Evaluate the numerical expression following the standard order of operations: 18 - 3 × (4 + 2) + 16 ÷ 4.
Pensamiento Matematico
Question · Easy
Find x
Short
What is the simplified result of the fractional operation: (2/3) + (5/6) - (1/4)?
A backpack originally priced at $650 MXN is offered with a 20% promotional discount. If an additional 5% discount is applied to the discounted price for paying in cash, what is the final price paid?
Question · Medium
To prepare a concrete mixture, a builder combines cement, sand, and gravel in a ratio of 1 : 2 : 3 by weight. If 180 kg of concrete mixture is required in total, how many kilograms of sand are needed?
Simplify the algebraic expression by combining like terms: 4x^2 - 3x + 7 - (2x^2 + 5x - 4).
Solve for x in the linear equation: 3(2x - 5) + 4 = 5(x - 1) - 2.
At a local cinema, 2 adult tickets and 3 child tickets cost $310 MXN in total. If 3 adult tickets and 1 child ticket cost $290 MXN, what is the price of an adult ticket?
What are the solutions to the quadratic equation 3x² - x - 2 = 0?
A rectangular garden has a length that is 5 meters longer than its width. If the total area of the garden is 84 square meters, what is the perimeter of the garden?
Question · Hard
In a right-angled triangle, one of the acute angles measures 34°. What is the measure of the other acute angle?
A 10-meter ladder leans against a vertical wall. If the base of the ladder is placed 6 meters away from the base of the wall on level ground, how high up the wall does the ladder reach?
A circular plaza has a diameter of 20 meters. Using π ≈ 3.14, what is the area of the plaza?
A water reservoir is shaped as a right cylinder with a base radius of 3 meters and a height of 5 meters. If the reservoir is currently filled to 80% of its total capacity, how many cubic meters of water does it contain? (Use π ≈ 3.14)
A student received the following scores on five mathematics quizzes: 7, 9, 6, 10, and 8. What is the mean (average) score?
The daily temperatures (in °C) recorded during one week in Guadalajara were: 24, 28, 22, 25, 31, 27, and 23. What is the median temperature of the week?
A standard six-sided die is rolled once. What is the probability of rolling a prime number?
In a survey of 40 students, 18 usually cycle to school, 12 walk, and 10 use public transit. If one student is selected at random, what is the probability that the student does not use public transit?
Simplify the exponential expression: (3x^3 y^2)^2 × (2x^2 y^3).
A delivery van leaves a warehouse traveling north at a constant speed of 60 km/h. Exactly two hours later, a passenger car leaves the same warehouse along the same highway traveling at 90 km/h. How many hours after the car departs will it overtake the delivery van?
A vertical utility pole of height 2.5 meters casts a shadow of 1.5 meters on level ground. At the exact same time, a nearby tree casts a shadow of 9.0 meters. What is the height of the tree?
What is the slope of the straight line defined by the linear equation: 4x - 2y = 10?
In a right triangle, the side adjacent to acute angle θ has a length of 12 cm, and the hypotenuse has a length of 13 cm. What is the value of cos(θ)?
Expand and simplify the product of binomials: (2x + 3)(x - 4).
Which ordered pair (x, y) satisfies the system of linear inequalities: 2x + y ≤ 10 x - y > 2?
A quality inspector records the weights (in grams) of eight sampled parts: 45, 52, 48, 61, 44, 55, 50, and 58. What is the statistical range of this dataset?
Express the decimal number 0.000408 in standard scientific notation.
An agricultural plot has the shape of a trapezoid with parallel bases measuring 24 meters and 36 meters, and a perpendicular distance between them of 15 meters. What is the total area of the plot?
A student selects an outfit consisting of one shirt, one pair of pants, and one pair of shoes. If the student has 4 shirts, 3 pairs of pants, and 2 pairs of shoes, how many different outfit combinations are possible?
Simplify the rational algebraic expression: (x^2 - 9) / (2x^2 + 6x).
What is the Euclidean distance between P(-2, 3) and Q(4, -5) in the Cartesian plane?
What is the greatest common factor (GCF) of the numbers 36 and 54?
A cyclist travels along a straight road at a constant velocity of 6 m/s for 45 seconds. How far does the cyclist travel during this time interval?
Pensamiento Cientifico
According to Newton's second law of motion (F = m × a), what net force is required to accelerate a 1,200 kg vehicle at a rate of 2.5 m/s^2?
A 2.0 kg physics textbook rests on a classroom shelf 1.8 meters above the floor. Taking the acceleration due to gravity as g = 9.8 m/s^2, what is the gravitational potential energy of the book relative to the floor?
Which phase transition represents the direct change of a substance from a solid to a gas without passing through an intermediate liquid phase?
An electrically neutral atom of chlorine has an atomic number (Z) of 17 and a mass number (A) of 35. How many protons, neutrons, and electrons does this neutral atom contain?
Which family of chemical elements in the periodic table is characterized by having stable, filled valence electron shells, resulting in minimal chemical reactivity under standard laboratory conditions?
Balance the chemical equation for the complete combustion of propane gas: C3H8 + __ O2 → 3 CO2 + 4 H2O. What stoichiometric coefficient is required for O2?
Which cellular organelle is responsible for generating the vast majority of chemical energy in eukaryotic cells in the form of adenosine triphosphate (ATP) through aerobic respiration?
During the light-dependent reactions of oxygenic photosynthesis in plant chloroplasts, what is the primary source of electrons and the byproduct gas released into the atmosphere?
In garden pea plants, tall stem height (T) is completely dominant over dwarf stem height (t). If a homozygous tall plant (TT) is cross-pollinated with a homozygous dwarf plant (tt), what percentage of the F1 generation is expected to display tall stems?
In a terrestrial ecosystem food chain (Grass → Grasshopper → Frog → Snake → Hawk), if the primary producers (grass) capture 10,000 kJ of solar energy into net primary production, approximately how much energy is available to the secondary consumers (frogs), assuming an average 10% trophic transfer efficiency?
An electric toaster operates connected to a 120 V household electrical outlet. If the internal heating element draws a current of 5.0 A, what is the electrical resistance of the heating element?
What optical wave phenomenon causes a drinking straw partially submerged in a transparent glass of water to appear bent or displaced at the liquid-air interface?
A laboratory student dissolves 15 grams of sodium chloride (NaCl) in enough distilled water to prepare 250 mL of saline solution. What is the mass-volume concentration of this solution expressed in grams per liter (g/L)?
An aqueous solution has a measured hydronium ion concentration corresponding to a pH of 3.0. How is this solution classified, and what color change would occur if a sample were tested with blue litmus paper?
Which organ system in the human body is primarily responsible for filtering metabolic nitrogenous waste products (such as urea) from the blood and regulating systemic fluid balance?
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