Let 'w' be the width and 'l' be the length. The perimeter formula is P = 2(l + w). We are given P = 96 meters. We are also told that l = 2w. Substitute 'l' in the perimeter formula: 96 = 2(2w + w) => 96 = 2(3w) => 96 = 6w. Divide by 6: w = 16 meters. Now find the length: l = 2w = 2 * 16 = 32 meters. The area of a rectangle is A = l * w. So, A = 32 * 16 = 512 square meters.

Due process of law requires that legal proceedings be fair and that individuals have the right to be heard before they are deprived of life, liberty, or property. Option A, a person being arrested and detained indefinitely without charges, directly violates this principle as it denies the individual the right to a fair legal process, including knowing the charges against them and having an opportunity to defend themselves. Option B relates more to equal protection. Option C relates to freedom of speech, and Option D to freedom of religion, both also covered in the Bill of Rights but not primarily by the due process clause in this specific context.

The formula for time is Time = Distance / Speed. Given Distance = 300 km and Speed = 60 km/h. So, Time = 300 km / 60 km/h = 5 hours.

Article V, Section 1 of the 1987 Philippine Constitution states that 'Suffrage may be exercised by all citizens of the Philippines not otherwise disqualified by law, who are eighteen years of age or over, and who shall have resided in the Philippines for at least one year and in the place wherein they propose to vote for at least six months immediately preceding the election.' Therefore, the minimum age is eighteen years old.

Let 'S' be the original salary. An increase of 15% means the new salary is 100% + 15% = 115% of the original salary. So, 1.15 * S = Php 34,500. To find the original salary, divide the new salary by 1.15: S = 34,500 / 1.15 = Php 30,000.

Under Article VII, Section 21 and Article VI, Section 21 of the 1987 Constitution, the power to concur with treaties and international agreements entered into by the President is exclusively vested in the Senate. A vote of at least two-thirds of all the Members of the Senate is required. The House of Representatives does not share this power. The other options are either shared powers or powers primarily of the House of Representatives.

To find the total distance the car can travel, multiply the tank capacity by the kilometers per liter. Distance = Tank Capacity * Kilometers per Liter. Distance = 45 liters * 12 km/liter = 540 kilometers.

Article II outlines several fundamental duties and policies of the state. While promoting a vibrant arts and culture scene is a desirable societal goal, it is not explicitly listed as a fundamental duty or principle of the State in Article II in the same direct manner as protecting the life, liberty, and property of the people (Section 5), promoting social justice (Section 10), or maintaining peace and order (Section 4). The question asks what is NOT a fundamental duty as outlined in Article II. The promotion of arts and culture is more specifically addressed in Article XIV, Section 14.

Let the shares be 2x, 3x, and 5x. We know that B receives Php 1,500, so 3x = 1,500. Divide by 3 to find x: x = 500. The total sum of money is the sum of all shares: 2x + 3x + 5x = 10x. Substitute x = 500: Total sum = 10 * 500 = Php 5,000.

Article IV, Section 1 enumerates who are citizens of the Philippines. It states: '(1) Those who are citizens of the Philippines at the time of the adoption of this Constitution; (2) Those whose fathers or mothers are citizens of the Philippines; (3) Those born before January 17, 1973, of Filipino mothers, who elect Philippine citizenship upon reaching the age of majority; and (4) Those who are naturalized in accordance with law.' Therefore, a person whose mother is a Filipino citizen is explicitly considered a citizen.

This is an inverse proportion problem. The total work units remain constant. Work = Number of Men * Days. So, 3 men * 8 days = 24 'man-days' of work. If 6 men are working, let 'D' be the number of days: 6 men * D days = 24 man-days. D = 24 / 6 = 4 days. As the number of men doubles, the time taken is halved.

