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Bryan Valdivia

Numerade educator

Anhidrotic ectodermal dysplasia is an X-linked recessive disorder in humans characterized by small teeth, no sweat glands, and sparse body hair. This trait is usually seen in men, but women who are heterozygous carriers of the trait often have irregular patches of skin with few or no sweat glands (see the illustration below). a. Explain why women who are heterozygous carriers of a recessive gene for anhidrotic ectodermal dysplasia have irregular patches of skin lacking sweat glands. b. Why does the distribution of the patches of skin lacking sweat glands differ among the females depicted in the illustration, even between the identical twins?

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Satyam Gupta

Numerade educator

Sketch the graph of the piece wise-defined function. ( Try doing it without a calculator.) In each case, give any points of discontinuity. $$f(x)=\left\{\begin{array}{ll}{-3-x} & {\text { if } x \leq 0} \\ {1} & {\text { if } 0< x<1} \\ {x^{2}} & {\text { if } x \geq 1}\end{array}\right.$$

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Babita Kumari

Numerade educator

What happens if you take $B=A$ in the trigonometric identity $\cos (A-B)=\cos A \cos B+\sin A \sin B ?$ Does the result agree with something you already know?

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Light Cone from a Flashlight A flashlight shines on a wall, as shown in the figure. What is the shape of the boundary of the lighted area? Explain your answer.

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AB contains midpoint M and points C and D, as shown. Compare the lengths. If you cannot draw a conclusion, write impossible to tell. Explain your reasoning a. AM and MB b. AC and MB c. MC and MD d. MB and DB

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Paul Gabriel

Numerade educator

A carbon atom, with a half-full outer shell of electrons— four in a shell that can hold eight—readily shares its electrons with other atoms and forms a vast number of molecules, many of which are the organic molecules that form the bulk of living matter. Looking at the periodic table, what other element do you think might play a role like carbon in life forms on some other planet?

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Eduard Sanchez

Numerade educator

You hang a book bag on a spring scale and place the bag on a platform scale so that the platform scale reads 25.7 $\mathrm{N}$ and the spring scale reads 17.6 $\mathrm{N} .$ (a) Draw a force diagram to represent the situation. (b) What is the magnitude of the force that Earth exerts on the bag?

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David Collins

Numerade educator

Brass is a substitutional alloy consisting of a solution of copper and zinc. A particular sample of red brass consisting of 80.0$\%$ Cu and 20.0$\%$ Zn by mass has a density of 8750 $\mathrm{kg} / \mathrm{m}^{3} .$ (a) What is the molality of $\mathrm{Zn}$ in the solid solution? (b) What is the molarity of $\mathrm{Zn}$ in the solution?

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Consider a monopolistically competitive market with $N$ firms. Each firm's business opportunities are described by the following equations: Demand: $Q = 100/N - P$ Marginal Revenue: $MR = 100/N - 2Q$ Total Cost: $TC = 50 = Q^2$ Marginal Cost: $MC = 2Q$ a. How does $N$, the number of firms in the market, affect each firm's demand curve? Why? b. How many units does each firm produce? (The answers to this and the next two questions depend on $N$.) c. What price does each firm charge? d. How much profit does each firm make? e. In the long run, how many firms will exist in this market?

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Pax World Balanced is a highly respected, socially responsible mutual fund of stocks and bonds (see Viewpoint). Vanguard Balanced Index is another highly regarded fund that represents the entire U.S. stock and bond market (an index fund). The mean and standard deviation of annualized percent returns are shown below. The annualized mean and standard deviation are for a recent 10 -year period. Pax World Balanced: $\bar{x}=9.58 \% ; s=14.05 \%$ Vanguard Balanced Index: $\bar{x}=9.02 \% ; s=12.50 \%$ a. Compute the coefficient of variation for each fund. If $\bar{x}$ represents return and s represents risk, then explain why the coefficient of variation can be taken to represent risk per unit of return. From this point of view, which fund appears to be better? Explain. b. Compute a $75 \%$ Chebyshev interval around the mean for each fund. Use the intervals to compare the two funds. As usual, past performance does not guarantee future performance.

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Darlene H.