The correct formula for determining total resistance in a circuit containing three resistors in parallel is [tex]\mathbf{R_t=R_1+R_2...+R_n}[/tex]. Thus, option C is correct.
What is total resistance?Two or more resistors are said to be connected in series when the same amount of current flows through all the resistors. In such circuits, the voltage across each resistor is different. In a series connection, if any resistor is broken or a fault occurs, then the entire circuit is turned off. The construction of a series circuit is simpler compared to a parallel circuit.
the total resistance is given as:
Rₜₒₜₐₗ = R₁ + R₂ + ….. + Rₙ
The total resistance of the system is just the total sum of individual resistances.
For example, consider the following sample problem.
A resistor with an electrical resistance value of 100 ohms is connected to another with a resistance value of 200 ohms. The two resistances are connected in parallel. What is the total resistance across the system?
Here, R₁ = 100 Ω and R₂ = 200 Ω
Rₜₒₜₐₗ = 100 + 200 = 300 Ω
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Complete question:
Which is the correct formula for determining total resistance in a circuit containing three resistors in parallel?
a. [tex](R_1^{-1}+R_2^{-1}...R_n^{-1})^{-1}[/tex]
b. [tex]L_t=L_1+L_2...+L_n[/tex]
c. [tex]R_t=R_1+R_2...+R_n[/tex]
d. [tex]X_L_ = 2 \pi f \times L[/tex]
A soft-drink bottle resonates as air is blown across its top. what happens to the resonant frequency as the level of fluid in the bottle decreases?
Because a system's resonant frequency is related to its mass, the resonant frequency of a system falls as the level of fluid in the system drops.
What exactly is the distinction between frequency and resonant frequency?Natural frequency, as it is commonly understood, is the usual supply source frequency, which is often 50 or 60 hertz. The resonant frequency is 1/2pi multiplied by 1/LC.
Depending on where you reside, the natural frequency is either 50Hz or 60Hz. Resonance can happen at any multiple of the fundamental frequency (natural).
A larger amplitude of sound waves signifies a higher sound pressure and hence a bigger volume in acoustics. In general, resonant frequencies are unfavourable for loudspeakers.
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a gas expands from i to f along the three paths indicated in the figure. calculate the work done on the gas along paths (a) iaf, (b) if, (c) ibf
A gas expands from I to f along the three paths shown in the diagram. compute the work done on the gas along paths (a) W = 810.4 J (b) W = 506.5 J (c) Wtot = 202.6 J
Along pathIAF,
the work done is the area under the curve,
W = (4 atm)(2 L)
W = 8 L-atm
Now, what's a liter-atmosphere? We solved that in the last chapter. But let's do it again here. 1.0 atm =1.013 x 10 + 5 Pa = 1.013 x 10 5N/m2
1 L-atm = 1 L-atm [ 10 - 3m3 / L] [(1.013 x 105 N/m2) /atm]
1 L-atm = 101.3 N-m = 101.3 J
W = 8 L-atm [101.3 J/L-atm]
W = 810.4 J
Along pathIBF,
the work done is still the area under the curve. Now we can describe that as the area of the rectangle BFDA plus the area of the triangle IBF.
W = ABFDA +AIBF
W = (1 atm)(2 L) +(1/2)(3 atm)(2 L)
W = 5 L-atm
W = 5 L-atm [101.3 J/L-atm]
W = 506.5 J
Along pathIAF,
There is no work done along the path IB; this is a constant volume process (this is also known as an isometric process). Along path BF, there is work done.
Wtot = WIB +WBF
Wtot = 0 + 2L-atm
Wtot = 2 L-atm
Wtot = 202.6J
Gas, along with liquid, solid, and plasma, is one of the four natural states of matter. A gas has neither a fixed shape nor a fixed volume. The gas's atoms or molecules fill the container. Even when gravity is present, the gas expands until it is uniformly distributed throughout the container.
Correct question is:
A gas expands from I to F along the three paths indicated in the figure below. Calculate the work done on the gas along each of the following paths.
(a) IAF (in J) =
(b) IF (in J) =
(c) IBF (in J) =
The images supporting question is attached below
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Taste substance binding elicits conformational change of taste receptor T1r heterodimer extracellular domains
Sweet and umami tastes are perceived by T1r taste receptors in oral cavity. T1rs are class C G-protein coupled receptors (GPCRs), and the extracellular ligand binding domains (LBDs) of T1r1/T1r3 and T1r2/T1r3 heterodimers are responsible for binding of chemical substances eliciting umami or sweet taste. However, molecular analyses of T1r have been hampered due to the difficulties in recombinant expression and protein purification, and thus little is known about mechanisms for taste perception. true or false
Due to challenges with recombinant expression and protein purification, T1r molecular studies have been impeded. The mechanisms underlying taste perception are so poorly understood. The claim is accurate.