The Bill of Rights (Article III) enumerates the fundamental rights and freedoms of individuals and serves as a limitation on the powers of the government. It protects citizens from potential abuses of power by the state, ensuring that specific actions are prohibited or require due process. Option A is incorrect as some rights can be limited by law. Option C is incorrect as it applies to all persons in the Philippines. Option D is incorrect as it is a core function of the Bill of Rights to restrict government power.

Profit = Selling Price - Cost Price = 1,000 - 800 = Php 200. Percentage Profit = (Profit / Cost Price) * 100%. Percentage Profit = (200 / 800) * 100% = 0.25 * 100% = 25%.

Article IX-C, Section 2(1) of the 1987 Philippine Constitution explicitly grants the Commission on Elections (COMELEC) the power to 'Enforce and administer all laws and regulations relative to the conduct of an election, plebiscite, initiative, referendum, and recall.' This includes promulgating and enforcing rules for fair elections.

The sum of five numbers is 5 * 18 = 90. The sum of the remaining four numbers is 4 * 16 = 64. The removed number is the difference between the initial sum and the new sum: 90 - 64 = 26.

Article III, Section 14 (1) and (2) of the 1987 Philippine Constitution guarantees the right of the accused to be heard by himself and counsel, to be informed of the nature and cause of the accusation against him, to have a speedy, impartial, and public trial, to meet the witnesses face to face, and to have compulsory process to secure the attendance of witnesses and the production of evidence in his behalf. The denial of the right to counsel is a direct violation of this specific provision, ensuring that every accused person has legal representation.

The volume of a cylinder is V = π * r^2 * h. Given r = 3m and h = 10m. V = 3.14 * (3^2) * 10 = 3.14 * 9 * 10 = 3.14 * 90 = 282.6 cubic meters. The tank is filled to 80% capacity, so the volume of water is 0.80 * 282.6 = 226.08 cubic meters.

Article VII, Section 4 of the 1987 Philippine Constitution states: 'The President and the Vice-President shall be elected by direct vote of the people for a term of six years which shall begin at noon on the thirtieth day of June next following the day of the election and shall end at noon of the same date, six years thereafter. The President shall not be eligible for any reelection. No person who has succeeded as President and has served as such for more than four years shall be qualified for election to the same office at any time.'

Simple Interest (I) = Principal (P) * Rate (R) * Time (T). I = 10,000 * 0.05 * 3 = Php 1,500. The total amount (A) will be Principal + Interest. A = 10,000 + 1,500 = Php 11,500.

Article XI, Section 5 of the 1987 Philippine Constitution establishes the Office of the Ombudsman, which 'shall act as the protector of the people and shall investigate on its own or on complaint by any person, any act or omission of any public official, employee, office or agency, when such act or omission appears to be illegal, unjust, improper, or inefficient.' Its primary role is to combat graft and corruption.

Total number of balls = 4 (red) + 3 (blue) + 5 (green) = 12 balls. Number of non-green balls = 4 (red) + 3 (blue) = 7 balls. Probability of NOT a green ball = (Number of non-green balls) / (Total number of balls) = 7/12.

Article II, Section 13 focuses on the youth's role and well-being. Establishing youth development programs and leadership training directly promotes their intellectual and social well-being and prepares them for nation-building. Options A and B are related to economic policies, and Option D is about environmental protection, while important, they are not directly and primarily aimed at the youth's holistic development as described in Section 13.

Substitute the given values into the expression: 2(5)^2 - 3(5)(-2) + (-2)^2. Calculate each term: 2(25) - (-30) + 4. This becomes 50 + 30 + 4 = 84.

Article VI, Section 5 (1) of the 1987 Philippine Constitution states: 'The House of Representatives shall be composed of not more than two hundred and fifty members, unless otherwise provided by law, who shall be elected from legislative districts apportioned among the provinces, cities, and the Metropolitan Manila area in accordance with the number of their respective inhabitants, and on the basis of a uniform and progressive ratio, and those who, as provided by law, shall be elected through a party-list system of registered national, regional, and sectoral parties or organizations.' The party-list representatives constitute twenty per centum of the total number of representatives.

