Knhs STEM Qualifying Exam 2019

Falling leaves do not involve the application of gas pressure. Burning fuels involve the release of gases that create pressure, vulcanizing tires involves the use of gas pressure to shape and mold the tires, and rising hot air balloons involve the use of gas pressure to lift the balloon off the ground. However, falling leaves are a result of gravity and do not require the application of gas pressure.

The common ratio between any two consecutive terms can be found by dividing the second term by the first term. In this case, dividing -12 by 3 gives us -4. Therefore, the common ratio between any two consecutive terms is -4.

The quotient obtained when (x+9) divides (x^2 - 81) is (x-9). This can be determined by performing long division. When (x+9) is divided into (x^2 - 81), the result is x-9 with no remainder. Therefore, the correct answer is B. X-9.

The given mathematical model P(x) = 3x^2 + 6x - 120,000 represents the computation for profit in a textile store. To find the computed profit when the number of meters being sold is 250, we substitute x = 250 into the equation.

P(250) = 3(250)^2 + 6(250) - 120,000
P(250) = 3(62,500) + 1,500 - 120,000
P(250) = 187,500 + 1,500 - 120,000
P(250) = 69,000

Therefore, the computed profit when 250 meters are sold is P69,000.00, which corresponds to option B.

The leading term in a polynomial function is the term with the highest degree. In this case, the polynomial function P(x) has terms with degrees 4 and 5. The term 2x^5 has the highest degree, so it is the leading term. Therefore, the correct answer is A. 2.

When we divide the expression (5b^2 + 15b - 35) by (b + 5), we can use synthetic division to simplify the process. By setting b + 5 equal to zero, we find that b = -5. Plugging -5 into the expression, we get (5(-5)^2 + 15(-5) - 35) which simplifies to (125 - 75 - 35) = 15. Therefore, the remainder is 15.

When the volume of a gas is doubled at constant pressure, according to Charles's Law, the temperature of the gas also doubles. Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is held constant. Therefore, if the volume is doubled, the temperature will also double.

The given expression is a binomial raised to the power of 3. To expand it, we use the binomial theorem. The expansion of (2x – 3)3 will have four terms. The first term is obtained by cubing the first term of the binomial, which is (2x)^3 = 8x^3. The second term is obtained by multiplying the square of the first term by the second term of the binomial, which is (2x)^2 * (-3) = -36x^2. The third term is obtained by multiplying the first term of the binomial by the square of the second term, which is (2x) * (-3)^2 = 54x. The fourth term is obtained by cubing the second term of the binomial, which is (-3)^3 = -27. Therefore, the correct expansion is 8x^3 – 36x^2 + 54x – 27.

The measure of angle F in square FATE is given as 4x + 30. To find the value of x, we can set up an equation. Since all angles in a square are equal, the measure of angle F should be 90 degrees. Therefore, we have the equation 4x + 30 = 90. Solving for x, we subtract 30 from both sides to get 4x = 60. Dividing both sides by 4, we find x = 15 degrees. Therefore, the value of x is 15 degrees, which corresponds to option C.

The arithmetic sequence increases by 5/4 each time. Adding 5/4 to the last term, 23/4, gives us 28/4, which simplifies to 7. Therefore, the next term in the sequence is 7.

Photosynthetic organisms, such as plants and algae, have the ability to convert solar energy into chemical energy stored in sugar molecules through the process of photosynthesis. During photosynthesis, these organisms use sunlight, water, and carbon dioxide to produce glucose and oxygen. The chlorophyll pigment in their cells captures the energy from sunlight and converts it into chemical energy, which is stored in the form of glucose. This process is essential for the survival of these organisms and plays a crucial role in the Earth's ecosystem by producing oxygen and serving as a source of energy for other organisms.

When a polynomial expression is divided by (x-1) and obtains a remainder of 10, it means that the expression satisfies the remainder theorem. According to the remainder theorem, if a polynomial f(x) is divided by (x-a) and the remainder is R, then f(a) = R. In this case, (-5(1)^3 + 4(1)^2 - 3(1) + K) = 10. Simplifying the equation, we get -5 + 4 - 3 + K = 10. Combining like terms, we have K - 4 = 10. Solving for K, we get K = 14. Therefore, the value of K is 14.

