Zipf's Law, developed by George Zipf in 1949, states that in a given country, the population of a city is inversely proportional to the city's rank by size in the country.Assuming Zipf's Law: Interpret the meaning of the constant of proportionality $k$ in this context.

The blood mass of a mammal is proportional to its body mass. A rhinoceros with body mass 3000 kilograms has blood mass of 150 kilograms. Find a formula for the blood mass of a mammal as a function of the body mass and estimate the blood mass of a human with body mass 70 kilograms.

(a) What does loom mean in these lines? (b) What other meaning can loom have? (c) Interpret: How do the multiple meanings of loom contribute to the overall meaning of this passage?

Describe a situation in which you were exposed to ETS. Include how you felt afterward phusically and mentally. Then write about how you could have prevented being exposed to ETS in that situation.

The number of species of lizards, N, found on an island off Baja California is proportional to the fourth root of the area, $A$, of the island ${ }^{66}$ Write a formula for $N$ as a function of $A$. Graph this function. Is it increasing or decreasing? Is the graph concave up or concave down? What does this tell you about lizards and island area?

(a) With respect to the parallel RLC circuit, derive an expression for $R$ in terms of $C$ and $L$ to ensure the response is underdamped. (b) If $C = 1\text{ nF}$ and $L = 10\text{ mH}$, select $R$ such that an underdamped response is (just barely) achieved. (c) If the damping ratio is increased, does the circuit become more or less underdamped? Explain. (d) Compute $\alpha$ and $\omega_d$ for the value of $R$ you selected in part (b).

The minimum distance form Earth to the Sun is 91.4 million miles. The maximum distance is 94.5 million miles. a. Represent these two distances on a number line. b. Write an absolute value equation that represents the minimum and maximum distances.

Display the set of data in a stem-and-leaf plot.

68,63,70,59, 78,64,68,73,61,66,70

Fill in the blank in the sentence below with the correct term(s). Congruent figures have the _______ size and the _______ shape.

T and M are events such that n(U) = 30, n(T) = 10, n(M) = 17, and $n\left((T \cup M)^{\prime}\right)=5$. Draw a Venn diagram to display this information.

Discuss the advantages and disadvantages of histograms versus stem-and-leaf plots.

Andrea is attending a university where the cost for one year is $\$ 13,500$ . She has a scholarship worth $\$ 5,000$ and a grant worth $\$ 1,700$ . She earns $\$ 40$ a day at her job. How many days does she need to work to pay for 30$\%$ of the remaining amount?

Western University has only one women’s softball scholarship remaining for the coming year. The final two players that Western is considering are Allison Fealey and Emily Janson. The coaching staff has concluded that the speed and defensive skills are virtually identical for the two players, and that the final decision will be based on which player has the best batting average. Crosstabulations of each player’s batting performance in their junior and senior years of high school are as follows:

$$\begin{matrix} & \text{Allison} & \text{Fealey} & \text{Emily } & \text{Janson}\\ \hline\\ \text{Outcome} & \text{Junior} & \text{Senior} & \text{Outcome} & \text{Junior} & \text{Senior}\\ \text{Hit} & \text{15} & \text{75} & \text{Hit} & \text{70} & \text{35}\\ \text{No Hit} & \text{25} & \text{175} & \text{No Hit} & \text{130} & \text{85}\\ \text{Total At-Bats} & \text{40} & \text{250} & \text{Total At Bats} & \text{200} & \text{120}\\ \end{matrix}$$

A player’s batting average is computed by dividing the number of hits a player has by the total number of at-bats. Batting averages are represented as a decimal number with three places after the decimal. a. Calculate the batting average for each player in her junior year. Then calculate the batting average of each player in her senior year. Using this analysis, which player should be awarded the scholarship? Explain. b. Combine or aggregate the data for the junior and senior years into one crosstabulation as follows:

$$\begin{matrix} \text{Outcome} & \text{Fealey} & \text{Janson}\\ \hline\\ \text{Hit}\\ \text{No Hit}\\ \hline\\ \text{Total At-Bats}\\ \end{matrix}$$

Calculate each player’s batting average for the combined two years. Using this analysis, which player should be awarded the scholarship? Explain. c. Are the recommendations you made in parts (a) and (b) consistent? Explain any apparent inconsistencies.

The functions below are polynomials in factored form. Graph the function. Identify the x-intercepts. What can you say about the x-intercepts and the linear binomial factors in the functions? h(x) = x(x + 1)(x - 2)