Let D be the distance between City A and City B. Time to City B = D/80. Time to City A = D/60. Total time = D/80 + D/60 = 7 hours. Find a common denominator for 80 and 60, which is 240. (3D + 4D) / 240 = 7. 7D / 240 = 7. Multiply both sides by 240/7: D = 7 * (240/7) = 240 km.

This important provision, which protects the sanctity of contracts from legislative interference, is explicitly stated in Article III, Section 10 of the 1987 Philippine Constitution. It is part of the Bill of Rights, ensuring that private agreements are generally upheld.

The area of a square is side * side (s^2). If the area is 144 sq m, then s^2 = 144. Taking the square root, s = 12 meters. The perimeter of a square is 4 * side. So, the fencing needed is 4 * 12 = 48 meters.

Article III, Section 12 (1) states: 'Any person under investigation for the commission of an offense shall have the right to be informed of his right to remain silent and to have competent and independent counsel preferably of his own choice. If the person cannot afford the services of counsel, he must be provided with one. These rights cannot be waived except in writing and in the presence of counsel.' Therefore, the right to remain silent is explicitly guaranteed.

Let C's share be x. Then B's share is 3x. A's share is 2 * (3x) = 6x. The total sum is A + B + C = 6x + 3x + x = 10x. We know 10x = 2,400. So, x = 240. B's share is 3x = 3 * 240 = Php 720.

Article II, Section 4 of the 1987 Philippine Constitution states: 'The prime duty of the Government is to serve and protect the people. The Government may call upon the people to defend the State and, in the fulfillment thereof, all citizens may be required, under conditions provided by law, to render personal military or civil service.' This means that while citizens may be required to render such service, it must be under conditions provided by law.

Set up a proportion: Flour1 / Sugar1 = Flour2 / Sugar2. So, 2.5 / 1.5 = Flour2 / 4.5. Cross-multiply: 2.5 * 4.5 = 1.5 * Flour2. 11.25 = 1.5 * Flour2. Flour2 = 11.25 / 1.5 = 7.5 cups.

While the right to a clean and healthful environment is a crucial aspect of state policy and is recognized by jurisprudence as an enforceable right (e.g., Oposa v. Factoran), it is not explicitly enumerated as a distinct section within the Bill of Rights (Article III) itself. The other options are direct provisions: freedom of speech (Sec. 4), right to form associations (Sec. 8), and right to privacy (Sec. 2 & 3).

The difference in fullness is 4/5 - 2/5 = 2/5. This 2/5 of the tank capacity corresponds to 12 liters. So, (2/5) * Total Capacity = 12 liters. To find the total capacity, divide 12 by 2/5: Total Capacity = 12 / (2/5) = 12 * (5/2) = 60 / 2 = 30 liters.

Article VI, Section 23 (1) of the 1987 Philippine Constitution states: 'The Congress, by a vote of two-thirds of both Houses in joint session assembled, voting separately, shall have the sole power to declare the existence of a state of war.' This power is explicitly vested in the Congress, not solely the President or the Supreme Court.

Let the original price be P. Increased by 20%: P * (1 + 0.20) = 1.20P. Decreased by 20% from the new price: 1.20P * (1 - 0.20) = 1.20P * 0.80 = 0.96P. The final price is 0.96P, which means it is 96% of the original price. The net change is P - 0.96P = 0.04P, which is a 4% decrease. It's a common mistake to think it's no change or 0%.

This fundamental principle regarding the State ownership of natural resources, often referred to as the Regalian Doctrine, is enshrined in Article XII, Section 2 of the 1987 Philippine Constitution, which deals with National Economy and Patrimony.

Let the first odd integer be x. The next two consecutive odd integers will be x + 2 and x + 4. Their sum is x + (x + 2) + (x + 4) = 147. Combine like terms: 3x + 6 = 147. Subtract 6 from both sides: 3x = 141. Divide by 3: x = 47. The smallest integer is 47.