The function P(x) = (2x^2 - 5x + 2) (x+3) will cross the x-axis thrice because it is a quadratic function multiplied by a linear function. The quadratic function has two x-intercepts, and the linear function has one x-intercept. When the two functions are multiplied together, the x-intercepts of both functions combine, resulting in three x-intercepts in total.

As the volume of a gas decreases at constant temperature, the particles of the gas are forced into a smaller space. This results in more frequent collisions between the particles and the walls of the container, leading to an increase in pressure. Therefore, the correct answer is B. increases.

The correct answer is A. Heredity. Heredity refers to the passing of traits from parents to offspring, and DNA is responsible for carrying the genetic information that determines these traits. DNA's molecular structure, with its unique sequence of nucleotides, allows it to be replicated and passed on accurately during cell division and reproduction. This ensures that genetic information is inherited and maintained across generations, making DNA a crucial molecule for heredity.

not-available-via-ai

The polynomial function P(x) = xn is true when N is a non-negative number. This is because raising any real number to the power of a non-negative number will always result in a real number. However, if N were to be a negative number or a fraction, the function would not be defined for all real numbers. Therefore, the correct answer is B. N is a non-negative number.

The roots of a quadratic equation can be found using the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / 2a. In this equation, a = 1, b = -5, and c = -36. Plugging these values into the quadratic formula, we get x = (-(-5) ± √((-5)^2 - 4(1)(-36))) / 2(1). Simplifying further, we have x = (5 ± √(25 + 144)) / 2. This becomes x = (5 ± √169) / 2. Since √169 = 13, we have x = (5 ± 13) / 2. This gives us two possible roots: x = (5 + 13) / 2 = 18 / 2 = 9, and x = (5 - 13) / 2 = -8 / 2 = -4. Therefore, the correct answer is B. (9,-4).

A chemical equation is balanced by adding coefficients to the reactants and products. Coefficients are whole numbers that are placed in front of the chemical formulas to indicate the number of molecules or atoms involved in the reaction. By adjusting the coefficients, the number of atoms of each element on both sides of the equation can be made equal. This ensures that the law of conservation of mass is satisfied, as the total mass of the reactants is equal to the total mass of the products.

The blown out tire during a long summer drive could be due to high temperature. The heat from the summer weather can cause the air inside the tire to expand, leading to increased pressure. If the pressure exceeds the tire's maximum capacity, it can result in a blowout.

The correct answer is D. The mathematical model used to determine the distance between two points whose coordinates are (x1, y1) and (x2, y2) is the distance formula, also known as the Euclidean distance formula. This formula calculates the straight-line distance between two points in a two-dimensional Cartesian coordinate system. It is derived from the Pythagorean theorem and can be expressed as √((x2 - x1)^2 + (y2 - y1)^2).

Occupational radiation exposure is known to be a significant risk factor for developing cancer. Prolonged exposure to radiation can damage DNA and other cellular structures, leading to the development of cancerous cells. This can manifest in various forms of cancer, including but not limited to leukemia, thyroid cancer, lung cancer, and skin cancer. Therefore, cancer is considered the primary health problem associated with occupational radiation exposure.

Flowers and bees have a mutualistic relationship. Bees collect nectar from flowers as a food source, while inadvertently transferring pollen from one flower to another, aiding in the process of pollination. This benefits both the flowers and the bees, as the flowers reproduce through pollination and the bees obtain food.

The correct answer is C because when we factor out the common factor of 3 from (3a + 1), we get 3(a + 1/3). None of the other options have a factor of 3, so they cannot be factors of (3a + 1).

The equation of a circle with center (h,k) and radius r is given by (x-h)^2 + (y-k)^2 = r^2. In this question, the center of the circle is given as (3,2) and the point (9,10) is on the circle. To find the radius, we can use the distance formula between the center and the point on the circle. The distance between (3,2) and (9,10) is sqrt((9-3)^2 + (10-2)^2) = sqrt(36 + 64) = sqrt(100) = 10. Therefore, the equation of the circle is (x-3)^2 + (y-2)^2 = 10^2 = 100, which matches option B.

