Create a situation that would require both the functions,f(x) and g(x), and is related to the situations you have already outlin
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Answer:
Step-by-step explanation:
<u>Complete Question:</u>
A monkey is swinging from a tree. On the first swing, she passes through an arc whose length is 24 m. With each swing, she travels along an arc that is half as long as the arc of the previous swing. Which expression gives the total length the monkey swings in her first n swings?
<u>Solution:</u>
First Swing:
24 m
Second Swing:
Half of first, so
24(1/2)
Third Swing:
Half of second, so:
24(1/2)(1/2)
Fourth Swing:
24(1/2)(1/2)(1/2)
So we see the general formula as:
<u>Note:</u> n -1 because (1/2) plays a role from second swing, which is n - 1
where n is the number of swings
Answer:
Step-by-step explanation:
Hello!
Data
Year/Firefighters
2000: 20
2001: 18
2002: 23
2003: 30
2004: 20
2005: 12
2006: 24
2007: 9
2008: 25
2009: 15
2010: 8
2011: 11
2012: 15
2013: 34
<u>Common measures of variation</u>
<u>Variance</u>
S²=
∑X= 20 + 18 + 23 + 30 + 20 + 12 + 24 + 9 + 25 + 15 + 8 + 11 + 15 + 34
∑X= 264
∑X²= 20² + 18² + 23² + 30² + 20² + 12² + 24² + 9² + 25² + 15² + 8² + 11² + 15² + 34²
∑X²= 5770
n= 14
S²=
S²= 60.90
<u>Standard deviation</u>
The standard deviation is the square root of the variance
S= √S²= √60.90= 7.80
<u>Coefficient of variation</u>
Is a relative standard deviation, it is defined as the division of the standard deviation (S) by the mean (X[bar)]. It has not units and is usually expressed in percentage. It shows the variability in relation to the mean.
C.V.= *100 =
*100= 41.36%
The mean or average is a measurement of position and gives you an idea of the central value of the distribution of the data.
X[bar]= ∑X/n= 264/14= 18.86
<u>Range</u>
In the interval between the max and min values. It allows you to have an idea of the dispersion of the values.
R= Xmax - Xmin= 34 - 8= 26
Xmax= 34
Xmin= 8
<u>Inter Quartile Range</u>
Is the difference between Quantile 1 (C₁) and Quantile 3 (C₃). It shows the 50% mid values of the sample.
IQR= C₃ - C₁= 23.5 - 11.5 = 12
Quantile 1 (C₁) is the value that leaves 25% of the sample below and 75% of the sample above.
Pos1: n/4= 14/4= 3.5
The first quantile is the number between position 3 and position 4
8, 9, 11, 12, 15, 15, 18, 20, 20, 23, 24, 25, 30, 34
C₁= (11+12)/2= 11.5
Quantile 3 (C₃) is the value that leaves 75% of the sample below and 25% of the sample above.
Pos3: n*3/4= 14*3/4= 10.5
The third Quantile is between position 10 and 11
8, 9, 11, 12, 15, 15, 18, 20, 20, 23, 24, 25, 30, 34
C₃= (23+24)/2= 23.5
The measurements of variation don't allow you to know the origin of the data, that it is from consecutive years.
I hope it helps!