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1. If , what is the maximum possible whole number value of a?
2. The table above shows the seating configuration for several commercial airplanes. The day before a particular flight departs, a travel agent books the last seat available for a client. If the seat is on one of the two Boeing 777s, what is the probability that the seat is a Business Class seat, assuming that all seats have an equal chance of being the last one available?
3. Heating water accounts for a good portion of the average home's energy consumption. Tankless water heaters, which run on natural gas, are about 22% more energy efficient on average than electric hot water heaters. However, a tankless hot water heater typically costs significantly more. Suppose one tankless water heater costs $160 more than twice as much as a conventional hot water heater. If both water heaters cost $1,000 together, how many more dollars does the tankless water heater cost than the conventional one?
4. Medically speaking, remission is a period in which the symptoms of a disease or condition subside or, for some diseases, a period during which the condition stops spreading or worsening. In a certain drug trial in which a drug designed to treat cancer was tested, exactly 48% of patients experienced remission while take the drug. What is the fewest number of patients who could have participated in this trial?
When the top of a pyramid (or a cone) is cut off, the remaining bottom part is called a frustum. Suppose the top third (based on the height) of the square pyramid shown above is cut off and discarded. What will be the volume, in cubic meters, of the remaining frustum?
6. After a surface has been cleaned, bacteria begin to regrow. Because bacteria reproduce in all directions, the area covered is usually in the shape of a circle. The diameter of the circle in millimeters can give scientists an idea of how long the bacteria have been growing. For a certain kind of bacteria, the equation can be used to find the number of hours, that the bacteria have been growing. If the diameter of a circle of these bacteria is 0.12 millimeters, how many hours have the bacteria been growing?
7. Daniel works for a pest control company and is spraying all the lawns in a neighborhood. The figure above shows the layout of the neighborhood and the times that Daniel started spraying the lawns at two of the houses. Each lawn in the neighborhood is approximately 0.2 acres in size and takes the same amount of time to spray.
How many minutes will it take Daniel to spray all of the lawns in the neighborhood?
8. Daniel works for a pest control company and is spraying all the lawns in a neighborhood. The figure above shows the layout of the neighborhood and the times that Daniel started spraying the lawns at two of the houses. Each lawn in the neighborhood is approximately 0.2 acres in size and takes the same amount of time to spray.
Daniel uses a mobile spray rig that holds 20 gallons of liquid. It takes 1 gallon to spray 2,500 square feet of lawn. How many times, including the first time, will Daniel need to fill the spray rig, assuming he fills it to the very top each time? [1 acre = 43,560 square feet]
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