The area of a square is equal to the side length squared, so the area of the square with a side of 12 cm is 12^2 = 144 cm^2. The area of a rectangle is equal to the length multiplied by the width, so we can set up the equation 144 = 8 * length. Dividing both sides by 8 gives us length = 144/8 = 18 cm. Therefore, the length of the rectangle is 18 cm.

An appliance remote control system uses infrared waves. Infrared waves have a longer wavelength than visible light, but shorter than radio waves. They are commonly used for communication purposes, such as remote controls, because they can transmit signals over short distances without interference from other devices. Infrared waves are also used in various other applications, such as thermal imaging and night vision technology.

The probability of picking a non-white ball can be calculated by dividing the number of non-white balls (10 green balls + 6 blue balls = 16) by the total number of balls (10 green balls + 8 white balls + 6 blue balls = 24). Therefore, the probability is 16/24, which can be simplified to 2/3.

The wave with the lowest frequency has the longest wavelength. In diagram C, the distance between the peaks or troughs of the wave is the longest compared to the other diagrams. This indicates a lower frequency since frequency is inversely proportional to wavelength.

Mr. Torres has three options for traveling to work each day: by train, car, or jeep. Since he has to travel for five days (Monday to Friday), the total number of ways he can report for work is the product of the number of options for each day. Since each day has three options, the total number of ways is 3 * 3 * 3 * 3 * 3 = 243 ways.

Chloroplasts are specialized organelles found in plant cells where the process of converting food molecules to harness energy occurs. They contain a pigment called chlorophyll which absorbs sunlight and uses it to convert carbon dioxide and water into glucose through photosynthesis. This glucose is then used by the cell to produce ATP, the main source of energy for cellular processes. Therefore, chloroplasts play a crucial role in energy production in plant cells.

The value of the expression 10!/(4!7!) can be calculated by simplifying the factorials. 10! means 10 factorial, which is the product of all positive integers from 1 to 10. Similarly, 4! means 4 factorial, which is the product of all positive integers from 1 to 4, and 7! means 7 factorial, which is the product of all positive integers from 1 to 7. By dividing 10! by the product of 4! and 7!, we can simplify the expression to (10*9*8)/(4*3*2*1) = 720/24 = 30. Therefore, the correct answer is D. 30.

To find the value of P(-2), we substitute -2 for x in the expression P(x) = 7x^4 - 5x^3 + 2x^2 - 3.
So, P(-2) = 7(-2)^4 - 5(-2)^3 + 2(-2)^2 - 3.
Simplifying this expression, we get P(-2) = 7(16) - 5(-8) + 2(4) - 3.
Further simplifying, P(-2) = 112 + 40 + 8 - 3 = 157.
Therefore, the value of P(-2) is 157, which is option C.

In the light-dependent stage of photosynthesis, the conversion of light energy into chemical energy takes place. This process occurs in the specialized organelle called the chloroplast. Within the chloroplast, the thylakoid is the specific site where the light-dependent reactions occur. Thylakoids are membrane-bound structures that contain chlorophyll and other pigments necessary for capturing light energy. They are arranged in stacks called grana, which are interconnected by lamellae. The stroma, on the other hand, is the fluid-filled space surrounding the thylakoids where the light-independent reactions of photosynthesis occur. Therefore, the correct answer is D. thylakoid.

The probability of drawing an ace from a deck of cards is 4/52, since there are 4 aces in a deck of 52 cards. The probability of rolling an even number on a die is 3/6, since there are 3 even numbers (2, 4, and 6) out of 6 possible outcomes. To find the probability of both events occurring, we multiply the probabilities together: (4/52) * (3/6) = 12/312 = 1/26. Therefore, the probability that the card drawn is an ace and an even number appears on the die is 1/26.

Homeostasis is the characteristic of organisms that deals with the maintenance of the body's internal environment. It refers to the ability of an organism to regulate its internal conditions, such as temperature, pH levels, and nutrient balance, in order to maintain a stable and optimal internal environment for proper functioning. This process involves various physiological mechanisms that work together to keep the body's internal conditions within a narrow range, despite external changes or fluctuations. Homeostasis is crucial for the survival and normal functioning of organisms.

