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Answers toStudent Questions

Economics

How does the price of related goods influence demand?

Related goods are goods that are bought with another good (complements), or instead of another good (substitutes). An example of complementary goods is movie tickets and beverages. Often, when someone buys a movie ticket, they will also buy a beverage. Notice that the strength of this relationship changes depending on the product: it is more common for someone to buy a drink on its own—without going to the movies—than for someone to buy a movie ticket and not buy a drink. The law of demand states that when the price of a good increases, the quantity demanded for that good decreases, and vice versa. So, if the price of movie tickets goes up, people will buy fewer movie tickets. For the theatre, this means that not only will they sell fewer movie tickets, but they will also sell fewer drinks: this shows the complementary relationship between movie tickets and drinks. An example of substitute goods are two competing movie theatres. If people usually go to the movies at MovieZone **or** CinePlace, but not both simultaneously, then these brands are strong substitutes for each other. The strength of this relationship is determined by consumer behavior. A consumer who wants to go to the movies is likely to prefer either MovieZone or CinePlace to a different activity, like going to a museum. So museums are a weak substitute for either of the theatres. As above, the law of demand dictates that if MovieZone raises the price of tickets, the quantity demanded will fall. This effect is amplified if consumers are very willing to switch to CinePlace. For this reason, firms aim to build brand loyalty, weakening the strength of the substitution relationship with competing brands. |If the price of MovieZone tickets | The quantity demanded for MovieZone tickets | The demand for drinks |The demand for CinePlace tickets | | :-: | :-: | :-: |:-:| | increases | decreases | also decreases |increases| | decreases | increases| also increases | decreases|

Environmental Systems and Societies

How does latitude affect climate?

In general, the farther you move from the Equator, the colder the climate becomes. At 0° latitude (the Equator), the climate is warm, while at 90° latitude (the Poles), it is cold. However, climate is actually shaped by insolation (sunlight received), temperature, and precipitation, which show distinct trends as latitude increases. Let’s examine how these three factors vary at different latitudes. At the Equator, the Sun’s rays strike the Earth almost directly throughout the year. As a result, insolation and temperatures remain high all year. The strong solar energy heats the air, increasing evaporation. The resulting water vapour leads to a humid climate with heavy rainfall. Water vapour also acts as a greenhouse gas, trapping heat and further raising temperatures. Countries such as **Ecuador, Brazil, Uganda**, and **Indonesia** all have warm tropical climates with high rainfall. At about 30° latitude, the Sun’s rays hit directly at the height of summer but at an angle of roughly 30° in the middle of winter. This creates hot summers and cooler winters, with insolation and temperature varying by season. Due to the Hadley circulation, air descending at this latitude is dry and causes low rainfall. As a result, these regions are dominated by **deserts**, with low precipitation, dry air, and extreme day–night temperature swings. At around 40° latitude, the Sun’s rays always strike at an angle, with the steepest angle in summer and the shallowest in winter. This creates warm summers and cold winters. Here, the Ferrell cells move heat and moisture poleward, producing moderate to high rainfall. Cities such as **Beijing, Istanbul, Madrid**, and **New York** sit at about 40° North, while **Argentina, Chile, Wellington (New Zealand)**, and **Tasmania (Australia)** lie near 40° South. These areas experience seasonal climates with significant precipitation, but local features such as proximity to oceans or mountains strongly influence the exact climate. At around 66° latitude, we reach the Arctic Circle (North) and the Antarctic Circle (South). From here until the Poles, the tilt of the Earth creates polar days (24 hours of sunlight) at the height of summer and polar nights (24 hours of darkness) at the height of winter. The extremely low insolation results in very cold temperatures. Precipitation is also minimal because evaporation is weak, and most moisture is already released around 60° latitude by the Polar cells, effectively creating polar deserts in the Arctic and Antarctic.

