Can you please help me. It’s late and I just wanna sleep.
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The distance from the kayak to the mountain to the nearest whole number is 43 meters.
The situation will form a right angle triangle as shown below in the diagram.
<h3>Properties of a right angle triangle:</h3>- One of its angle is 90 degrees.
- The sides and angle can be found by using trigonometric ratios.
The height(opposite side) of the triangle is the kayak distance from the mountain to the lake below. The distance from the kayak to the mountain is the adjacent side of the triangle.
Therefore, using trigonometric ratios,
tan 35 = opposite / adjacent
tan 35° = 30 / a
a = 30 / tan 35°
a = 30 / 0.70020753821
a = 42.8444402023
a = 42.84 meters
a ≈ 43 meters
learn more on the angle of depression: brainly.com/question/13969247?referrer=searchResults
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!