approximately 1.645 (one-tailed test).

Since the calculated z-score (3.854) is greater than the critical value (1.645), we can reject the null hypothesis.

Conclusion: The test rejects the null hypothesis, indicating that the proportion of algae in the water is significantly greater than 0.7. This suggests that there may be a risk of reduced oxygen levels and potential fish mortality due to excessive algae growth.

e) To compute the p-value for this test, we would calculate the probability of obtaining a z-score as extreme as 3.854 or greater, assuming the null hypothesis is true (i.e., the proportion is less than or equal to 0.7).

The p-value is the probability of obtaining a z-score greater than 3.854 in a standard normal distribution. This probability is extremely low, approaching zero.

Decision: Since the p-value is less than the significance level of 0.05, we reject the null hypothesis. The evidence suggests that the proportion of algae in the water is significantly greater than 0.7, indicating a potential environmental problem.

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The probability that the second marble is not red given that the first marble was not red is 5/9.

To solve this problem, we can use the conditional probability formula. The probability that the second marble is not red given that the first marble was not red can be calculated as follows:

P(second marble is not red | first marble is not red) = P(second marble is not red and first marble is not red) / P(first marble is not red)

First, we need to calculate P(first marble is not red). Since there are 3 red marbles out of a total of 3+5+2=10 marbles, the probability of drawing a non-red marble on the first draw is:

P(first marble is not red) = (5+2)/10 = 7/10

Next, we need to calculate P(second marble is not red and first marble is not red). If the first marble is not red, then there are 7 marbles left in the container, of which 5 are blue and 2 are white. Therefore, the probability of drawing a non-red marble on the second draw given that the first marble was not red is:

P(second marble is not red and first marble is not red) = (5/9)*(7/10) = 35/90

Finally, we can plug these values into the conditional probability formula:

P(second marble is not red | first marble is not red) = (35/90) / (7/10) = 5/9

Therefore, the probability that the second marble is not red given that the first marble was not red is 5/9.o solve this problem, we can use the conditional probability formula. The probability that the second marble is not red given that the first marble was not red can be calculated as follows:

P(second marble is not red | first marble is not red) = P(second marble is not red and first marble is not red) / P(first marble is not red)

First, we need to calculate P(first marble is not red). Since there are 3 red marbles out of a total of 3+5+2=10 marbles, the probability of drawing a non-red marble on the first draw is:

P(first marble is not red) = (5+2)/10 = 7/10

Next, we need to calculate P(second marble is not red and first marble is not red). If the first marble is not red, then there are 7 marbles left in the container, of which 5 are blue and 2 are white. Therefore, the probability of drawing a non-red marble on the second draw given that the first marble was not red is:

P(second marble is not red and first marble is not red) = (5/9)*(7/10) = 35/90

Finally, we can plug these values into the conditional probability formula:

P(second marble is not red | first marble is not red) = (35/90) / (7/10) = 5/9

Therefore, the probability that the second marble is not red given that the first marble was not red is 5/9.

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Regardless of what the Inspector chooses, the Owner's expected payoff is the same (33.33). The Owner does not have a better option than waiting for the Inspector to choose container B.

This problem can be modeled as a game of incomplete information. The Inspector and Owner are players in the game, and each has two possible strategies: either choose container B, or switch to container C. The payoffs for each player depend on the strategy they choose and which container contains the counterfeit goods.

To solve this game, we can use backward induction. We start by considering the final decision point: whether to switch to container C after seeing that container A does not contain the counterfeit goods. Let's consider the two cases:

If the counterfeit goods are in container B, then the Inspector knows that container C also does not have the counterfeit goods. In this case, the payoff for choosing container B is 100 (if they find the counterfeit goods) or -100 (if they do not).

If the counterfeit goods are in container C, then the Inspector knows that container B does not have the counterfeit goods. In this case, the payoff for switching to container C is 100 (if they find the counterfeit goods) or -100 (if they do not).

Since the Inspector does not know which container has the counterfeit goods, they should choose the strategy with the higher expected payoff. To calculate the expected payoffs, we need to consider the probability that the counterfeit goods are in each container. Since the owner chose one container at random, each container has a 1/3 chance of containing the counterfeit goods.

If the Inspector chooses container B, the expected payoff is:

Expected payoff (choose container B) = (1/3) * 100 + (2/3) * (-100) = -33.33

If the Inspector switches to container C, the expected payoff is:

Expected payoff (switch to container C) = (1/3) * 100 + (2/3) * (-100) = -33.33

Therefore, regardless of what the Inspector chooses, their expected payoff is the same (-33.33). This means that the Inspector does not have a better option than choosing container B, and switching to container C does not improve their chances of finding the counterfeit goods.

For the Owner, if the Inspector chooses container B, then the Owner's expected payoff is:

Expected payoff (Inspector chooses container B) = (1/3) * (-100) + (2/3) * 100 = 33.33

If the Inspector switches to container C, then the Owner's expected payoff is:

Expected payoff (Inspector switches to container C) = (1/3) * (-100) + (2/3) * 100 = 33.33

Therefore, regardless of what the Inspector chooses, the Owner's expected payoff is the same (33.33). The Owner does not have a better option than waiting for the Inspector to choose container B.

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The table shows the estimated digit and significant figures of each measurement and their representation with x.

