A student needs to solve the arithmetic operation: (3/4 - 1/6) ÷ (5/8 + 1/2). Which of the following represents the most simplified result?
Matematicas
Question · Medium
Slope: up or down? Pick fast
Short
If 6 bricklayers can build a perimeter wall in 15 days working at a constant rate, how many days would it take 10 bricklayers working at the same pace to complete the identical wall?
Which of the following expressions is equivalent to simplifying the radical expression √(75) - 2√(12) + √(27)?
What is the least common multiple (mínimo común múltiplo, mcm) of the numbers 24, 36, and 40?
A laboratory measures a biological specimen with a length of 0.0000458 meters. How is this measurement correctly written in standard scientific notation?
Which algebraic expression represents the statement: 'The difference between the square of a number and three times the successor of that same number'?
What is the resulting expression after completely factoring the polynomial 4x^2 - 12x - 40?
Question · Hard
What are the real solutions to the quadratic equation 2x^2 - 7x + 3 = 0?
What is the solution (x, y) to the system of linear equations 2x + 3y = 13 and 4x - y = 5?
Which interval represents the solution set for the linear inequality 3(x - 2) ≤ 5x + 4?
What is the slope (pendiente, m) and y-intercept (ordenada al origen, b) of the linear equation 4x - 2y + 8 = 0?
Two triangles, ABC and DEF, are similar (ΔABC ~ ΔDEF). If side AB = 6 cm corresponds to side DE = 15 cm, and the perimeter of ΔABC is 24 cm, what is the perimeter of ΔDEF?
A 17-meter support cable runs from the top of a vertical antenna to a ground anchor 8 meters from the antenna's base on level ground. How tall is the antenna?
What is the total area of a trapezoid whose parallel bases measure 14 cm and 8 cm, with a perpendicular height of 6 cm?
A right circular cylinder has a base radius of 3 cm and a height of 10 cm. Using π ≈ 3.14, what is the total volume of the cylinder?
In a right triangle, the acute angle θ has an adjacent side of 12 cm and a hypotenuse of 13 cm. What is the value of tan(θ)?
An observer on level ground looks at the top of a monument with an angle of elevation of 30°. If the observer is standing 60 meters from the base of the monument, what is the height of the monument? (Use tan 30° = √3 / 3 ≈ 0.577)
In an oblique triangle ABC, side a = 8 cm, side b = 6 cm, and the included angle C measures 60°. What is the length of side c? (Recall: cos 60° = 0.5)
Consider the following sample of examination scores: 7, 9, 6, 8, 10, 8, 6, 8, 9. What are the median and the mode of this dataset?
A dataset has values 4, 6, 8, 10, and 12. Given that the mean is 8, what is the population variance (varianza poblacional, σ^2)?
An urn contains 5 red balls, 4 blue balls, and 3 green balls. If one ball is drawn at random, what is the probability that it is NOT blue?
How many different 3-person committees can be formed from a group of 8 candidate teachers without regard to internal rank?
A vehicle starts from rest and accelerates uniformly at 3 m/s^2 along a straight highway for 8 seconds. What total distance does it cover during this interval?
Ciencias Experimentales
A constant net horizontal force of 60 N is applied to a box with a mass of 15 kg sitting on a frictionless surface. What acceleration does the box experience according to Newton's Second Law?
A 2 kg stone is dropped from a cliff 20 meters high. Neglecting air resistance and taking g = 9.8 m/s^2, what is its kinetic energy just before striking the ground?
Which principle of fluid mechanics states that any pressure applied to an enclosed, incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of the vessel?
Which mode of thermal energy transfer does NOT require any material medium and can propagate through the vacuum of space via electromagnetic waves?
An electrical circuit has a 12 V battery connected across a 4 Ω resistor. According to Ohm's Law, what is the electric current flowing through the circuit?
Which of the following processes represents an example of a chemical change (cambio químico) rather than a physical change?
An aluminum ion, Al³⁺, has atomic number Z = 13 and mass number A = 27. How many protons, neutrons, and electrons does this ion have?
Across a given period in the periodic table from left to right, what general trend is observed regarding electronegativity and atomic radius?
What type of chemical bond forms between potassium (K, an alkali metal with low electronegativity) and chlorine (Cl, a halogen with high electronegativity)?
When balancing the chemical combustion reaction of propane: C3H8 + O2 -> CO2 + H2O, what is the stoichiometric coefficient in front of oxygen gas (O2)?
What is the molarity (M) of a solution prepared by dissolving 40 grams of sodium hydroxide (NaOH) in enough distilled water to achieve a final solution volume of 500 mL? (Molar masses: Na = 23 g/mol, O = 16 g/mol, H = 1 g/mol)
Which cellular organelle is responsible for synthesizing adenosine triphosphate (ATP) through the process of aerobic cellular respiration?
A sample of double-stranded DNA contains 30% adenine. According to Chargaff's base-pairing rules, what percentage of its bases is guanine?
During which phase of oxygenic photosynthesis is atmospheric carbon dioxide (CO2) fixed into glucose carbohydrates within the stroma of chloroplasts?
In which specific stage of mitosis do sister chromatids separate at their centromeres and migrate toward opposite poles of the dividing cell?
In pea plants, tall stem height (T) is completely dominant over dwarf stem height (t). If two heterozygous tall plants (Tt × Tt) are crossed, what phenotypic ratio is expected in their offspring?
According to Charles Darwin's theory of evolution by natural selection, what is the primary driving mechanism that produces evolutionary adaptations across generations?
Which level of ecological organization consists of all the interacting populations of different species that inhabit a specific geographic area at the same time?
According to Lindeman's rule of ecological efficiency, approximately what percentage of usable chemical energy stored in one trophic level is transferred to the next higher trophic level?
In the biogeochemical nitrogen cycle, which biological process converts atmospheric nitrogen gas (N2) into bioavailable ammonia (NH3) or ammonium ions (NH4+)?
Which of the following atmospheric gases is the primary contributor to anthropogenic greenhouse warming resulting from the combustion of fossil fuels and extensive deforestation?
Which pre-Hispanic civilization is historically designated as the 'Cultura Madre' (Mother Culture) of Mesoamerica due to its early urban planning, colossal stone heads, and religious symbolism?
Ciencias Sociales
In the administrative structure of the Viceroyalty of New Spain, what was the highest judicial tribunal that also held governmental and advisory functions alongside the Viceroy?
Which historic document, presented by José María Morelos y Pavón in 1813 to the Congress of Anáhuac in Chilpancingo, declared Mexico's absolute independence and the sovereignty of the people?
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