中三數學題 (英文題目) [40分] 急

答得幾多得幾多，謝謝。
(1) A card is randomly selected from 4 cards numbered '1', '2', '3', '4'. After recording its number, the card is put back.
(1a) The above process is then repeatd. Find the proberbility of getting a prime number in both trials.
(1b) The process is repeated for 50 times, and the results are as follows.
圖片參考：http://imgcld.yimg.com/8/n/HA05425562/o/701108290056613873450520.jpg


Find the experimental probability of getting a prime number.

(2) The figure shows an object made by metal plates. The upper part is in the shape of a hemisphere while the lower part is in the shape of a right circular cone. The two parts share a common base. The base radius and height oh the cone are 2 cm and 8 cm respectively.


圖片參考：http://imgcld.yimg.com/8/n/HA05425562/o/701108290056613873450531.jpg


(2a) Find the capacity of the object in terms of 兀.
(2b) There is some water inside the object. Theradius of the water surface is 1 cm. Fine the volume of water in terms of 兀.

(3) In the figure, the conpass bearings of A and C from B are N40oW and S75oW respectively. The compass bearing of C from A is S10oE. If AC=20 km and BC=11km, find the distance between A and B.


圖片參考：http://imgcld.yimg.com/8/n/HA05425562/o/701108290056613873450532.jpg


(4) It is given that three points X(3,1), Y(-5,9) and Z(2,-4) are the vertices of a triangle. XP and G are a median and the centroid of the triangle respectively.


圖片參考：http://imgcld.yimg.com/8/n/HA05425562/o/701108290056613873450543.jpg


(7a) Find the coordinates of P.
(7b) Hence find the coordinates of G.

(8) In the figure, L1 : 3x - y + 6 = 0, L2 : y = -6 and L3 : 3y + 12 = 0 are given. Their slopes are 3, 0 and -1/3 respectively. L3 intersects L1, L2 and the y-axis at B, C and D respectively.


圖片參考：http://imgcld.yimg.com/8/n/HA05425562/o/701108290056613873450544.jpg


(8a) Show that L1 ⊥ L3
(8b i) Find the coordinates of B and C.
(8b ii) Find BD : DC
[Hint: Let BD : DC = 1 : r]

(9a) A regular polyhedron.

圖片參考：http://imgcld.yimg.com/8/n/HA05425562/o/701108290056613873450555.jpg


(9) Given that DF = 3 cm
(9a) Prove that ΔDEF ~ ΔABC
(9b) Find the area of ΔDEF
(9c) Find the total surface area of the solid.
(All the answer correct to 3 sig. fig.)