Number of Measurement Estimated Digit Significant Figures

14.8 m 3 ✓

$10.25 - ✓

0.05 L - ✓

1.000 g/mL - ✓

1.200 - ✓

6200 cm - ✓

403 kg - ✓

For each measurement, the estimated digit is replaced with an x to represent the number with the correct number of significant figures. The correct representations for each measurement are:

Note that in some cases, the representation requires adding zeros to the right of the decimal point to indicate the number of significant figures. In other cases, the representation requires rounding up or down to the correct number of significant figures.

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Answer:

2.4ths hope this helpssssss

She has to work more harder or she needs to cut her expenses are the only two choices for her.

The price one must pay to acquire anything is referred to as an expense.

An expense is a recurring expense, such as the salary of an employee or the rent for a retail location, whereas a cost normally refers to the amount paid to purchase an item.

She has two options: she either work harder to earn more money or she may spend less money. Increasing the value being added (income) or decreasing the value being subtracted (expenses) will make the difference less negative/positive because income - expense is negative.

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Answer:

table below shows the number of students who received each letter grade during each of the first three grading periods. Both teachers have 40 students in each class.

1. Construct Matrix A to represent Mr. Alvarez’s grades and Matrix B to represent Ms. Bento’s grades.

Step-by-step explanation:

hshhdbdkek

Answer:

Predatory animals rely on reefs for food.

Step-by-step explanation:

More animals live there instead of open ocean so this answer makes the most sence.

Have a good day!

Answer:

Predatory animals rely on reefs for food.

Step-by-step explanation:

global warming make waters temp go up not down

dead reefs are gray which is a different color just an obvious example

the last two contradict each other and fish use them as home so fish that eat those fish will go towards the food not away

Answer:

Solve for √3−2x.

√3−2x=4√x

To remove the radical on the left side of the equation, square both sides of the equation.

√3−2x²=(4√x)²

Simplify each side of the equation.

3−2x=16x

Solve for x.

=> x=16

Step-by-step explanation:

Answer:

x = \(\frac{1}{6}\)

Step-by-step explanation:

Given

\(\frac{\sqrt{3-2x} }{\sqrt{4x} }\) = 2 ( square both sides )

\(\frac{3-2x}{4x}\) = 4 ( multiply both sides by 4x )

3 - 2x = 16x ( add 2x to both sides )

3 = 18x ( divide both sides by 18 )

\(\frac{3}{18}\) = x , that is

x = \(\frac{1}{6}\)

The length of the model is 3.33 feet and the wingspan is 1.87 feet, which are reasonable and manageable sizes for a model of this type.

What is scale conversion?

Scale conversion is the process of determining the size of a model based on the size of the original object being modeled.

One way to determine a reasonable scale for the model is to consider the desired size of the model relative to the actual size of the plane. For example, if we want the model to be 1/30th the size of the actual plane, we can use the following formula to find the length and wingspan of the model:

Model length = Actual length ÷ Scale factor

Model wingspan = Actual wingspan ÷ Scale factor

Using these formulas, the length of the model would be:

Model length = 96 feet + 8 inches ÷ 30 = 3 feet 4 inches ÷ 30 = 3.33 feet

And the wingspan of the model would be:

Model wingspan = 56 feet ÷ 30 = 1.87 feet

The reason for choosing a 1/30th scale factor is that it results in a model that is relatively small but still large enough to show the details of the design. It also provides a good balance between size and detail, allowing the model to be easily handled and displayed while still showcasing the key features of the actual plane.

Using this scale, the length of the model is 3.33 feet and the wingspan is 1.87 feet, which are reasonable and manageable sizes for a model of this type.

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The given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants.

Mutually exclusive and exhaustive variables: A variable is mutually exclusive and exhaustive if it includes all possible outcomes and each outcome can only be assigned to one variable category.a. Days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday - Mutually exclusive and exhaustiveb. Days: Weekday and Weekend - Mutually exclusive and exhaustive c. Letters: Vowels and Consonants - Mutually exclusive and exhaustive. Letters: Alphabets and Consonants - Not mutually exclusive and exhaustiveThe given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants. Hence, the options a and c are correct.

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The probability that a randomly selected day from 2013 will have a group trades total within 78,000 of the mean is approximately 0.5.

To calculate this probability, we need to first calculate the mean of the group trades total for 2013. We can do this by adding together the group trades total for all the days in 2013, and then dividing by the total number of days in 2013. Let's call this number M.

Next, we need to calculate the difference between the group trades total of a randomly selected day in 2013 and the mean M. Let's call this number D.

Finally, we can calculate the probability that D is less than or equal to 78,000 by dividing 78,000 by the absolute value of D. This will give us the probability that a randomly selected day from 2013 will have a group trades total within 78,000 of the mean.

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Answer:

a

Step-by-step explanation:

Answer:

El 40.75% de los alumnos del centro docente estudian matemáticas.

Step-by-step explanation:

Dado que el 35 % de los estudiantes de un centro docente practica el fútbol, y el 70 % de los que practican el fútbol estudia Matemáticas, así como el 25 % de los que no practican el fútbol, para determinar los porcentajes de estudiantes de matemáticas en el centro docente se debe realizar el siguiente calculo, suponiendo que el total de alumnos del centro sea 100:

35 x 70 / 100 = 2,450 / 100 = 24.5%

100 - 35 = 65

65 x 25 / 100 = 1,625 / 100 = 16.25%

24.5 + 16.25 = 40.75

Así, el 40.75% de los alumnos del centro docente estudian matemáticas.