How do taste receptors work?The oral cavity's T1r taste receptors can detect sweet and umami flavors.T1rs are G-protein-coupled class C receptors (GPCRs)Chemicals that produce an umami or sweet taste bind to the extracellular ligand binding domains (LBDs) of the T1r1/T1r3 and T1r2/T1r3 heterodimers.The T1r receptors are responsible for the perception of sweet and umami tastes, but due to the challenges in studying them, there is limited understanding of how these receptors function.The units of pressure and temperature must be consistent with the units of R, which has a specific value depending on the units used.In the case of the bicycle tire, psi and Kelvin were used because they are the units that are consistent with the value of R in the ideal gas law.The units of pressure and temperature must be consistent with the units of R, which has a specific value depending on the units used.In this case, while it's possible to use other units, psi and Kelvin are the most convenient and standard units to use in this context.To llearn more about taste receptors refer:
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A spring has an unstretched length of 0.40 meter. The spring is stretched to a length of 0.60 meter when a 10.-newton weight is hung motionless from one end. The spring constant of this spring is?
O 10. N/m
O 17 N/m
O 25 N/m
O 50. N/m
The spring constant of this spring is 50 N/m, therefore, 4th option is correct.
What is spring constant?Spring constant is the amount of force (in newtons) required to extend a spring by one meter. In this case, the spring constant is 25 N/m. This can be calculated by taking the force (10 N) divided by the amount of extension (0.60 m - 0.40 m = 0.20 m).
[tex]$ \Rightarrow \mathrm{ \frac{10 N}{0.20 m} = 50N/m}[/tex]
The force necessary to expand or compress the spring by a specific quantity is measured, and the spring constant is then calculated. The force needed to extend or compress the spring by a specific amount may be calculated by measuring it, multiplying it by the extension or compression, and then dividing the result by the force.
The behavior of a system using springs, such as a shock absorber or any other device that employs springs, is significantly influenced by the spring constant. It may also be used to figure out how much force a spring can produce when it is squeezed or expanded.
Thus, The spring constant of this spring is 50 N/m, therefore, 4th option is correct.
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a man on a motorcycle plans to make a jump off of a ramp. if he leaves the ramp with a speed of 38.0 m/s and has a speed of 36.1 m/s at the top of his trajectory, determine his maximum height (h) (in m) above the end of the ramp. ignore friction and air resistance.
According to Newton's second law, there is no acceleration in the horizontal plane because there is no net force operating in that direction.4.63 m is the highest height attained.
Determine his maximum height ?The man's initial speed (u) is 31.0 m/s.
The trajectory's top speed is 29.5 m/s.
Gravitational acceleration (g) equals 9.8 m/s²
The vertical component of velocity becomes zero as the man reaches the top of the trajectory, leaving just the horizontal component to affect him.
Additionally, according to Newton's second law, there is no acceleration in the horizontal plane because there is no net force operating in that direction.As a result, the horizontal component of velocity never changes.
Thus, the horizontal component of beginning velocity is all that is referred to as speed at the top of the trajectory.where Ux and Uy are the man's initial vertical and horizontal velocities, respectively.
To find "H," enter the value from equation (1) and 9.8 for "g."
H = 90.75/2*9.8
H = 4.63 as a result.
As a result, 4.63 m is the highest height attained.
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A golf ball is struck with a velocity of 80 ft/s as shown. Determine the distance d to where it will land. Ans: d= 166 ft
A golf ball will travel 166 feet before landing if it is struck with an 80 ft/s velocity.
What is velocity?The directional speed of an object in motion, as measured by a specific unit of time and observed from a specific point of reference, is what is referred to as velocity. The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate. Speed is the absence of direction; velocity is the presence of direction. Since velocity is a vector quantity, we must specify both the magnitude (the speed) and the direction of travel when expressing it.
Here,
(Va)x= 80cos(10+45)°= 44.886
(Va)y= 80sin(10+45)°= 65.532
S=So + Vot + 1/2at^2
d sin 10°= 0 + 65.532t + 1/2 (-32.2)t^2
0.17d= 0 + 65.532t + (-16.1)t^2
Solving the equation gives,
d=166ft
t= 3.57seconds
The distance d to where it will land is 166 feet when a golf ball is struck with a velocity of 80 ft/s.
