What number is represented by the point plotted on the number line?
1 answer:
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Part A
The sequence is geometric because the y values are doubling each time
4*2 = 8
8*2 = 16
16*2 = 32
The common ratio is r = 2.
<h3>Answer: Geometric</h3>=======================================================
Part B
The recursive rule here would be
The first line says that "the first term is 4"
The second line says "the nth term is found by multiplying 2 by the previous (n-1) term". In other words, double any term to get the next term.
The fourth term is 32 which doubles to 64 and that's the fifth term. So the point (5,64) is on this exponential curve.
Answer: She takes <u>64 minutes</u> to complete station 5
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Part C
We see that a = 4 is the first term and r = 2 is the common ratio.
The explicit nth term formula is a(r)^(n-1) which becomes 4(2)^(n-1)
Plugging in the value n = 8 leads to
4(2)^(n-1)
4(2)^(8-1)
4(2)^7
4(128)
512
You can use the method shown in part B to keep doubling each term until you arrive at the 8th term. This is one way to confirm the answer.
<h3>Answer: 512 minutes</h3>Recall that the mean of a given set of numbers is the sum of the numbers divided by the number of numbers, therefore, the mean of the dataset is:
Now, the range of a data set is the difference between the maximum and the minimum, in this case, the maximum is 99, and the minimum is 15 therefore, the range is:
Finally, the standard deviation is given by the following formula:
where N is the sample size, x_i is an element of the set, and x^- is the mean. The standard deviation of the set is: