Chemical theory says that these data should lie on a straight line. If the correlation is not at least 0.997, something went wrong and the calibration procedure is repeated. Plot the data and find the correlation. Must the calibration be done again?

Unless stated otherwise, we assign the potential due to a point charge to be zero at an infinite distance from the charge. A point charge q=+3.0 nC moves through a potential difference $q = + 3.0 \mathrm { nC }$ moves through a potential difference $\Delta V = V _ { f } - V _ { i } = + 25 \mathrm { V }$. What is the change in the electric potential energy?

Evaluate the indefinite integral.

$$\int \frac{\cos \theta}{1+\sin \theta} d \theta$$

Keeping water supplies clean needs regular measurement of levels of pollutants. The measurements are indirect-a typical analysis involves forming a dye by a chemical reaction with the dissolved pollutant, then passing light through the solution and measuring its "absorbence." To calibrate such measurements, the laboratory measures known standard solutions and uses regression to relate absorbence to pollutant concentration. This is usually done every day. Here is one series of data on the absorbence of different levels of nitrates. Nitrates are measured in milligrams per liter of water.

Chemical theory says that these data should lie in a straight line. If the correlation is not at least 0.997, something went wrong and the calibration procedure is repeated. Plot the data and find the correlation. Must the calibration be done again?

The deadly Ebola virus is a threat to both people and gorillas in Central Africa. An outbreak in 2002 and 2003 killed 91 of the 95 gorillas in seven home ranges in the Congo. To study the spread of the virus, measure "distance" by the number of home ranges separating a group of gorillas from the first group infected. Here are data on distance and time in the number of days until deaths began in each later group:

$$\begin{array}{lcccccc} \text { Distance } & 1 & 3 & 4 & 4 & 4 & 5 \\ \hline \text { Time } & 4 & 21 & 33 & 41 & 43 & 46 \end{array}$$

(a) Make a scatterplot. Which is the explanatory variable? What kind of pattern does your plot show?

(b) Find the correlation r between distance and time.

(c) If time in days were replaced by time in the number of weeks until death began in each later group (fractions allowed so that 4 days becomes 4/7 weeks), would the correlation between distance and time change? Explain your answer.

Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. We have data on the lean body mass and resting metabolic rate for 12. women who are subjects in a study of dieting. Lean body mass, given in kilograms, is a person's weight leaving out all fat. Metabolic rate is measured in calories burned per 24 hours. The researchers believe that lean body' mass is an important influence on metabolic rate.

$$\begin{array}{l} \hline \text{Mass} & \text{36.1} & \text{54.6} & \text{48.5} & \text{42.0} & \text{50.6} & \text{42.0} & \text{40.3} & \text{33.1} & \text{42.4} & \text{34.5} & \text{51.1} & \text{41.2}\\ \text{Rate} & \text{995} & \text{1425} & \text{1396} & \text{1418} & \text{1502} & \text{1256} & \text{1189} & \text{913} & \text{1124} & \text{1052} & \text{1347} & \text{1204}\\ \hline \end{array}$$

Make a scatterplot to display the relationship between lean body mass and metabolic rate.

Select the best answer. You have data for many years on the average price of a barrel of oil and the average retail price of a gallon of unleaded regular gasoline. If you want to see how well the price of oil predicts the price of gas, then you should make a scatterplot with _____ as the explanatory variable. (a) the price of oil (b) the price of gas (c) the year (d) either oil price or gas price (e) time

Oysters are categorized for retail as small, medium, or large based on their volume. The grading process is slow and expensive when done by hand . A computer program estimates oyster volume based on the pixel area of 20 images of the oysters.

Table below shows the actual volume (in cm3 ) and 2D reconstructi on (in th ousands of pixels) for 30 oysters.

(a) We want to know if th e 2D imaging program is a good predictor of oyster volume. Th erefore, 2D reconstruction is our explanatory variable here. Make a scatterplot of 2D reconstruction and actual volume.

(b) Describe the overall pattern of the relationship: its form, direction, and strength. If approp riate , give the correlation coefficient . Would you say that the 2D system is an accurate way to assess oyster volume?

A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay under water. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study gives a scatterplot for one penguin titled "The Relation of Dive Duration (y) to Depth (x)." Duration y is measured in minutes and depth x is in meters. The report then says, "The regression equation for this bird is:

$$\hat { y } = 2.69 + 0.0138 x."$$

According to the regression line, how long does a typical dive to a depth of 200 meters last?

The strongest hydrogen bonds are formed between molecules of (1) $\mathrm{H}_{2} \mathrm{Te}$ (2) $\mathrm{H}_{2} \mathrm{Se}$ (3) $\mathrm{H}_{2} \mathrm{S}$ (4) $\mathrm{H}_{2} \mathrm{O}$

Select the best answer. The owner of a chain of supermarkets notices that there is a positive correlation between the sales of beer and the sales of ice cream over the course of the previous year. During seasons when sales of beer were above average, sales of ice cream also tended to be above average. Likewise, during seasons when sales of beer were below average, sales of ice cream also tended to be below average. Which of the following would be a valid conclusion from these facts? (a) Sales records must be in error. There should be no association between beer and ice cream sales. (b) Evidently, for a significant proportion of customers of these supermarkets, drinking beer causes a desire for ice cream or eating ice cream causes a thirst for beer. (c) A scatterplot of monthly ice cream sales versus monthly beer sales would show that a straight line describes the pattern in the plot, but it would have to be a horizontal line. (d) There is a clear negative association between beer sales and ice cream sales. (e) The positive correlation is most likely a result of the variable temperature; that is, as temperatures increase, so do both beer sales and ice cream sales.

(a) What are all the values that a correlation r can possibly take? (b) What are all the values that a standard deviations can possibly take?

Sales decay The sales decay for a product is given by $S=50,000 e^{-0.6 x}$, where $S$ is the monthly sales (in dollars) and $x$ is the number of months that have passed since the end of an advertising campaign. What will sales be $6$ months after the end of the campaign?