4) average=47.435
5)
| number rolled | frequency |
|---|---|
| 1 | 104 |
| 2 | 80 |
| 3 | 113 |
| 4 | 95 |
| 5 | 115 |
| 6 | 93 |
Because the probability of rolling each number on the dice is 1:6 when put through the simulator 600 times the theoretical probability is that each number will come up 100 times each so I would expect the experimental results to be around 100 for each number. In my test they are mostly scattered around 100 with the highest rolling being number 5 coming up 115 times and the lowest being 2 only coming up 80 times.
6)
| flip result | frequency |
|---|---|
| heads | 480 |
| tails | 520 |
The theoretical probability of getting heads or tails in a coin toss is 50:50. This means that theoretically when tested 1000 times both heads and tails will come up 500 times each so I would expect the experimental results to be around. In my test the results were heads came up 480 times and tails came up 520 times.
7)
| test | average |
|---|---|
| 1 | 48.575 |
| 2 | 51.368 |
| 3 | 53.172 |
The theoretical probability of getting each number 1 to 100 is 1:100 this means that the theoretical average is 50 so I would expect the experimental average to be around 50. In my test the averages are all scattered around 50 which is close to the theoretical probability.
8)
| test | average |
|---|---|
| 1 | 49.852 |
| 2 | 49.992 |
| 3 | 49.873 |
When this test was done 1000 times the results are closer 50 than when the test was done 100 times because the more times the test is done the more times the more accurate results are.
9)
This graph shows that the most frequent numbers were divisible by 5.
10) a.
This graph shows the frequency of remainders when the random numbers were divided by 4
10) b.
1)
126 | 64 | 32 | 16 | 8 | 4 | 2 | 1
52=00110100
100=01100100
7=00000111
200=1100110
2)
126 | 64 | 32 | 16 | 8 | 4 | 2 | 1
01000001 = 65
01110000 = 112
01010101 = 85
11111111 = 255
11111110 = 254
3)
32 + 42 = x2
9 + 16 = x2
x2 = 25
x = 5
102 + 112 = x2
100 + 121 = x2
x2 = 221
x = 14.86
62 + 52 + x2
36 + 25 = x2
x2 = 61
x = 7.81
202 + 172 = x2
400 + 289 = x2
x2 = 689
x = 26.25
4)
Area
5)
230000.0
42000000.0
2.4 x 10 3
1.35 x 106
6)
