How many possible values of m satisfy the inequality |m + 1| – |m – 3| > 4, if m is an integer?

Country P’s Olympic Committee is determining how much sponsorship money it needs to raise in order to cover its expenses in helping athletes train for and travel to next summer’s Olympic Games. There are four possible sources of funding: government grants, income from television rights, team sponsorship, and individual endorsement deals. The Committee’s task is to determine how to maximize funding from the latter three sources, in order to send as many athletes as possible to the Games, while minimizing the drain on government funding. Government funding is provided only when the team is unable to fully fund its activities.

A small number of the highest-profile athletes have secured individual endorsement deals; this money, however, belongs to that athlete alone and any such athletes are removed from the team funding calculations. An individual team is considered underfunded if its funding (not including government sources) covers less than 95% of the team’s expected expenses. Any surplus funding from TV rights or team sponsors reverts to the Olympic Committee and may be reallocated among other teams. The government will then provide funding to match up to 5% of team expenses or the amount needed to reach 100% funding, whichever is smaller.

B_n=(−1)ⁿ∗n+3 for all integers n ≥ 1. What is the 9th term of the sequence?

If y²−11 is negative, what is the greatest possible integer value for y ?

If n is a positive integer, what is the remainder when is divided by 10?

Research directed toward recovering ancient DNA began in 1984, when pieces of DNA were extracted from museum specimens of an animal extinct for about a century. Most such genetic material recovered from biological relics consists of tiny fragments, rather than the strings of thousands of molecules typically found in living organisms, but these fragments may contain sufficient information to identify a species through comparison with modern DNA from descendant species. However, the need to verify whether particular fragments actually come from ancient organisms or whether they come from modern contaminants, such as the sweat of people who have handled the specimens, is crucial. For example, some scientists claim to have extracted DNA fragments from 17-million-year-old magnolia leaves found in an unusual fossil deposit in Idaho. But other scientists suggest that this DNA is a modern contaminant; they argue that even under the most favorable conditions, the rate of degradation of DNA is such that useful genetic material could not be recovered from fossils that old and that since the leaves were trapped in wet deposits, it is particularly unlikely that any DNA would have survived so long. A solution to this debate lies in the fact that any ancient DNA should differ from that of related modern species. If the DNA extracted from the fossil leaves were actually a modern contaminant, this fact would be apparent from the information contained in the DNA.

By the early 1970s, historian Gabriel Kolko and economist George Stigler had independently reached compatible conclusions about the interests served by the United States government's regulation of business during the Progressive era (1890-1915). Kolko argued that big business led the struggle for federal regulation and that regulatory legislation was motivated primarily by legislators' desire to benefit business, not, as the view dominant up until that time had held, by the desire to protect the public interest. As Stigler explained, the federal government's ability to subsidize business, to control the entry of foreign goods, and to fix prices could be used by businesses to their advantage, just as campaign contributions from businesses could be used to advantage by legislators.

There is no denying Kolko's and Stigler's basic claims. Nevertheless, businesses within an industry did not always welcome being regulated, nor did industries necessarily respond uniformly to legislators' efforts to enact regulations affecting them. All but one major railroad in 1905 opposed an expansion of the regulatory power of the Interstate Commerce Committee (ICC) of the United States Senate, and though the Hepburn Act, which granted the ICC rate-making power in the railroad industry, was passed the following year, commercial users of the railroads were divided about the passage of the act: the coal industry opposed it, the agricultural industry favored it, and the lumber industry was split.

Karin: Every time I go to the park, I notice that there are lizards. Usually when I see one, it is a Lacerta viridis, so there are probably a large number of lizards of that species in the park.

Lina: There might be a lot of lizards of that species in the park, but your experiences don't give much evidence that there are.

Select for Supports Karin's inference the statement that, if true, most strongly supports the inference that Karin draws, and select for Supports Lina's position the statement that, if true, most strongly supports the position that Lina expresses. Make only two selections, one in each column.

A drugstore chain can return empty lipsticks that it originally sold to the supplier for recycling. To encourage customers to return their empty lipsticks to its stores rather than throw them in the trash, the drugstore chain has instituted a new policy allowing customers to bring empty lipsticks to a store and exchange them for a new, full lipstick, as shown in the diagram.

Select from each drop-down menu the option that creates the most accurate statement based on the information provided.

Dara has 11 empty lipsticks originally purchased from this drugstore chain. If Dara exchanges these for new lipsticks under the store policy, wears the new lipsticks until they run out, and then repeats these actions (with the lipsticks that are now empty) to the fullest extent possible—without acquiring any additional lipsticks outside of the exchange program—then Dara will be able to acquire and wear

new lipsticks, and will have  upon reaching “End”.

For each year from 2011 through 2015, the graph shows the number of employees of a certain company during that year, together with the total amount paid by the company in compensation to its employees during that year.

Select from each drop-down menu the option that completes the statement so that it has the most support from the information provided.

The year in which the average (arithmetic mean) annual compensation per employee was GREATEST was

The year in which the average (arithmetic mean) annual compensation per employee was LEAST was