这几天有几道题让我痛苦的都想打退堂鼓了。。。拜托大家帮个忙啊~~~

  1..  if 1/2 of the air in a tank is removed with each stroke of a vacuum pump, what fraction of the original amount of air has been removed after 4 strokes?      
        A.15/16   B. 7/8  C.1/4 D. 1/8  E. 1/16

2.   right triangle PQR is to be constructed in the xy-plane so that the right angle is an P and PRis parallel to the x-axis. The z- and y-coordinates of P,Q,and R are to be integers that satisfy the inequalities -4<=x<=5 and 6<=y<=16. how many different triangles with these properties could be constructed?   
        A. 110  B. 1100 C. 9900 D. 10000   E. 12100
   

3.   Does the integer k have a factor p such that 1<p<k?
   (1)  k>4!
   (2) 13!+2<=k<=13!+13


4.  On Jane's credit card account, the average daily balance for a 30-day billing cycle is the average (arithmetic mean) of the daily balances at the end of each of the 30 days, at the beginning of a certain 30-day billing cycle, Jane's credit card account had a balance of $600, Jane made a payment of $300 on the account during the billing cycle. if no other amounts were added to or subtracted from the account during the billing cycle, what was the average daily balance on Jane's account for the billing cycle?

  (1) Jane's payment was credited on the 21st day of the billling cycle
  (2) the average daily balance through the 25th day of the billling cycle was $540


拜托拉有空帮我解一下吧~~~谢啦谢啦~~~

1. 这是几何级数的问题。第一次抽去 1/2，剩下 1/2。第二次抽去剩下的 1/2，所以抽去 1/4，剩下 1/4。如此一直计算下去。

2. P、Q、R 都是在 -4<=x<=5 and 6<=y<=16 这个长方形里面的 lattice points。长方形里面一共有 10 乘 11 个 lattice point。所以 P 可以有 110 个选择。选完 P 后选 R。R 的 y 坐标一定要与 P 的一样，所以 R 只有 x 坐标有选择。因为 R 和 P 不同点，所以只有 10 减 1 个选择。最后选 Q。Q 的 y 坐标不能与 P、R 的一样，不然 PQR 就不是三角形。因为 P 是直角，所以 Q 的 x 坐标要和 P 的相等。所以 Q 有 10 个选择（y 坐标）。那么答案就是 110 × 9 × 10 = 9900。

第三、四题请看附件。