Article III, Section 14 (2) states that 'In all criminal prosecutions, the accused shall be presumed innocent until the contrary is proved, and shall enjoy the right to be heard by himself and counsel, to be informed of the nature and cause of the accusation against him, to have a speedy, impartial, and public trial, to meet the witnesses face to face, and to have compulsory process to secure the attendance of witnesses and the production of evidence in his behalf.' Denying the defense the ability to present their witnesses directly violates the right 'to have compulsory process to secure the attendance of witnesses and the production of evidence in his behalf.'

This is an inverse proportion problem. The total work units remain constant. Work = Number of Workers * Days. So, 10 workers * 15 days = 150 'worker-days' of work. If 5 additional workers are hired, the total number of workers becomes 10 + 5 = 15 workers. Let 'D' be the number of days: 15 workers * D days = 150 worker-days. D = 150 / 15 = 10 days.

Political rights pertain to the right of citizens to participate in the establishment or administration of government. The right to suffrage (Article V) is the most direct example of a political right, allowing citizens to vote and choose their leaders. Freedom of expression, right to liberty, and right to property are generally considered civil rights, protecting individual freedoms and property from government interference.

The ratio of milk to water is 5:3. The total ratio parts are 5 + 3 = 8 parts. Each part represents 40 liters / 8 parts = 5 liters/part. The volume of water is 3 parts * 5 liters/part = 15 liters.

Article VI, Section 2 of the 1987 Philippine Constitution clearly states: 'The Senate shall be composed of twenty-four Senators who shall be elected at large by the qualified voters of the Philippines, as may be provided by law.'

Let the principal amount be P. After 10 years, the amount becomes 3P. The interest earned is A - P = 3P - P = 2P. Using the simple interest formula I = PRT, we have 2P = P * R * 10. Divide both sides by P: 2 = 10R. So, R = 2/10 = 0.20. As a percentage, the rate is 20%.

The power of eminent domain is the inherent right of the State to take private property for public use upon payment of just compensation. This is enshrined in Article III, Section 9 of the Bill of Rights: 'Private property shall not be taken for public use without just compensation.' Option A correctly defines this power. Option B describes taxation, Option C describes police power, and Option D is incorrect as it requires just compensation and public use.

Let the tank's capacity be 1 unit. Pipe A fills 1/6 of the tank per hour. Pipe B fills 1/8 of the tank per hour. When both are open, their rates add up: 1/6 + 1/8 = (4/24) + (3/24) = 7/24 of the tank per hour. The time it takes to fill the tank is the reciprocal of their combined rate: 1 / (7/24) = 24/7 hours. 24/7 hours is approximately 3.43 hours.

Article XIV, Section 6 states: 'The national language of the Philippines is Filipino. As it evolves, it shall be further developed and enriched on the basis of existing Philippine and other languages. Subject to provisions of law and as the Congress may deem appropriate, the Government shall take steps to initiate and sustain the use of Filipino as a medium of official communication and as language of instruction in the educational system.' Section 7 adds: 'For purposes of communication and instruction, the official languages of the Philippines are Filipino and, until otherwise provided by law, English. The regional languages are the auxiliary official languages in the regions and shall serve as auxiliary media of instruction therein.' So, Filipino and English are official, and regional languages are auxiliary media of instruction.

Let the width be w meters. Then the length is w + 5 meters. The area is length * width, so w * (w + 5) = 104. Expand: w^2 + 5w = 104. Rearrange into a quadratic equation: w^2 + 5w - 104 = 0. We need two numbers that multiply to -104 and add to 5. These numbers are 13 and -8. So, (w + 13)(w - 8) = 0. Possible values for w are -13 or 8. Since width cannot be negative, w = 8 meters.