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14. which one of the following accurately describes the force of gravity? a. the force of gravity is slightly lower at the bottom of a mountain than it is at the top. b. the gravity acceleration is in the same direction as the force of gravity, and thus away from the center of the earth. c. the gravity acceleration is in the same direction as the force of gravity, and thus toward the center of the earth. d. the gravity acceleration has no effect on a body moving in directly the opposite direction of the force of gravity. mark for review (will be highlighted on the review page)
c. the gravity acceleration is in the same direction as the force of gravity, and thus toward the center of the earth: accurately describes the force of gravity.
What is gravity?The force that pulls items toward the centre of a planetary or other body is known as gravity. The gravitational pull maintains each of the planet in orbit about the sun. The degree to which a coordinate in space-time is invisibly bent determines the intensity of the gravitational "field" at any given place in space or time. Massive items tumble down these bends in the direction of one another. The stronger the attraction between items, the more matter there is, and the closer together things are. And unlike electricity and magnetism, which may either repel or attract, gravity always draws objects together.
Thus, correct option is: c
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A 0.5 Kg ball is kicked and has a maximum kinetic energy of 225 J. What is the maximum height above the ground the ball will reach?
I am looking more for the formula because i have several to work.
Answer:
45.9 m
Explanation:
KE = 1/2mv² = 225 J
PE = mgh
If all the KE is converted to PE, then:
(0.50 kg)(9.8 m/s²)(h) = 225 J
h = (225 J) / (0.50 kg)(9.8 m/s²) = 45.9 m
Macmillan Learning
A black mamba snake has a length of 2.60 m and a top speed of 4.50 m/s. Suppose a mongoose and a black mamba find
themselves nose to nose. In an effort to escape, the snake accelerates past the mongoose at 8.37 m/s² from rest.
How much time ftop does it take the snake to reach its top
speed?
How far dsnake does the snake travel in that time?
How much time freact does the mongoose have to react before
the black mamba's tail passes the mongoose's nose?
ftop
dsnake =
freact=
S
m
S
Answer:
Explanation:
Δt = Δv/a = (4.5 m/s) / (8.37 m/s²) = 0.538 s = time to reach top speed
d = Vi + 1/2at²
d = 0 + 1/2(8.37 m/s²)(0.538 s)² = 1.21 m = distance snake traveled while accelerating
t = d/v = (2.60 m - 1.21 m) / (4.5 m/s) = 0.31 s = reaction time before snake tail passes mongoose nose
According to the question of speed, ftop is 0.9578 s, dsnake is 2.14 m, freact is 0.4773 s.
What is speed?
Speed is the rate at which an object moves from one place to another. It is expressed in units of distance per unit of time, such as miles per hour or kilometers per hour. Speed is a scalar quantity, meaning that it has magnitude but no direction. Acceleration, on the other hand, is a vector quantity that has both magnitude and direction. Speed is directly related to the amount of time it takes an object to move from one point to another, and is inversely proportional to the time it takes to cover a given distance. Speed can also be affected by external factors such as wind, terrain, and friction. Speed is an important concept in physics and is often used to calculate the kinetic energy of an object.
ftop = 0.5 × (8.37 m/s²) / (4.50 m/s) = 0.9578 s
dsnake = 0.5 × (4.50 m/s) × (0.9578 s) = 2.14 m
freact = 2.14 m / (4.50 m/s) = 0.4773 s
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Suppose you are in charge of stocking a fish pond with fish for which the rate of population dP growth is modeled by the differential equation SP_0.02p2 dt (a) If P(0) = 50, find lim P(t) . Justify your answer: Sketch the graph of P(t) . (70 (b) If P(0) = 300, find lim P(t) . Justify your answer. Sketch the graph of P(t) . 170 (c) If P(0) = 500, find lim P(t) . Justify your answer Sketch the graph of P(t) [70 Which of these graphs, a, b, O €, has an inflection point? Which are increasing? Which are decreasing?
(a) The limit of the exponential function is infinity. (b)the limit of the exponential function is infinity. (c)the limit of the exponential function is infinity.
What is differential equation?A differential equation is an equation which has one or more terms and the derivatives of one variable with respect to the other variable dy/dx = f(x), where “x” is an independent variable and “y” is dependent variable.
