Question 1

1. 3
2. 1
3. 2
4. 2

Question 2

1. 15/24 → 15/23, 14/23

   14/24 → 14/23, 13/23

2. (10/25) x (9/24) x (15/23) = 9/92

   (10/25) x (15/24) x (9/23) = 9/92

   (15/25) x (10/24) x (9/23) = 9/92

   9/92 x 3 = 27/92

3. P(A|B) = P(A and B) / P(B)

   P(A|B) = (9/92) / (27/92)

   P(A|B) = 1/3

4. P(A and B) = P(A) x P(B)

   (9/92) = (15/25) x (27/92)

   = 81/460

   They are not equal therefore not independent

Question 3

1. The lines DBC and DAC are subtended from the same point which means that angle ADE = angle BCE and angle DAE = angle CBE. Therefore they are similar triangles since they have 2 similar angles.

2. (2x-6)/(x+3) = (x-2)/(x+1)

   (2x-6)(x+1) = (x-2)(x+3)

   2x^2 + 2x - 6x - 6 = x^2 + 3x - 2x - 6

   2x^2 - 4x - 6 = x^2 + x - 6

   x ^2 - 5x = 0

   x(x-5) = 0

   x = 5 or x=5

3. c^2 = a^2 + b^2 - 2abcosc

   c^2 = 8^2 + 6^2 - (2x8x6xcos60)

   c^2 = 52

   c = 2 root 13

4. AE = 3

   BE = 6

   DE = 4

   CE = 8

   LSF = 2

   8+6+7 = 21

   2 root 13 x 2 = root 13 = 3.6

   21 + 3+4+ 4 =32

Question 4

1. h^2 + 12^2 = 24^2

   h^2 = 24^2 - 12^2

   h = root 432

   h = 12 root 2

2. V = 1/3 Ah

   V = 1/3 (24x24) x 12 root 2

   = 3258

3. 3 root 0.75 x 12 root 2 = 15.4

Question 5