The greatest prime divisor of 1,935 is
Answer(s): D
1935 ÷ 5 = 387387 = 3 × 129 = 3 × 3 × 43Prime factors: 3, 5, 43Largest prime divisor = 43.
For a certain time period at a water treatment plant, water was pumped into a tank that has a capacity of 12,000 liters. The function g(t) = 2,500 + 100t gives the number of liters in the tank t minutes after the beginning of the time period until the end of the time period. If the length of the time period was between 30 minutes and 60 minutes, which of the following could be the number of additional liters of water that it would take to fill the tank to capacity afer the end of the time period? (Choose all that apply.)
Answer(s): B,C,D
The amount of water in the tank at the end of the pumping period is g(t) = 2500 + 100t,where t (in minutes) is between 30 and 60.The additional water needed to fill the 12,000-liter tank is12,000 g(t) = 12,000 (2500 + 100t) = 9500 100t.Evaluate this expression for the extreme t values:· If t = 30: 9500 100(30) = 9500 3000 = 6500.· If t = 60: 9500 100(60) = 9500 6000 = 3500.Thus, the number of additional liters could be any value between 3,500 L and 6,500 L.Among the choices, the values in this range are 4000, 5000, 6000.
A large cube and a small cube are made of granite of uniform density. The large cube has edges of length 1.2 meters and weighs 4,752 kilograms.If the small cube has edges of length 10 centimeters, what is the weight, in grams, of the small cube?
The large cube has edge length 1.2 m, so its volume is(1.2 m)3 = 1.728 m3.Its weight is 4,752 kg, so the density of the granite isThe small cube has edge length 10 cm = 0.1 m, giving it a volume of (0.1 m)3 = 0.001 m3.Weight of the small cube:2,750 kg/m3 × 0.001 m3 = 2.75 kg =2,750 g.
FILL BLANKWhat is the area of the shaded region shown in the xy-plane?
Answer(s): A
Reading the coordinates from the picture (going counter-clockwise):These six points form the outer (gray) hexagon.Area of the outer hexagon (shoelace formula)The white triangle has vertices (0, 0), (2, 0), (1, 2).Its base is 2 and its height is 2, soSo, the area of the shaded region is 18 square units.
In a study, the 4 shortest performance times for a certain task, expressed as minutes:seconds, were 3:52, 3:50,3:51, and 3:46. Let x be the average (arithmetic mean) of these 4 times.Quantity AThe number of seconds by which 4 minutes exceeds xQuantity B9
First convert each time to seconds and find their average.3:52 = 3(60) + 52 = 232 s3:50 = 3(60) + 50 = 230 s3:51 = 3(60) + 51 = 231 s3:46 = 3(60) + 46 = 226 sTotal for the four times:232 + 230 + 231 + 226 = 919 sAverage (Quantity ):x = 919 ÷ 4 = 229.75 sFour minutes equals 4 × 60 = 240 sQuantity A is the number of seconds by which 240 s exceeds :240 229.75 = 10.25 sQuantity B is 9 s. Since 10.25 > 9, Quantity A > Quantity B.Quantity A is greater.
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