(a) P(t) = 50e^(0.02t^2)
The limit as t approaches infinity of P(t) is infinity. This can be seen by using L'Hopital's rule and finding that limit of exponential function is infinity. The graph of P(t) would be a parabola that starts at 50 and increases as t increases.
(b) P(t) = 300e^(0.02t^2)
The limit as t approaches infinity of P(t) is infinity. This can be seen by using L'Hopital's rule and finding that limit of the exponential function is infinity. The graph of P(t) would be parabola that starts at 300 and increases as t increases.
(c) P(t) = 500e^(0.02t^2)
The limit as t approaches infinity of P(t) is infinity. This can be seen by using L'Hopital's rule and finding that limit of exponential function is infinity. The graph of P(t) would be parabola that starts at 500 and increases as t increases.
All of the graphs are increasing and have no inflection point. They are increasing because the exponential function e^(0.02t^2) is positive, and it will always increase as the t increases.
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a 11.8-kg cylinder rolls without slipping on a rough surface. at an instant when its center of gravity has a speed of 10.2 m/s, determine the following.
The answers are:
a.) The translational kinetic energy of its center of gravity: 638.144J
b.)The rotational kinetic energy about its center of gravity 319.072 J
c.) Its total kinetic energy 957.216 J
Given:
M = 11.8 kg cylinder
V = speed of center of gravity = 10.2m/s
(a) Translational kinetic energy = 1/2mv²
1/2x 11.8kg x 10.2²
= 11.8x108.16/2
= 1276.288/2
= 638.144 J
This is the translational energy
(b) Rotational energy =1/2Iw²
I = mv²/2
w = v/r
When we substitute
1/2[mv²/2][v/r]²
= 1/4mv²
= 1/4 x 11.8 x 10.2²
= 1276.288/4
= 319.072
This is the rotational energy
(c) Total kinetic energy:
We add the values of A and B above to get this.
638.144 J + 319.072 J
= 957.216J
Complete question: A 11.8-kg cylinder rolls without slipping on a rough surface. At an instant when its center of gravity has a speed of 10.2 m/s, determine the following. (a) the translational kinetic energy of its center of gravity (b) the rotational kinetic energy about its center of gravity (c) its total kinetic energy.
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A bicycle tire is spinning clockwise at 3.40 rad/s. During a time period Δt = 2.50 s, the tire is stopped and spun in the opposite (counterclockwise) direction, also at 3.40 rad/s. Calculate the change in the tire's angular velocity Δω and the tire's average angular acceleration αav. (Indicate the direction with the signs of your answers.)
a) The change in the angular velocity is - 3.40 rad/s.
b) The angular acceleration is -1.36rad/s^2.
What is the change in the angular velocity?We have to note that the change in the angular velocity would be obtain as the difference between the initial and the final angular velocity of the bicycle tire.
Then we would have that;
Change in the angular velocity = 0 rad/s - 3.40 rad/s = - 3.40 rad/s
We know that the angular acceleration = Change in the angular velocity/Time
= - 3.40 rad/s/2.5 s
= -1.36rad/s^2
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in julius caesar, cassius offering his dagger to brutus so that brutus can stab him is an example of cassius's:
Cassius accuses Brutus of wrongdoing in this scenario. Brutus responds by accusing Cassius of bribery and reminding him that they killed Caesar in order to prevent him from becoming corrupt, not to become corrupt themselves.
What does the juxtaposition in Cassius' monologue serve?Cassius' resentment is revealed through these contrasting elements as a result of his perceived equality with Caesar, but his reality that he is lower than him. As a result, Cassius' anger demonstrates how perceived disparity promotes resentment and envy, causing a poisonous relationship.
The argument becomes heated, and Cassius pulls his knife, daring Brutus to murder him
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choose a process and system that match the following energy description: the kinetic energy of an object becomes gravitational potential energy of the system\
One process and system that matches the following energy description: "the kinetic energy of an object becomes gravitational potential energy of the system" is a roller coaster.
How does the conversion of gravitational potential energy to kinetic energy and vice versa in a roller coaster contribute to the thrill and excitement of the ride?The conversion of gravitational potential energy to kinetic energy and vice versa in a roller coaster contributes to the thrill and excitement of the ride because it creates a sense of acceleration, speed and height. As the roller coaster car goes up the hill, the rider feels a pull in their stomach as they gain potential energy, and as the car goes down the hill, they feel a rush of speed as they gain kinetic energy. This back and forth conversion of energy creates a sense of unpredictability and excitement for the rider. Additionally, the change in speed and direction also create an illusion of weightlessness as the riders feel themselves being pulled out of their seats. This all together creates an exciting and thrilling experience for the riders.
