- Messages
- 110
- Reaction score
- 166
- Points
- 53
Thanks a lot11 part b)i)
The numbers of smallest triangles as power of 2 are increasing powers by 2.
Hence after 2^4, it'll be 2^6, 2^8 etc.
Work out 2^6, and 2^8 and put its values in number of smallest triangles row.
6c)
Probability of choosing a N is 2/6. So probabibility of NOT getting N is (1-2/6) which is 4/6.
Hence till 4th card probability will be:
4/6 * 3/5 * 2/4 * 2/3, which is 2/15. The denominators are decreasing, because cards are being chosen without replacement.
_______________________________________________________________________
Question 11:
Okay, if the total area of the shapes is X. And the area of the shaded part is k. It means k is a number that is multiplied with the area to give shaded area.
For example in the first one, if the total area of a triangle is X, and the shaded area is 1/3 of the total area (of X). Then to calculate this shaded area it'll be 1/3 * X. In this case k is 1/3. It's a number multiplied by X (total area) to give the shaded area.
Now the second one, We can calculate the area of the sector by 72/360 * pi * radius squared. If the total area (X) of the circle is pi * radius squared, what are you multiplying with it to get shaded area? That's 72/360. So 72/360 is k.
For the third one, EF = FG, hence if we assume EF is 1, then FG will also be 1. Therefore EG will be 2. Now since they are similar triangles, (EF/EG)squared will give area. Therefore 1squared/2squared is answer. which is equal to 1/4.
For the fourth one, a hexagon is made of 6 equilateral triangles. Hence each angle will be 60 degrees. So to find total area (X) it'll be 6 * length * length * sin60. now the area that is shaded has the same area as any triangle from the center to the two sides. So they want to find area of only 1 triangle out of the 6 triangles. Hence k will be 1/6.
Last one, shaded area is area of sector - area of triangle. Which is 90/360*pi*radius squared - 1/2 * radius squared. Work this out and factorise, it'll give 1/4*radius squared (pi - 2). Now this is the shaded area. They want k which is the value you multiply with the whole sector to give this shaded area. so divide the shaded area by area of whole sector. the answer will be pi - 2/pi.
Question 9)e):
Now probability that the weather is fine is 3/4. Now if the weather is fine for 5 consecutive days the probability will be (3/4)^5. So probability that it is NOT fine for 5 consecutive days will be 1 - (3/4)^5. Your working was wrong because it depicts that weather was fine for the first four days, then fifth day it was not fine. You didn't take to account that the weather could not be fine on the 1st, 2nd, 3rd or 4th day even. Hence this is the best method.
Cheers
