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Ankur S

Numerade educator

10. The emissivity of tungsten is 0.35. A tungsten sphere with a radius of ( 3.00 mathrm{~cm} ) is suspended within a large evacuated enclosure whose walls are at ( 300 mathrm{~K} ). What power input is required to maintain the sphere at a temperature of ( 2500 mathrm{~K} ) if heat conduction along the supports is neglected? The power input is equal to ( H_{ ext {net }} ) [ P=H_{ ext {net }}=A e sigmaleft(T^{4}-T_{s}^{4} ight) ]

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\begin{tabular}{|c|c|c|c|} \hline & K & C & F \\ \hline Water boils & & \( 100^{\circ} \) & \( 212^{\circ} \) \\ \hline & \( \uparrow \) & \( \uparrow \) & \( \uparrow \) \\ \hline & \( 100 \mathrm{~K} \) & & \\ \hline & \( \downarrow \) & \( \downarrow \) & \( \downarrow \) \\ \hline Water freezes & 273 & \( 0^{\circ} \) & \( 32^{\circ} \) \\ \hline Mercury melts & 234 & & \\ \hline CO2 solidifies & & \( -78^{\circ} \) & \\ \hline Oxygen liquifies & & & \( 298^{\circ} \) \\ \hline Absolute zero & 0 & \( -273^{\circ} \) & \\ \hline \end{tabular} Exercise 1: Complete the table to show the relationship among Kelvin, Celsius, and Fahrenheit temperature scales. Round off the temperatures to the nearest degrees.

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For Nos. 56 - 60. The researchers collected data from several sampling locations within the seagrass meadow, measuring: Seagrass depth (meters) at each location and the average number of fish per square meter observed at each location. The researchers hypothesize that there is a linear relationship between seagrass depth and fish abundance. They use a simple linear regression model to represent this relationship and obtained the model defined by, Fish Abundance \( (Y)=10+0.5^{*} \) Seagrass Depth \( (X) \) Interpret the slope and estimate/predict let's say what would be the estimated/predicted fish abundance if the seagrass depth is about \( 3 \mathrm{~m} \) ?

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For Nos. \( 52 \mathbf{- 5 5} \). Sea otters are keystone predators in kelp forests, and their presence plays a crucial role in maintaining healthy kelp ecosystems. Researchers are studying the relationship between the abundance of sea otters (number of otters per square kilometer) and the average kelp bed density ( \( \mathrm{kg} / \mathrm{m}^{2} \) ) within a specific kelp forest region. The researchers decide to use Spearman's rank correlation coefficient (rho) to analyze the relationship between sea otter abundance and kelp bed density. They obtain a rho value of -0.72 with a statistically significant p-value (less than 0.05). Interpret the strength and direction of the relationship between sea otter abundance and kelp bed density based on the Spearman's rank correlation coefficient (rho) of -0.72 ?

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For Nos. \( 34 \mathbf{- 4 2} \). Microplastics are tiny plastic particles increasingly found in marine environments, raising concerns about their impact on wildlife. Oysters are filter-feeding bivalves that play a crucial role in maintaining water quality. Researchers are investigating the effect of microplastics on oyster filtration efficiency. The researchers collected a random sample of oysters from a clean environment. For the treatment group the oysters are exposed to a controlled amount of microplastics in seawater for a specific time period. On the other hand, the oysters kept in clean seawater without microplastics for the same duration in the control group. Does the difference in filtration rate between pre-exposure and post-exposure within the treatment group (exposed to microplastics) differ significantly from the difference observed in the control group (no microplastics) at a significance level of \( \alpha=0.05 ? \) \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline Oyster & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline Before Exposure & 20 & 23 & 18 & 25 & 19 & 22 & 17 & 21 & 24 & 18 \\ \hline After Exposure & 15 & 18 & 12 & 19 & 14 & 21 & 16 & 20 & 22 & 17 \\ \hline \end{tabular}

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A random sample of 16 juvenile clownfish (Amphiprion ocellaris) was captured from a coral reef. The average time it took each fish to locate a suitable anemone for shelter was measured, with a mean time of 13 minutes. Assuming the population of search times is normally distributed with a variance of 9 minutes, can we conclude, at a significance level of 0.05, that the average search time for all juvenile clownfish on this reef is greater than 10 minutes?

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Researchers are studying the lifespans of two different lizard species found on an island: the brightly colored Gecko (Species A) and the camouflaged Forest Lizard (Species B). A random sample of 30 Gecko Geckos captured on the island showed an average lifespan in captivity of 8.2 years with a standard deviation of 1.4 years. A separate random sample of 40 Forest Lizards captured on the island showed an average lifespan in captivity of 7.5 years with a standard deviation of 0.8 years. Construct a 99% confidence interval to estimate the range within which the true difference in mean lifespan between Geckos and Forest Lizards likely falls.

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Which of the following statements is FALSE? A. A scatter plot investigates the strength and direction of the relationship between two quantitative variables. B. A chi-square test for independence is used to determine if there is a relationship between continuous variables. C. Correlation does not imply cause-and-effect relationship. D. A simple linear regression examines the relationship between one independent variable and one dependent variable.

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Suppose there is a relationship between the weight (X) and blood pressure (Y), and found out that r is positive, the A. X and Y are directly linearly related. B. X and Y are inversely linearly related

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