In a roller coaster, a train or cars are pulled to the top of a hill using a motor or chain lift. As the train goes up the hill, it gains gravitational potential energy. As the train goes over the hill and down the other side, it loses gravitational potential energy and gains kinetic energy. This process continues as the train goes through various hills and valleys on the roller coaster.
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HELPPP ASP !!!!!!!!!
1 mol of an ideal gas is placed in a sealed container. Which of the following would NOT cause the pressure to double? a. decreasing the volume by a factor of 2 b. adding another mol of gas c. increasing the temperature from 100oC to 200oC
In this situation, the pressure will change in direct proportion to the temperature. Double both the pressure and the temperature.
What happens when Boyle's law doubles the pressure?When the temperature is held constant, pressure decreases as volume increases and vice versa. As a result, when the volume is cut in half, the pressure is also cut in half, and vice versa.
What does Boyle's law increase?According to Boyle's Law, pressure and volume have an inverse relationship. The volume reduces as the pressure rises, and the volume rises as the pressure falls.
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all forms of matter have specific temperatures which they melt phazes condense or vaporize.
The particles in a liquid have enough energy to transform into gases at a specific temperature. Boiling (or vapourization) is the conversion of a liquid into a gas; condensation is the conversion of a gas into a liquid.
Melting is the process through which a solid transforms into a liquid (an older term that you may see sometimes is fusion). It is known as solidification when a liquid turns into a solid. Any pure substance's melting point, or the temperature at which melting starts, is a property of that substance. For a solid to turn into a liquid, energy is needed. Each pure material requires a specific quantity of energy to transform from a solid to a liquid. The symbol for this quantity, Hfus, stands for the substance's enthalpy of fusion (also known as heat of fusion). In Table 10.2, "Enthalpies of Fusion for Various Substances," a number of Hfus values are provided;
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calculate mechanical advantage of a machine whoch needs an effort of 5n to lift a load of 55n
Answer:
11
Explanation:
MA = Fout / Fin = 55 N / 5 N = 11
how many coulombs of charge are on the electrons in a nickel coin? follow this method to find the answer.
A nickel coin contains 5.2 x 10^22 Ni atoms as coulombs of charge.
What is coulombs of charge?In the International System of Units, the unit of electric charge is the coulomb. It is equivalent to the electrical charge delivered by a 1 ampere constant current in 1 second in the current version of the SI. The amount of charge carried by a current of one amp for one second is measured in coulombs, which is the unit of measurement used in the SI for electric charge. It may also be a property of a substance that causes electrical and magnetic effects to occur. The symbol for it is C. According to math, 1 Coulomb equals 1 Ampere x 1/sec.
Here,
The mass of a nickel coin is 5 g.
1 mol of Ni weighs 58 g.
1 mol=6.022 x 10²³ atoms of Ni.
in 58 g,
=6.022 x 10²³ atoms of Ni
then in 5 g the number of Ni atoms = - 6.022 x 10²³ /58 x 5
= 5.2 x 10²² Ni atoms,
Therefore number of Ni atoms as coulombs of charge are 5.2 x 10²² atoms in a nickel coin.
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directions: for the question or incomplete statement below, two of the suggested answers are correct. for this question, you must select both correct choices to earn credit. no partial credit will be earned if only one correct choice is selected. select the two that are best in each case. a school library allows students to borrow laptops. a computer program is used to count the number of times a particular laptop has been borrowed from the library open parenthesis, borrows, close parenthesis and the number of times the same laptop has been returned to the library open parenthesis, returns, close parenthesis. which of the following indicate that a particular laptop is not currently borrowed?
-Borrows = 0 , -Returns > 0, Since these two statements have the same truth value, they are both indicating that a particular laptop is not currently borrowed.
What is Equivalence theory?
This question is using the Theory of Equivalence, which states that two statements are logically equivalent if they have the same truth value.
In this case, the two statements are:
1) Borrows = 0
2) Returns > 0
Both choices indicate that a particular laptop is not currently borrowed from the library.
Borrows = 0 indicates that the laptop has not been borrowed at all. Since the library keeps track of the number of times a laptop is borrowed, if the number is zero, then it has not been borrowed.
Returns > 0 indicates that the laptop has been borrowed before, but it is not currently borrowed.
