How do negative signs on residuals affect the sum of squared residuals?

One industrial process has an energy consumption of $18.5 \mathrm{kWh} / \mathrm{kg}$ of $\mathrm{Mg}$. How many joules are required per mole $(1 \mathrm{kWh}=1$ kilowatt-hour $=$ $\left.3.6 \times 10^6 \mathrm{~J}\right)$? How does this energy compare with the energy of the following process?

$$\begin{align*} \mathrm{MgCl}_2(\mathrm{~s}) \rightarrow \mathrm{Mg}(\mathrm{s})+\mathrm{Cl}_2(\mathrm{~g}) \end{align*}$$

People with diabetes measure their fasting plasma glucose (FPG; measured in units of milligrams per milliliter) after fasting for at least 8 hours. Another measurement, made at regular medical checkups, is called HbA. This is roughly the percent of red blood cells that have a glucose molecule attached. It measures average exposure to glucose over a period of several months. The table below gives data on both HbA and FPG for 18 diabetics five months after they had completed a diabetes education class.

$$\begin{array}{ccc|cccc} \hline & \text { HbA } & \text { FPG } & & \text { HbA } & \text { FPG } \\ \text { Subject } & (\%) & (\mathrm{mg} / \mathrm{mL}) & \text { Subject } & (\%) & (\mathrm{mg} / \mathrm{mL}) \\ 1 & 6.1 & 141 & 10 & 8.7 & 172 \\ 2 & 6.3 & 158 & 11 & 9.4 & 200 \\ 3 & 6.4 & 112 & 12 & 10.4 & 271 \\ 4 & 6.8 & 153 & 13 & 10.6 & 103 \\ 5 & 7.0 & 134 & 14 & 10.7 & 172 \\ 6 & 7.1 & 95 & 15 & 10.7 & 359 \\ 7 & 7.5 & 96 & 16 & 11.2 & 145 \\ 8 & 7.7 & 78 & 17 & 13.7 & 147 \\ 9 & 7.9 & 148 & 18 & 19.3 & 255 \\ \hline \end{array}$$

Subject 15 is an outlier in the y direction. What effect do you think this subject has on the correlation? What effect do you think this subject has on the equation of the least-squares regression line? Calculate the correlation and equation of the least-squares regression line with and without this subject to confirm your answer.

What is the chance that the next person I meet will be different from me? The diversity index, from 0 (no diversity) to 100, measures the chance that two randomly selected people are of a different race or ethnicity. The diversity index in the United States varies widely from region to region, from as high as 81 in Hawaii to as low as 11 in Vermont. The bar graph at the top of the next column shows the national diversity index for the United States for four years the period from 1980 through 2010.

The data in the graph can be modeled by the formula

$$D=0.7 x+34 \text {, }$$

where $D$ is the national diversity index for the United States $x$ years after 1980.

How well does the formula model the national diversity index for 2010?

Use a graphing utility to approximate (rounded to two decimal places) the local maximum value and local minimum value of $f(x)=x^{3}-2 x^{2}-4 x+5,$ for -3 < x < 3.

Deflections of diving boards A diver stands at the very end of a diving board before beginning a dive. The deflection $d$ of the board at a position $s$ feet from the stationary end is given by $d=c s^2(3 L-s)$ for $0 \leq s \leq L$, where $L$ is the length of the board and $c$ is a positive constant that depends on the weight of the diver and on the physical properties of the board (see the figure). Suppose the board is $10$ feet long.

If the deflection at the end of the board is $1 \mathrm{foot}$, find $c$.

A sample of 250 observations is selected from a normal population for which the population standard deviation is known to be 25. The sample mean is 20. a. Determine the standard error of the mean. b. Explain why we can use formula to determine the 95 percent confidence interval. c. Determine the 95 percent confidence interval for the population mean

Provide structures for the semicarbazone and the $2,4$-dinitrophenylhydrazone of citral.

If you left a board lying on the grass for a few days, what would happen to the grass underneath the board? Why?

Determine whether each statement is true or false. If it is false, tell why.

Every pure imaginary number is a complex number.

Look at the following statement:
numbers = [10, 20, 30, 40, 50]
a. How many elements does the list have?
b. What is the index of the first element in the list?
c. What is the index of the last element in the list?

Use Stokes’ Theorem to evaluate

$$\mathbf{F}(x,y,z)=(x+y^2-2)\mathbf{i}+2xy\mathbf{j}+(x^2+yz^2)\mathbf{k};$$

S is the part of the paraboloid z = 4 - x squared - y squared above the xy-plane with an outward normal

Suppose that queue is an object of type queueType of size 50, queue contains 20 elements, and the index of the first element of queue is 35.

• After removing the next element from queue, what is the index of the first element?

Write the rational number as a decimal. Then tell whether the decimal is a terminating or a repeating decimal: 12/1000.