Article II, Section 6 of the 1987 Philippine Constitution states: 'The separation of Church and State shall be inviolable.' This principle means that the government cannot establish or favor any religion, nor can it prohibit the free exercise of religion, but it does not mean that religious institutions are completely prohibited from influencing public policy or that individuals cannot express their faith. It means there should be no official state religion and no undue interference by one in the affairs of the other. Option A captures the essence of this separation, preventing the state from establishing or endorsing any religion while also ensuring religious freedom.

Radius (r) = Diameter / 2 = 4m / 2 = 2m. Height (h) = 7m. Volume of cylinder (V) = π * r^2 * h. V = (22/7) * (2^2) * 7 = (22/7) * 4 * 7 = 22 * 4 = 88 cubic meters. If the tank is 3/4 full, it needs 1/4 more water to be completely full. Amount needed = (1/4) * 88 = 22 cubic meters.

Article XIII, Section 3 enumerates the rights of workers: 'They shall be entitled to security of tenure, humane conditions of work, and a living wage. They shall also participate in policy and decision-making processes affecting their rights and benefits as may be provided by law. The State shall promote the principle of shared responsibility between workers and employers and the preferential use of voluntary modes in settling disputes, including conciliation, and shall enforce their mutual compliance therewith to foster industrial peace.' The right to a guaranteed annual bonus is not explicitly listed as a constitutional right, although it may be provided by law or collective bargaining agreements.

Let the number of boys be 3x and the number of girls be 5x. The difference between girls and boys is 5x - 3x = 2x. We are told this difference is 12, so 2x = 12. Therefore, x = 6. Number of boys = 3 * 6 = 18. Number of girls = 5 * 6 = 30. Total number of students = 18 + 30 = 48.

Article VI, Section 4 of the 1987 Philippine Constitution states: 'No Senator shall serve for more than two consecutive terms.' Each term for a Senator is six years, as per Section 4. Therefore, a Senator may serve a maximum of two consecutive terms.

After 1 year: 20,000 * (1 + 0.10) = 20,000 * 1.10 = 22,000. After 2 years: 22,000 * (1 + 0.10) = 22,000 * 1.10 = 24,200. This is an example of compound growth.

The writ of habeas corpus is a legal remedy that requires a person under arrest to be brought before a court or judge, especially to secure the person's release unless lawful grounds are shown for their detention. This is a fundamental right protecting against arbitrary arrest and detention. Option A accurately describes this. Option B refers to a search warrant, Option C to a subpoena, and Option D is incorrect as it is a remedy for unlawful detention.

To find out how much milk is needed for 2/3 of the recipe, multiply the original amount of milk by 2/3: (3/4) * (2/3) = (3*2) / (4*3) = 6/12. Simplify the fraction: 6/12 = 1/2 cup.

Article IX of the 1987 Philippine Constitution establishes three independent constitutional commissions: the Civil Service Commission (CSC), the Commission on Elections (COMELEC), and the Commission on Audit (COA). The Commission on Human Rights (CHR) is also a constitutional body created under Article XIII, but it is not listed among the three 'Constitutional Commissions' under Article IX.

First, convert the speed from km/h to m/s. 72 km/h = 72 * (1000 meters / 1 km) * (1 hour / 3600 seconds) = 72 * 1000 / 3600 m/s = 72000 / 3600 m/s = 20 m/s. Now, calculate the distance: Distance = Speed * Time = 20 m/s * 5 seconds = 100 meters.

The Archipelagic Doctrine, as reflected in Article I (National Territory) of the 1987 Philippine Constitution, treats the archipelago as a single, integrated unit, and the waters around, between, and connecting the islands, regardless of their breadth and dimensions, form part of the internal waters of the Philippines. This means that the land and waters are considered one geographic entity. Option A accurately describes this principle.

Commissionable sales = Total Sales - Sales Threshold = 120,000 - 50,000 = Php 70,000. Commission = 5% of 70,000 = 0.05 * 70,000 = Php 3,500. Total Income = Base Salary + Commission = 15,000 + 3,500 = Php 18,500.

