...5. The product of the first five terms of a geometrical progression is 243. Find the third term. 6. Two vessels contain mixtures of wine and water : in one there is twice as much wine as water, in the other three times as much water as wine. How much must be drawn...

...11. Write down the coeificients of a;' in the expansions of (1 + x)*, (1 - a;)-2, and (1 - *)-*. 12. Two vessels contain mixtures of wine and water ; in...that its contents may be half wine and half water. 13. A ship did a measured mile in four minutes less on a perfectly calm day under steam than on a windy...

...of (1 - x)~* and(lx)-i. 195. Two vessels contain mixtures of wine and water ; in one there is thrice as much wine as water, in the other five times as...drawn off from each to fill a third vessel which holds 7 gallons, in order that its contents mzy be half wine and half water. 196. Find the nth term and the...

...much water as wine ; find how much must be drawn off from each to fill a third vessel which holds 7 gallons, in order that its contents may be half wine and half water. 196. Find the w'* term and the sum of the first n terms of (l-) 1.6 + 2.7 + 378 + ' ' ' and (ii.) 8-12...

...together. 194. Write down the co-efficients of xr in the expansions of (1 — х)~2 and(l-х)-». 195. Two vessels contain mixtures of wine and water ; in one there is thrice as much wine as water, in the other five times as much water as wine ; find how much must be...

...much water as wine. Find how much must be drawn off from each to fill a third vessel which holds 7 gallons, in order that its contents may be half wine and half water. 38. There is a number of 3 digits, the last of which is double the first ; when the number is divided...

...now there were only a third as many men again as women. What were the original numbers of each ? 37. Two vessels contain mixtures of wine and water ; in one there is 3 times as much wine as water, in the other 5 times as much water as wine. Find how much must be drawn...

...cent on debts previously incurred, and then has $110 remaining: what was the amount of his debts ? 26. Two vessels contain mixtures of wine and water ; in...that its contents may be half wine and half water. 87. There are two mixtures of wine and water, one of which contains twice as much water as wine, and...

...cent on debts previously incurred, and then has $110 remaining: what was the amount of his debts ? 26. Two vessels contain mixtures of wine and water ; in...as much water as wine. Find how much must be drawn oft' from each to fill a third vessel which holds seven gallons, in order that its contents may be...

...quotient of the resulting number increased by 23, divided by the given number, is 2. Find the number. 32. Two vessels contain mixtures of wine and water. In one there is three times as much wine as water, and in the other five times as much water as wine. How many gallons must be taken from each to fill...