The committee can be formed by selecting 3 females out of 8 available females and 4 males out of 6 available males. The number of ways to select 3 females out of 8 is given by the combination formula C(8,3) = 8! / (3! * (8-3)!) = 56. Similarly, the number of ways to select 4 males out of 6 is given by the combination formula C(6,4) = 6! / (4! * (6-4)!) = 15. Therefore, the total number of ways to form the committee is 56 * 15 = 840.

In synthetic division, the number of coefficients written in the first row is equal to the degree of the polynomial plus 1. Since the polynomial in this question is a 7th degree polynomial, there will be 7 coefficients of m. Adding 1 to that gives us a total of 8 coefficients that need to be written in the first row of the synthetic division procedure. Therefore, the correct answer is D. 8.

Gamma rays are a type of electromagnetic radiation that have a high frequency and are highly penetrating. They are often used in sterilizing medical equipment in hospitals because they have the ability to kill bacteria, viruses, and other microorganisms. Gamma rays have a shorter wavelength and higher energy than other types of rays, such as infrared, radio, and ultraviolet rays, making them more effective in sterilization processes.

When a balloon is submerged in hot water, the temperature of the air inside the balloon increases. According to Charles's Law, the volume of a gas is directly proportional to its temperature, assuming the pressure remains constant. Therefore, as the temperature increases from 30°C to 50°C, the volume of the balloon will also increase. Since the initial volume is 200mL, the new volume will be greater than 200mL. Among the given options, the only volume greater than 200mL is 213mL, so the correct answer is C. 213 mL.

The value of the expression C(8, 6) represents the number of ways to choose 6 items from a set of 8 items without considering their order. This can be calculated using the formula for combinations, which is C(n, r) = n! / (r! * (n-r)!). Plugging in the values, we get C(8, 6) = 8! / (6! * (8-6)!) = 8! / (6! * 2!) = (8 * 7) / (2 * 1) = 56 / 2 = 28. Therefore, the correct answer is C. 28.

Reproduction is the correct answer because it is the process through which genetic information is passed on from one generation to another. Organisms produce offspring that resemble their parents through the process of reproduction, ensuring the continuation of genetic traits and characteristics.

A chemical reaction is a process in which the law of conservation of mass applies. This means that the total mass of the reactants before the reaction is equal to the total mass of the products after the reaction. This principle states that matter cannot be created or destroyed in a chemical reaction, only rearranged. Therefore, the mass of the reactants must be equal to the mass of the products.

As electromagnetic waves travel in a vacuum, the speed at which they propagate remains constant. This is a fundamental property of electromagnetic waves and is known as the speed of light. Regardless of the wavelength or frequency of the wave, the speed at which it travels in a vacuum is always the same, approximately 3 x 10^8 meters per second.

During glycolysis, one molecule of glucose is broken down into two molecules of pyruvate. In this process, a net of two molecules of ATP is produced. Therefore, the correct answer is A. 2.

A harmonic sequence is a sequence of numbers in which the reciprocals of the terms are in arithmetic progression. In option C, the reciprocals of the terms are not in arithmetic progression, therefore it is not an example of a harmonic sequence.

During a drought, the lack of water leads to the drying up of an area, which in turn affects the availability of food for animals and plants. This scarcity of food can result in death or migration of the organisms. Therefore, the limiting factor that affects an area that dries up due to drought is the availability of food.

Boyle's Law explains the mechanism of the gc compressor. Boyle's Law states that at a constant temperature, the volume of a gas is inversely proportional to its pressure. In the case of a gc compressor, as the pressure increases, the volume of the gas decreases. This is achieved by decreasing the size of the gas chamber, which compresses the gas. Therefore, Boyle's Law is applicable to the mechanism of the gc compressor.

The polynomial equation with roots -1, 1, and 4 can be written as P(x) = (x + 1)(x - 1)(x - 4). Expanding this equation gives P(x) = x^3 - 4x^2 - x + 4, which matches option D. Therefore, option D is the correct answer.

In a geometric sequence, each term is found by multiplying the previous term by a constant called the common ratio. To find the common ratio, we divide the 10th term by the 4th term. 25/2 divided by 800 is 1/32. Therefore, the common ratio is 1/32. To find the 14th term, we multiply the 10th term (25/2) by the common ratio (1/32) four times. (25/2) * (1/32)^4 simplifies to 25/16. Therefore, the 14th term is 25/16.