The correct answer is the first one in the list of choices: 28, 40, 11 and 23.
There are other ways to randomly sample. This problem illustrates how random sampling can be accomplished using a printed random number table.
Mrs. Fuller needs to randomly sample four members from a population of size 47. Each member of the population is given a unique 2-digit number, in order from 01 to 47.
Mrs. Fuller has a random number table she wishes to use to randomly select four members. She chooses a line from the table, line 128, which reads as follows:
53537 96428 40115 27467 90826 52358 14570 54184
The numbers are separated into sets of 5; this is done for readability. The digits 0-9 appear randomly in each set of 5.
If we envision this line of random numbers as a series of 2-digit numbers, we can use the first four unique 2-digit numbers between 01 and 47 to represent the population members in our sample.
Note that we don't use repeats of numbers we have already selected; we need all four to be different.
Let's reformat the line of 5-digit numbers into a series of two-digit numbers instead.
53 53 79 64 28 40 11 52 74 67 90 82 65 23 58 14 57 05 41 84
Now let's go from left to right and look for the first four 2-digit numbers between 01 and 47. We can't use 53, 79 or 64; those are outside of our desired range.
The fifth 2-digit number is 28, so we can use that. Immediately after it are 40 and 11, so those are good. It's a bit further to the last usable 2-digit number, 23. The four numbers we select appear in BOLD below.
53 53 79 64 28 40 11 52 74 67 90 82 65 23 58 14 57 05 41 84
Hence, the correct answer is the first one in the list of choices: 28, 40, 11 and 23.
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The nthterm for the sequence is 4n + n².
The two consecutiveterms in the sequence where the difference will be 245 are 120 and 121.
A sequence is a group of numbers where there is a relation between each consecutive value.
We have,
5, 12, 21, 32,
We see that,
The difference between the consecutive numbers is 7, 9, 11, 13, 15,
We can make a formula for the nth term.
4n + n²
Where n = 1, 2, 3, 4, ,,,,
Now,
Let the two consecutiveterms be n and (n +1).
4(n + 1) + (n + 1)² - 4n - n² = 245
4n + 4 + n² + 2n + 1 - 4n - n² = 245
4 + 2n + 1 = 245
2n + 5 = 245
2n = 240
n = 120
And,
n + 1 = 121
So,
The two consecutiveterms in the sequence where the difference will be 245 are 120 and 121.
Thus,
The nthterm for the sequence is 4n + n².
The two consecutiveterms in the sequence where the difference will be 245 are 120 and 121.
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