Many top market global brands have been struggling to increase sales or market share in recent years. The news of Burberry's continuing success leaves some wondering how the company is delivering such a strong performance, with a revenue increase of $35 \%, 105$ new stores added and a productivity boost of $11 \%$ in the last $12$ months. 'While the luxury industry faces global challenges in the year ahead, we remain confident in our team's ability to outperform, underpinned by the consistent execution of our key strategies,' said Burberry's chief executive. The sales figures show that the company's plan to survive the financial crisis by targeting flagship markets has so far been successful. Burberny's USP of being an 'iconic British luxury brand' has been enhanced in the last few years to attract a new, younger market segment while keeping current customers satisfied. Now the company is targeting young, digitally aware consumers in the world's wealthiest markets. As rising internet penetration and increasing familiarity with online shopping is a burgeoning trend, the company's focus is mainly on digital integration. The company's targets are $25$ of the world's wealthier cities (including London, New York and Beijing); according to Burberry these account for more than half of the global luxury fashion trade. These target markets also benefit from high levels of tourism and very wealthy residents. The company is investing in underpenetrated markets such as Asia Pacific, Latin America and the Middle East, as these are forecast to see continued growth in consumption of luxury goods as tourism, salaries and store openings increase. Non-apparel, including handbags, small leather goods, scarves, shoes, belts and jewellery, remain a key driver of the company's growth, contributing $40 \%$ of retail sales in the last $12$ months. Low prices have never been a consideration for Burberry as its management perceives that its consumers demand exclusivity and style $–$ and these do not integrate well with low prices.

Evaluate the ways Burberry differentiates its products from its competitors in the market for female clothing.

Global Positioning System (GPS) satellites transmit radio signals used by receivers on the Earth to determine position with very high precision. The operating principle is that a receiver gets signals simultaneously from several different satellites (typically at least four) and uses them to "triangulate" its position. This method relies on precise knowledge of the time and also the time it takes for a satellite signal to reach the receiving position. Until a few years ago, the U.S. government intentionally degraded the timing information so that it had an uncertainty of about $350 \mathrm{~ns}$. Based on this timing error, estimate the precision in meters with which the position can be determined.

Let G be the set of all integers x that can be written as the sum of the squares of two integers, $x=a^{2}+b^{2}.$ For example, $13=3^{2}+2^{2}$ is in G, while 7 fails to be in G. a. List all integers $x \leq 10$ that are in G. b. Show that G is closed under multiplication: If $x=a^{2}+b^{2}$ and $y=c^{2}+d^{2}$ are in G, then so is their product xy. c. Given that $2642=31^{2}+41^{2}$ and $3218=37^{2}+43^{2},$ write $8,501,956=2642 \cdot 3218$ as the sum of the squares of two positive integers. You may use technology.

Aster Company is considering an investment in technology to improve its operations. The investment will require an initial outlay of $800,000 and yield the following expected cash flows. Management requires investments to have a payback period of two years, and it requires a 10% return on its investments.

Required

1. Determine the payback period for this investment.
2. Determine the break-even time for this investment.
3. Determine the net present value for this investment.

Analysis Component

4. Should management invest in this project? Explain.

Use the technology of your choice to a. obtain and interpret the standard error of the estimate. b. obtain a residual plot and a normal probability plot of the residuals. c. decide whether you can reasonably consider Assumptions 1-3 for regression inferences met by the two variables under consideration. How important are birdies (a score of one under par on a given hole) in determining the final total score of a woman golfer? From the U.S. Women’s Open Web site, we obtained data on number of birdies during a tournament and final score for 63 women golfers. The data are presented on the WeissStats CD.

Industry sector and outsourcing. Many companies have selected to outsource segments of their business to external providers in order to cut costs and improve quality and/or efficiencies. Common business segments that are outsourced include Information Technology (IT) and Human Resources (HR). Consider only the companies that have outsourced their IT and HR business segments. Do these data suggest significant differences between companies in the financial and industrial goods sectors with regard to their outsourcing decisions?

The global sea level could rise due to partial melting of the polar ice caps. The table represents a function $R$ that models this expected rise in sea level in centimeters for the year $t$. (This model assumes no changes in current trends.)

$${\begin{array}{|c|c|c|c|c|c|} \hline t(yr)&1990&2000&2030&2070&2100\\ \hline R(t)(cm)&0&1&18&44&66\\ \hline \end{array}}$$

Is $R$ a one-to-one function? Explain.

Use $R(t)$ to find a table for $R^{-1}(t)$. Interpret $R^{-1}$.

Sugerencias. Lee las siguientes sugerencias sobre como proteger el medioambiente. Luego, con un(a) companero/a, habla de la importancia que tiene cada una. Identifica aquellas que estan mas relacionadas con la situacion en tu comunidad y explica lo que estan haciendo los ciudadanos para corregir el problema. -Hay que combatir el calentamiento global. -Hay que proteger el medioambiente para tener un buen futuro. -No hay que destruir los bosques. -Hay que evitar los productos quimicos.

Domestic Airfare. The Global Business Travel Association reported the domestic airfare for business travel for the current year and the previous year. Below is a sample of 12 flights with their domestic airfares shown for both years.

$$\begin{array}{cccc} \text { Current Year } & \text { Previous Year } & \text { Current Year } & \text { Previous Year } \\ 345 & 315 & 635 & 585 \\ 526 & 463 & 710 & 650 \\ 420 & 462 & 605 & 545 \\ 216 & 206 & 517 & 547 \\ 285 & 275 & 570 & 508 \\ 405 & 432 & 610 & 580 \end{array}$$

b. What is the sample mean domestic airfare for business travel for each year?

Use graphing technology to generate the table below. Then identify patterns within the table. Be sure to extend your table far enough to confirm your patterns. You do not to copy the entire table but recording useful values may be helpful to identify patterns. Which values are helpful? How many patterns can you find? "

$$\begin{matrix}\text{x} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5} & \text{6} & \text{7} & \text{8} & \mathrm{\ldots}\\ \mathrm{\log _{2}(x)} & & & & & & & & & \mathrm{\ldots}\\\end{matrix}$$

"

Here are data from a small bookstore.

The regression line is given by:$ $\widehat{\text{Sales}}=8.10+0.9134 Number of Salespeople Working. The assumptions and conditions for regression are met, and from technology, we learn that$S E(b_1)$=0.0873$s_c$=1.477

a) What are the predicted Sales on a day with 12 employees working?

Apple Computer wants to have $2.1 billion available 5 years from now in order to finance initial production of a device that applies IOT technology for home use. The company expects to set aside uniformly increasing amounts of money each year to meet its goal, starting with$100 million at the end of year 1. How much will the constant increase, G, have to be each year at a rate of return of 18% per year? Try your skill by using the Goal Seek tool to find the required gradient. Start the evaluation with G = $50 million per year.

The table shown lists the average global temperature for each decade from 1880 to 2009 .

What is the range of the data set

Here is a table of values from the U.S. Bureau of Labor Statistics (disk file BLS_Output):

For the series of Output per hour of labor:

b) Explain the Trend component. (Remember: Direction, Form, and Strength)