Two metal cans are right circular cylinders of different sizes. The interior base of can A has an area of 5π square inches, and the height of the oil in can A is 6 inches. The interior base of can B has an area of 10π square inches, and the height of the oil in can B is 2 inches. Oil is to be moved from can A to can B so that the height of the oil will be the same in both cans. Which of the following is closest to what will be the new height of the oil, in inches?
|
|
A large pump and a small pump are available to fill a public fountain with 7,500 gallons of water. The pumps can be used alone or simultaneously. Working alone at their respective constant rates, the small pump would take 1.6 times as long as the large pump to fill the fountain. Working simultaneously at their respective constant rates, the two pumps would take 3 hours to fill the fountain. How long would the small pump take to fill the fountain, working alone at its constant rate?
|
|
The 9 computers in an office are to be interconnected by cables so that each computer is connected directly to each of the other computers. If each cable that connects a pair of the computers counts as one cable, how many cables are needed?
|
|
The number 24 has the property that it is divisible by its units digit, 4. How many of the integers between 10 and 70 are divisible by their respective units digits?
|
|
A caterer has 20 liters of fruit punch that is 12 percent grape juice, by volume. How many liters of fruit punch that is 20 percent grape juice, by volume, must be added to the original 20 liters of fruit punch in order to create fruit punch that is 15 percent grape juice, by volume?
|
Every positive integer can be represented uniquely in base $$11$$ by
$$(a_n......a_2 a_1 a_0)_{11}$$= $$a_n(11^{n})+......a_2(11^{2})+a_1(11^{1})+a_0(11^{0})$$
for some nonnegative integer $$n$$. In the expression, the coefficient $$a_i$$ of $$11^i$$ is one of the digits from 0 to 9 or A, which represents 10, for $$0 ≤ i ≤ n$$, but $$a_n≠ 0$$. For example, $$(4A5)_{11}=599$$ because
$$(4A5)_{11}= 4(11^2)+10(11^1)+5(11^0)$$.
What is the value of $$(8,423)_{11}- (6,682)_{11}$$?
|
