The article “Human Lateralization from Head to Foot: Sex-Related Factors” (Science, 1978: 1291–1292) reports for both a sample of right-handed men and a sample of right-handed women the number of individuals whose feet were the same size, had a bigger left than right foot (a difference of half a shoe size or more), or had a bigger right than left foot.

$$\begin{array}{|c|c|c|c|c|} \hline & & & & \text { Sample } \\ & \mathbf{L}>\mathbf{R} & \mathbf{L}=\mathbf{R} & \mathbf{L}<\mathbf{R} & \text { Size } \\ \hline \text { Men } & 2 & 10 & 28 & 40 \\ \hline \text { Women } & 55 & 18 & 14 & 87 \\ \hline \end{array}$$

Does the data indicate that gender has a strong effect on the development of foot asymmetry? State the appropriate null and alternative hypotheses, compute the value of $\chi^{2}$, and obtain information about the P-value.

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. $y^{-5}-3 y^{-3}$

A radio telescope has a diameter of 100 ft and a maximum depth of 15 ft. (a) Write an equation of a parabola that models the cross section of the dish if the vertex is placed at the origin and the parabola opens up. (b) The receiver must be placed at the focus of the parabola. How far from the vertex, to the nearest tenth of a foot, should the receiver be located?

Solve each equation or inequality. $|4 x-12| \geq-3$

Write an equation for each ellipse. $e=\frac{4}{5}$; vertices at (-5, 0), (5, 0)

What is the difference between a list and a dictionary?

Write a function sumWithoutSmallest that computes the sum of a list of values, except for the smallest one, in a single loop. In the loop, update the sum and the smallest value. After the loop, return the difference.

Find the domain of each function. Write answers using interval notation. $f(x)=\frac{x^{2}-25}{x+5}$

The paper “Slender High-Strength RC Columns Under Eccentric Compression” (Magazine of Concrete Res., 2005: 361–370) gave the accompanying data on cylinder strength (MPa) for various types of columns cured under both moist conditions and laboratory drying conditions.

$$\begin{array}{lcccccc} & & & \text { Type } \\ \hline & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { M: } & 82.6 & 87.1 & 89.5 & 88.8 & 94.3 & 80.0 \\ \text { LD: } & 86.9 & 87.3 & 92.0 & 89.3 & 91.4 & 85.9 \\ & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline \text { M: } & 86.7 & 92.5 & 97.8 & 90.4 & 94.6 & 91.6 \\ \text { LD: } & 89.4 & 91.8 & 94.3 & 92.0 & 93.1 & 91.3 \end{array}$$

a. Estimate the difference in true average strength under the two drying conditions in a way that conveys information about reliability and precision, and interpret the estimate. What does the estimate suggest about how true average strength under moist drying conditions compares to that under laboratory drying conditions? b. Check the plausibility of any assumptions that underlie your analysis of (a).

a. Show that $E\left(\bar{X}_{i . .}-\bar{X}_{\ldots}\right)=\alpha_{i}$, so that $\bar{X}_{i . .}-\bar{X}_{\ldots}$ is an unbiased estimator for $\alpha_{i}$ (in the fixed effects model). b. With $\hat{\gamma}_{i j}=\bar{X}_{i j .}-\bar{X}_{i . .}-\bar{X}_{. j .}+\bar{X}_{\ldots}$, show that $\hat{\gamma}_{i j}$ is an unbiased estimator for $\gamma_{i j}$ (in the fixed effects model).

Solve the following initial value problem. $u^{\prime}(x)=\frac{1}{x^{2}+16}-4, u(0)=2$

Divide. $\left(20 k^{2}-35 k\right) \div(5 k)$

Define a dictionary that maps the course numbers of the courses you are currently taking to their corresponding course titles.

Find an equation for each line in the form $a x+b y=c,$ where a, b, and c are integers with no factor common to all three and $a \geq 0.$ x-intercept -6, y-intercept -3