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1052 toothpicks can be grouped into 4 groups of third power of 6 (), 5 groups of second power of 6 (
), 1 group of first power of 6 (
) and 2 groups of zeroth power of 6 (
).
The number 1052, written as a base 6 number is 4512
Given: 1052 toothpicks
To do: The objective is to group the toothpicks in powers of 6 and to write the number 1052 as a base 6 number
First we note that,
This implies that exceeds 1052 and thus the highest power of 6 that the toothpicks can be grouped into is 3.
Now, and
. This implies that
exceeds 1052 and thus there can be at most 4 groups of
.
Then,
So, after grouping the toothpicks into 4 groups of third power of 6, there are 188 toothpicks remaining.
Now, and
. This implies that
exceeds 188 and thus there can be at most 5 groups of
.
Then,
So, after grouping the remaining toothpicks into 5 groups of second power of 6, there are 8 toothpicks remaining.
Now, and
. This implies that
exceeds 8 and thus there can be at most 1 group of
.
Then,
So, after grouping the remaining toothpicks into 1 group of first power of 6, there are 2 toothpicks remaining.
Now, and
. This implies that the remaining toothpicks can be exactly grouped into 2 groups of zeroth power of 6.
This concludes the grouping.
Thus, it was obtained that 1052 toothpicks can be grouped into 4 groups of third power of 6 (), 5 groups of second power of 6 (
), 1 group of first power of 6 (
) and 2 groups of zeroth power of 6 (
).
Then,
So, the number 1052, written as a base 6 number is 4512.
Learn more about change of base of numbers here:
Answer:
The 95% confidence interval would be given by (6.03;7.49)
Step-by-step explanation:
Notation
represent the sample mean
population mean (variable of interest)
s represent the sample standard deviation
n=50 represent the sample size
Solution
The confidence interval for the mean is given by the following formula:
(1)
We can calculate the mean and the sample deviation we can use the following formulas:
(2)
(3)
The mean calculated for this case is
The sample deviation calculated
In order to calculate the critical value we need to find first the degrees of freedom, given by:
We assume a standard confidence level of 0.95 or 95%, the value of and
, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,49)".And we see that
Now we have everything in order to replace into formula (1):
The 95% confidence interval would be given by (6.03;7.49)