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Each of Rachelle' s clients is a resident of one of four cities-$$R, S, T$$, or $$W$$. Of these clients, 20 percent are residents of City $$R$$, 25 percent are residents of City $$S$$, and $$x$$ percent are residents of City $$T$$. Which of the following expressions represent, for all possible values of $$x$$, the number of Rachelle's clients who are residents of City $$W$$ as a fraction of all her clients?

Indicate all such expressions.
A gardener plans to cover a rectangular plot of land with pine bark mulch to a depth of 4 inches.The plot measures 8 feet by 12 feet, and the gardener will buy mulch packed in bags. If each bag contains 3.5 cubic feet of mulch and costs $6,what is the cost of the least number of bags that the gardener will need to cover the plot? (Note: 1 foot=12 inches.)


AC is a diameter of the circle with center $$D$$.

Quantity A

$$BD$$

Quantity B

$$5$$


The table above shows four categories of methods of transportation to work, including the category None for people who work at home. For each category and for the years 2000 and 2010, the table shows the percent of workers in a certain city who used that method most of the time during the year. Based on the information given, which of the following statements must be true?

Indicate all such statements.
The pieces of art in a certain collection are classified as either ancient or modern. All pieces in the collection are 3 are on display in one of two wings of a museum, $$C$$ or $$D$$. Of the pieces in the collection on display in $$C$$, $$\frac{1}{3}$$ are ancient pieces, and of the pieces in the collection on display in $$D$$, $$\frac{1}{4}$$ are ancient pieces. The number of modern pieces on display in $$C$$ is equal to the number of modern pieces on display in $$D$$. Of all the ancient pieces in the collection, what fraction are on display in wing $$C$$?
If $$x$$ and $$y$$ are positive integers and $$xy=36$$, then $$(x+y)^2$$ CANNOT be
$$(x+h)(x+j)=x^2+kx+12$$ In the equation above, $$h$$, $$j$$, and $$k$$ are constants. If $$h$$ and $$j$$ are integers, which of the following could be the value of $$k$$?

Indicate all such values.
Werner and Kim are working independently at decoding a message. The probability that Werner will decode the message is equal to the probability that Kim will decode the message. The probability that both Werner and Kim will decode the message is 0.16.

Quantity A

The probability that Werner will not decode the message

Quantity B

0.5
The pieces of art in a certain collection are classified as either ancient or modern. All pieces in the collection are on display in one of two wings of a museum, C or D. Of the pieces in the collection on display in C, $$\frac{1}{3}$$ are ancient pieces, and of the pieces in the collection on display in D, $$\frac{1}{4}$$ are ancient pieces. The number of modern pieces on display in C is equal to the number of modern pieces on display in D. Of all the ancient pieces in the collection, what fraction are on display in wing C?
Each salesperson in a retail store is paid a commission based on the amount of his or her daily sales. For daily sales up to and including $200, the commission is $$r$$ percent of the daily sales. For daily sales over $200, the commission is $$2r$$ percent of the daily sales. On Friday, Amanda had daily sales of $300 and Bill had daily sales of $200. If the total of Amanda' s and Bill' s commissions on Friday was $40, what is the value of $$r$$?
There are two overlapping circular regions on a level field, and the centers of the regions are 40 meters apart. One circular region has a radius of 25 meters, and within the region there is a marker located 5 meters away from its border. The other circular region has a radius of 30 meters, and within the region there is a marker located 7 meters away from its border. What is the greatest possible distance, in meters, between the two markers?
Last year a youth organization sold candy bars for $1.50 each for a fund-raiser. This year the organization members plan to repeat the fund-raiser, but they project that the number of candy bars sold will be reduced from last year's number by 1/3 of the number sold last year. If this projection is correct, what price per candy bar would result in the same total amount of revenue this year as last year?
If $$x$$, $$y$$, and z are integers greater than 1 and $$xyz=231$$, what is the value of $$x+y+z$$?


The table above shows the values of one share of stock for companies $$A B$$, and c at the close of the stock market yesterday, where $$x$$ is in dollars and $$x > 2$$. Which of the following statements individually provide(s) sufficient additional information to determine the value of $$x$$? Indicate all such statements.
In Vermont the number of acres of forest area in 1992 was $$76.5$$ percent of the total number of acres of land area. Which of the following is closest to the number of millions of acres of land area in Vermont?
For Maine, which of the following is closest to the average annual increase in the number of acres of forest area from 1907 to 1992?
The number of acres of forest area in Rhode Island in 1992 was what percent greater than it was in 1907?
If Transit Company T will run $$60$$ trains per day, then the projected annual revenue is approximately what percent greater than the projected annual cost?
If Transit Company T will run $$40$$ trains per day for a year. approximately what is the projected average revenue per day?
Transit Company T's projected annual cost consists of staffing costs, fuel costs, and equipment costs in the ratio of 1 to 2 to 5. If the company will run $$50$$ trains per day, approximately what is the projected annual cost for fuel?

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