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A phase diagram shows the temperatures and pressures at which a chemical substanceexists in a certain phase (solid, liquid, or gas). A sample phase diagram for a fictionalsubstance is shown in the figure, where T is temperature in Kelvin and P is pressure in atmospheres. Where on the diagram a certain temperature and pressurecombination falls determines the state(s) in which the substance exists. For example,if a certain temperature-pressure pairing falls in the gas area (but not on the linesegment between gas and liquid), the substance exists only as a gas. However, if thetemperature-pressure pairing is on the line segment between gas and liquid, the substanceexists as both a gas and a liquid. Assuming T > 0 and P > 0, which of the following systems of inequalities could be used to describe thetemperature and pressure ranges in which this substance exists only as a liquid?
Suppose that on a coordinate plane, (0, 0) is a solution to the system of inequalitiesgiven above. Which of the following conclusions about k1 and k2 must be true?
3. An architect is working on a design for a solar power plant. While double-checkingthe blueprint, he realizes that he has made an error: The solar panels will not fiton the roof unless the dimensions of the roof are increased by 0.5%. Which of thefollowing expresses this change in the dimensions of the roof as a fraction of theoriginal dimensions?
4. A graphic designer created an image for a school banner. He uses this image for smalland medium banners. To produce a large banner, the designer increases the size ofthe image by 112.5% to 18 inches tall by 22.5 inches wide. What was the size of theoriginal image?
5. A typical song downloaded from the Internet is 4 megabytes in size. Lindy has satelliteInternet, and her computer downloads music at a rate of 256 kilobytes per second.If 1 megabyte equals 1,024 kilobytes, about how many songs can Lindy download in 2hours?
6. Cecilia leaves home for school on her bike at 9:05 AM, riding at an average speed of 10 miles per hour. Fifteen minutes later, her motherrealizes that Cecilia forgot to take her lunch. Cecilia's mother immediately getsinto her car and drives after Cecilia at an average speed of 25 miles per hour. Atwhat time will Cecilia's mom catch up to her?
The bar graphs show the amounts, in dollars, invested by a company for materials andlabor to produce a certain product and the value of the sales for that product. Thecompany claims that the amount invested for materials and labor is never more than60% of the value of the sales. Which year or years disprove this claim?
8. A sporting goods store ordered an equal number of white and yellow tennis balls. Thetennis ball company delivered 30 extra white balls, making the ratio of white ballsto yellow balls 6:5. How many tennis balls did the store originally order?
9. The density of a substance can be found by dividing the mass of the substance by the volume ofthe substance. The table gives the density of several pure metals in grams per cubiccentimeter. Suppose a rectangular sheet of a pure metal weighs about 515.9 grams andmeasuresinch by 2 inches by 8 inches. Assuming the sheet is one of the metals in the table,which metal is it? (There are approximately 2.54 centimeters in 1 inch.)
10. A bike messenger delivers a package from the courthouse to a law firm downtown, travelingat an average speed of 24 miles per hour. On the way back, the bike messenger getsstuck in traffic, which reduces his average speed for the return trip by 12.5 percent.What was the bike messenger's average speed, in miles per hour, for the round trip?
11. The mayor of Dunderville proposes a new ordinance that would give a tax credit toparents who homeschool their children. Ten percent of Dunderville's residents approveof the ordinance. Of these, 7 out of 10 are women. All of Dunderville's other residentsare against the ordinance. If there are equal numbers of men and women in Dunderville,then what fraction of Dunderville's male residents approve of the ordinance?
12. Each crop duster who works for Gary's Crop Dustin' 4 Cheap can dust half an acre ofcrops in 25 minutes. The company must dust eight 0.75-acre lots and twelve 1.5-acrelots to complete a certain job. What is the minimum number of crop dusters neededto complete the job in 5 hours?
13. Amal, Geoffrey, and Julia each have some fireworks. If Amal gives half of his fireworksto Geoffrey, then Amal and Geoffrey will have fireworks in a 2:3 ratio. If Julia hasone-fifth as many fireworks as Geoffrey (after Amal gives half his fireworks to Geoffrey),then what is the ratio of the number of fireworks Amal has to the number of fireworksJulia has?
14. An oil tank has two pipes connected to it. If the tank is empty, Pipe A can fill itin 2 hours. If the tank is full, Pipe B can empty it in 3 hours. If both pipes areactivated at the same time when the tank is empty, how many hours will it take forthe tank to be filled to 60% of its capacity?
15. An all-natural health clinic stocks teas and herbs in a 5:11 ratio at one of its warehouses.In an effort to cut overhead costs, the owners close this warehouse and transfer itsstock to a larger warehouse, increasing that warehouse's inventory of items by 20%.Which of the following could be the number of items at the larger warehouse afterthe transfer?
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