Since the library keeps track of the number of times a laptop is returned, if the number is greater than zero, then it has been returned and is therefore not currently borrowed.
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(a) A fundamental law of motion states that the acceleration of an object is directly proportional to the resultant force exerted on the object and inversely proportional to its mass. If the proportionality constant is defined to have no dimensions, determine the dimensions of force. (Use the following as necessary: M, L, and T.)
[force] =
(b) The newton is the SI unit of force. According to the results for (a), how can you express a force having units of newtons using the fundamental units of mass, length, and time? (Use the following units as necessary: kg, m, and s.)
The behavior of things is predicted by Newton's first law of motion when all external forces are equal.
What is Newton's second law?The first law, sometimes known as the law of inertia, asserts that if an object's forces are balanced, its acceleration will be zero meters per second.
When all forces are balanced, an object is said to be in equilibrium and won't accelerate. Newton postulated that an item will only accelerate in the presence of a net or unbalanced force. An object will accelerate if there is an imbalanced force present, changing its direction, speed, or both.
Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced. The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.
Therefore, The behavior of things is predicted by Newton's first law of motion when all external forces are equal.
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13. ssm The middle C string on a piano is under a tension of 944 N. The period and wavelength of a wave on this string are 3.82 ms and 1.26 m, respectively. Find the linear density of the string.
The linear density of the string is 2.86 x 10^-5 kg/m.
What is linear density?
Linear density, also known as linear mass density, is a measure of the mass of a material per unit length. It is typically used to describe the properties of thin, elongated objects such as strings, wires, and fibers. The unit of measurement for linear density is typically kilograms per meter (kg/m) or grams per centimeter (g/cm). It is calculated by dividing the mass of the material by its length.
To find the linear density of the string, we need to use the relationship between the tension, linear density, and wave properties, which is given by the equation:
Tension = (linear density) * (wave speed)^2
where wave speed is the product of the frequency and wavelength of the wave.
Given the tension, period and wavelength, we can find the linear density using the following steps:
Find the frequency of the wave using the period:frequency = 1 / period = 1 / 3.82 x 10^-3 s = 261.9 Hz
Find the wave speed using the wavelength and frequency:wave speed = wavelength * frequency = 1.26 m * 261.9 Hz = 331.9 m/s
Substitute the values into the equation:Tension = (linear density) * (wave speed)^2
944 N = (linear density) * (331.9 m/s)^2
Solve for linear density:linear density = Tension / (wave speed)^2 = 944 N / (331.9 m/s)^2 = 2.86 x 10^-5 kg/m
Therefore, the linear density of the string is 2.86 x 10^-5 kg/m.
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A 240-mL cup of low‑fat milk contains 10 mg of cholesterol. Express the cholesterol concentration in the milk in kilograms per cubic meter.
Answer:
Approximately [tex]0.042\; {\rm kg \cdot m^{-3}}[/tex].
Explanation:
Note the unit conversion for mass:
[tex]1\; {\rm g} = 10^{3}\; {\rm mg}[/tex].
[tex]1\; {\rm kg} = 10^{3}\; {\rm g}[/tex].
Therefore:
[tex]\begin{aligned}& 10\; {\rm mg} \times \frac{1\; {\rm g}}{10^{3}\; {\rm mg}} \times \frac{1\; {\rm kg}}{10^{3}\; {\rm g}} \\ =\; & 10\; {\rm mg} \times \frac{1\; {\rm kg}}{10^{6}\; {\rm mg}} \\ =\; & 10^{-5}\; {\rm kg}\end{aligned}[/tex].
Similarly, for volume:
[tex]1\; {\rm mL} = 1\; {\rm cm^{3}}[/tex].
[tex]1\; {\rm m^{3}} = 10^{3}\; {\rm dm^{3}} = 10^{6}\; {\rm cm^{3}}[/tex].
Thus, [tex]1\; {\rm m^{3}} = 10^{6}\; {\rm mL}[/tex].
[tex]\begin{aligned}& 240\; {\rm L} \times \frac{1\; {\rm m^{3}}}{10^{6}\; {\rm mL}} = 2.40\times 10^{-4}\; {\rm m^{3}}\end{aligned}[/tex].
Divide mass by volume to find the mass-to-volume ratio:
[tex]\begin{aligned}\frac{10^{-5}\; {\rm kg}}{2.40 \times 10^{-4}\; {\rm m^{3}}} \approx 0.042\; {\rm kg \cdot m^{-3}}\end{aligned}[/tex].
