Answer:
Step-by-step explanation:
Tom wanted to find the inverse of f(x)= 4x - 2 using the steps in the attached image.
Tom's first mistake was in Step 3.
To correct the mistake, he should not switch the variables.
The correct procedure is:
Step 1 : Given
f(x) = 4x - 2
Step 2 : Change f(x) to y
y = 4x - 2
Step 3 : Add 2 to both sides
Step 4: Divide each side by 4
Step 5: Change x to
Answer:
The measure of the arc PJ is
Step-by-step explanation:
step 1
Find the measure of angle L
we know that
In a inscribed quadrilateral opposite angles are supplementary
so
we have
substitute
step 2
Find the measure of arc KJ
we know that
The inscribed angle measures half that of the arc comprising
so
substitute the values
step 3
Find the measure of arc PJ
we know that
The inscribed angle measures half that of the arc comprising
so
substitute the values
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!
It is given in the question that
The school is 625 meters far from Alex house. It took him 15 minutes to go from home to school, and run back to home in 10 minutes.
Total distance is 625 meters and total time taken is
Average speed is