Article III, Section 8 of the 1987 Philippine Constitution states: 'The right of the people to form unions, associations, or societies for purposes not contrary to law shall not be abridged.' This is a fundamental right under the Bill of Rights.

Let the original number be 'x'. 'Increased by 15%' means x + 0.15x = 1.15x. So, 1.15x = 207. To find x, divide 207 by 1.15: x = 207 / 1.15 = 180.

The Preamble states the following goals: '...to build a just and humane society, and establish a Government that shall embody our ideals and aspirations, promote the common good, conserve and develop our patrimony, and secure to ourselves and our posterity the blessings of independence and democracy under the rule of law and a regime of truth, justice, freedom, love, equality, and peace.' While economic prosperity is a desirable outcome of good governance, it is not explicitly listed as a direct goal in the Preamble itself, unlike 'promoting the common good' or 'conserving and developing our patrimony' which relate to resources and welfare.

Time = Distance / Speed. Time = 2.5 km / 5 km/h = 0.5 hours. To convert hours to minutes, multiply by 60: 0.5 hours * 60 minutes/hour = 30 minutes.

Article VI, Section 3 of the 1987 Philippine Constitution specifies the qualifications for a Senator: 'No person shall be a Senator unless he is a natural-born citizen of the Philippines, and, on the day of the election, is at least thirty-five years of age, able to read and write, a registered voter, and a resident of the Philippines for not less than two years immediately preceding the day of the election.' Being a natural-born citizen and at least 35 years old on election day are among these requirements.

Let the side lengths of the two squares be s1 and s2. The area of a square is side squared (s^2). So, Area1 / Area2 = (s1^2) / (s2^2). We are given Area1 / Area2 = 4/9. This means (s1^2) / (s2^2) = 4/9. Taking the square root of both sides gives s1 / s2 = sqrt(4/9) = 2/3. We know s1 = 6 cm. So, 6 / s2 = 2/3. Cross-multiply: 2 * s2 = 6 * 3 => 2 * s2 = 18. Divide by 2: s2 = 9 cm.

Article III, Section 16 of the 1987 Philippine Constitution explicitly states: 'All persons shall have the right to a speedy disposition of their cases before all judicial, quasi-judicial, or administrative bodies.' This is distinct from the right to a speedy trial (Article III, Section 14) which applies specifically to criminal prosecutions.

Distance for the first part = Speed * Time = 80 km/h * 2 h = 160 km. Distance for the second part = Speed * Time = 60 km/h * 3 h = 180 km. Total Distance = 160 km + 180 km = 340 km. Total Time = 2 h + 3 h = 5 h. Average Speed = Total Distance / Total Time = 340 km / 5 h = 68 km/h.

An 'ex post facto' law (Article III, Section 22) is one that makes an act punishable in a manner in which it was not punishable when committed, or which increases the punishment for an act already committed, or which deprives a person of a defense available at the time the act was committed. Option A describes a law that retroactively criminalizes an act that was legal when performed, which is a classic example of an ex post facto law. Options B, C, and D do not involve retroactively changing the legal consequences of past actions.

Let the original length be L and the original width be W. Original Area = L * W. When dimensions are increased by 20%, the new length is 1.20L and the new width is 1.20W. New Area = (1.20L) * (1.20W) = 1.44LW. The increase in area is 1.44LW - LW = 0.44LW. Percentage increase = (0.44LW / LW) * 100% = 44%.

Article VII, Section 18 of the 1987 Philippine Constitution states: 'The President shall be the Commander-in-Chief of all armed forces of the Philippines and whenever it becomes necessary, he may call out such armed forces to prevent or suppress lawless violence, invasion, or rebellion. In case of invasion or rebellion, when the public safety requires it, he may, for a period not exceeding sixty days, suspend the privilege of the writ of habeas corpus or place the Philippines or any part thereof under martial law.' The President has this power, subject to certain limitations and review by Congress and the Supreme Court.