Physics

How to calculate percentage uncertainty

In science, all measurements have an associated uncertainty. This uncertainty communicates the precision to which the measurement was taken. If a scientific result is the product of a series of calculations of measured values, then the result itself will have an associated uncertainty to show the degree of confidence in the result. The percent uncertainty of a value is the same as the fractional or relative uncertainty of the value expressed as a percentage. It can be found from the following formula: $\hspace{3em}$ % uncertainty = $\dfrac{\textrm{absolute uncertainty}}{\textrm{measured value}} \times 100 \% $ For example, if the time for a cart to roll down a ramp is measured to be 3.6 s ± 0.2 s we can see the absolute uncertainty on the measurement is 0.2 s. We want to express this as a percentage of the measured value: $\hspace{3em}$ % uncertainty = $\dfrac{\textrm{absolute uncertainty}}{\textrm{measured value}} \times 100 \% = \dfrac{0.2}{3.6}=5.6 \%$ The method used to find the percentage uncertainty of a calculated value depends on the mathematical operation being performed. If the values involved are being added or subtracted, then the absolute uncertainties need to be added to find the absolute uncertainty on the result, and then the percentage uncertainty can be found. For example, if three length measurements are being added together: $\hspace{3em}$ (2.0 ± 0.1) cm + (8.2 ± 0.2) cm + (2.5 ± 0.5) cm The result will be the sum of the lengths and the absolute uncertainty will be the sum of the individual uncertainties: $\hspace{3em}$ Length = 2.0 + 8.2 + 2.5 = 12.7 cm $\hspace{3em}$ Absolute uncertainty = 0.1 + 0.2 + 0.5 = 0.8 cm $\hspace{3em}$ The result is expressed as 12.7 cm ± 0.8 cm. We can now find the percentage uncertainty on the answer as follows: $\hspace{3em}$ % uncertainty = $\dfrac{\textrm{absolute uncertainty}}{\textrm{measured value}} \times 100 \% = \dfrac{0.8}{12.7}=6.3 \%$ If two values are being divided or multiplied together, their individual percentage uncertainties must be found. The final result's percentage uncertainty will be the sum of the individual percentage uncertainties. For example, consider the following calculation of the density of an object. The mass $m$ and volume $V$ of the object are measured to be $\hspace{3em}$ $m$ = 4.5 g ± 0.2 g $\hspace{3em}$ $V$ = 2.5 cm$^3$ ± 0.5 cm$^3$ The density can be found from the formula $\hspace{3em}$ $\rho= \dfrac{m}{V}$ Giving $\hspace{3em}$ $\rho=\dfrac{4.5}{2.5}=1.8$ g cm$^{-3}$ Now we need to find the percentage uncertainty of the result. First, we find the percentage uncertainties on the mass and the volume: $\hspace{3em} \dfrac{\Delta m}{m} \times 100 \% = \dfrac{0.2}{4.5} \times 100 \% =4.4 \% \hspace{2em} \hspace{2em}$ and $\hspace{3em}\dfrac{\Delta V}{V} \times 100 \%= \dfrac{0.5}{2.5} \times 100 \%=20 \%$ Because we are dividing the terms, we add the percentage uncertainties: $\hspace{3em}$ density % uncertainty = mass % uncertainty + volume % uncertainty = 4.4% +20% $\hspace{10em}$ = 24%

Biology

How to differentiate between population density and population distribution?

Population density asks “How many?” while population distribution answers “Where and how are organisms spread?” Each describes a different pattern in space. Understanding the difference is important when studying ecosystems. Population density refers to the number of individuals of a species per unit area or volume. It is a numerical measure that tells you how crowded an area is. For example, a forest with 100 deer spread across 10 square kilometers has a population density of 10 deer per square kilometer. This measurement is useful for understanding the intensity of competition for resources, such as food, water, or territory, within a given habitat. In contrast, population distribution describes the pattern or spatial arrangement of individuals across a given area. It tells you how the population is spread out, not just how many there are. There are three main types of distribution patterns: uniform, where individuals are evenly spaced (often due to territorial behavior or competition); clumped, where individuals group in patches (often for social reasons or because resources are unevenly distributed); and random, where the position of one individual is independent of another (usually in habitats with abundant resources and little competition). To illustrate the difference, imagine two regions with the same population density of 50 people per square kilometer. In one region, those people may live evenly spaced across the land (uniform distribution), while in another, they may be concentrated in towns with empty countryside in between (clumped distribution). The density is the same, but the distribution reveals much more about how the population interacts with the environment and each other. In short, population density is a quantity—a measure of how many individuals exist in a specific area—while population distribution is a pattern—a description of how those individuals are arranged. Both are essential tools in studying populations, but they answer different questions: "How many?" versus "Where and how are the organisms distributed or spread?"

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