A large piece of jewelry has a mass of 132.6 g. A graduated cylinder initially contains 48.6 mL water. When the jewelry is submerged in the graduated cylinder, the total volume increases to 61.2 mL. (a) Determine the density of this piece of jewelry. (b) Assuming that the jewelry is made from only one substance, what substance is it likely to be? Explain.

Refer to the negative binomial host–parasitoid model. The negative binomial model is a discrete-generation host–parasitoid model of the form

$$\begin{array}{l} N_{t+1}=b N_{t}\left(1+\frac{a P_{t}}{k}\right)^{-k} \\ P_{t+1}=c N_{t}\left[1-\left(1+\frac{a P_{t}}{k}\right)^{-k}\right] \end{array}$$

for t = 0, 1, 2, . . . . Evaluate the negative binomial model for the first 10 generations when a = 0.02, c = 3, k = 0.75, and b = 0.5. For the initial host density, choose $N_0 = 15,$ and for the initial parasitoid density, choose $P_0 = 0.$

How many significant figures are in this measurement? 56.003 g

Classify the following sets of measurements as accurate, precise, both, or neither. (a) Checking for consistency in the weight of chocolate chip cookies: 17.27 g, 13.05 g, 19.46 g, 16.92 g (b) Testing the volume of a batch of 25-mL pipettes: 27.02 mL, 26.99 mL, 26.97 mL, 27.01 mL (c) Determining the purity of gold: 99.9999%, 99.9998%, 99.9998%, 99.9999%

The label on a pressurized can of spray disinfectant warns against heating the can above $130^{\circ} \mathrm{F}$. What are the corresponding temperatures on the Celsius and kelvin temperature scales?

Indicate the SI base units or derived units that are appropriate for the following measurements: (a) the length of a marathon race (26 miles 385 yards) (b) the mass of an automobile (c) the volume of a swimming pool (d) the speed of an airplane (e) the density of gold (f) the area of a football field (g) the maximum temperature at the South Pole on April 1, 1913

Evaluate the proposed proof of the following result. Result: $\lim _{x \rightarrow 1} \frac{1}{2 x-3}=-1.$ Proof: Let $\epsilon>0$ and choose $\delta=\min \left(1, \frac{7 \epsilon}{2}\right).$ Let $0<|x-1|<\delta=\min \left(1, \frac{7 \epsilon}{2}\right).$ Since |x − 1| < 1, it follows that 0 < x < 2 and so $|2 x-3| \leq|2 x|+|-3|=2|x|+3<4+3=7.$ Since $|x-1|<7 \epsilon / 2$ we have $\left|\frac{1}{2 x-3}+1\right|=\left|\frac{2 x-2}{2 x-3}\right|=\frac{2|x-1|}{|2 x-3|}<\frac{2}{7} \cdot \frac{7 \epsilon}{2}=\epsilon.$

Let A = [0, 1] denote the closed interval of real numbers between 0 and 1. Give an example of two different bijective functions $f_1$ and $f_2$ from A to A, neither of which is the identity function.

A 147-g piece of metal has a density of 7.00 g/mL. A 50-mL graduated cylinder contains 20.0 mL of water. What is the final volume after the metal is added to the graduated cylinder?

Indicate the SI base units or derived units that are appropriate for the following measurements: (a) the length of a marathon race (26 miles 385 yards) (b) the mass of an automobile (c) the volume of a swimming pool (d) the speed of an airplane (e) the density of gold (f) the area of a football field (g) the maximum temperature at the South Pole on April 1, 1913

The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each. (a) 0.0055 g active ingredients (b) 12 tablets (c) 3% hydrogen peroxide (d) 5.5 ounces (e) 473 mL (f) 1.75% bismuth (g) 0.001% phosphoric acid (h) 99.80% inert ingredients

Give the name of the prefix and the quantity indicated by the following symbols that are used with SI base units. (a) c (b) d (c) G (d) k (e) m (f) n (g) p (h) T

In a recent Grand Prix, the winner completed the race with an average speed of $229.8 \mathrm{~km} / \mathrm{h}$. What was his speed in miles per hour, meters per second, and feet per second?

Give the name and symbol of the prefixes used with SI units to indicate multiplication by the following exact quantities. (a) $10^3$ (b) $10^{-2}$ (c) $0.1$ (d) $10^{-3}$ (e) 1,000,000 (f) $0.000001$