answer:Since the function {eq}f(x) = x^3 - 2x^2 + 4x + 8 {/eq} is polynomial, it is continuous for all real numbers. Therefore, we can directly evaluate the limit by substituting {eq}x = -2 {/eq}: lim_{x to -2} (x^3 - 2x^2 + 4x + 8) = (-2)^3 - 2(-2)^2 + 4(-2) + 8 = -8 - 2 cdot 4 - 8 + 8 = -8 - 8 - 8 + 8 = boxed{-16} The limit of the function as {eq}x {/eq} approaches {eq}-2 {/eq} is {eq}-16 {/eq}.

answer:This feather appears to belong to a bird from the genus Bombycilla, specifically a Waxwing. The red tip on the feather is a distinguishing feature, contributing to the bird's name. There are two possible species within this genus: the Bohemian waxwing (B. garrulus) and the Cedar waxwing (B. cedrorum). Cedar waxwings are known for their gray bodies and red-tipped wing feathers. Image reference: [Cedar Waxwing](https://rctfan2.deviantart.com/art/Cedar-Waxwing-285656802) The presence of white patches near the tip of the secondary feathers typically indicates a Bohemian waxwing. However, since your feather lacks this feature and was found in Lexington, Kentucky, which is within the range of the Cedar waxwing, it is more likely to belong to B. cedrorum. To further confirm, it's important to note that Bohemian waxwings are not commonly found in the central western USA, which narrows down the identification to the Cedar waxwing. Thus, the feather most probably originates from a Cedar waxwing.

answer:A voltage divider, such as two 10k resistors in parallel with a 12V input, divides the voltage equally, providing 6V at the output node when no current is drawn. However, if 1mA is drawn, the output voltage changes due to voltage drops across the resistors. On the other hand, a single 6k resistor in series with a load would consistently drop 6V, delivering that voltage to a 100mA load. The series resistor can be designed to convert a known input voltage into a specific load voltage when the load current or resistance is constant. Variations in load parameters can cause deviations from the intended output voltage, with larger differences between input and load voltage leading to more significant variations. In certain situations, a voltage divider can provide a stable output voltage if the current through the lower resistor is large compared to the load current fluctuations. However, this can lead to significant power dissipation. In contrast, a single series resistor is more efficient for direct voltage translation but less adaptable to varying load conditions. To combine the stability of a voltage divider with the efficiency of a single resistor, you can add a fixed load resistor in parallel with the variable load, as demonstrated by using a 6.06k resistor with a 6k upper resistor in a voltage divider. This approach helps maintain a more stable output voltage while minimizing power waste.

answer:The reason is that there are more substitutes available for Tyson chicken (Option A is incorrect because it states the opposite). An increase in the number of substitutes leads to a higher price elasticity, as consumers can easily switch to alternative brands when prices change. In contrast, "chicken" as a class of items has fewer substitutes, meaning consumers are less sensitive to price changes for chicken in general (Option D is the correct answer). The time it takes to switch to a substitute brand (Option B) may also play a role, but the primary factor is the availability of substitutes. The share of income spent on each category (Option C) is not directly related to price elasticity in this context.