A degree may seem like a very small unit but an error of one degree in measuring an angle may be very significant. For example,
suppose a laser beam directed toward the visible center of the moon misses its assigned target by the amounts specified below. How far is it (in miles) from its assigned target in each case? (Use 234,000 miles as the distance from the surface of the earth to the surface of the moon.)
a: 1 degree
b: 30” (that’s 0 degree 0’ 30”)
a: 1 degree
b: 30” (that’s 0 degree 0’ 30”)
1 answer:
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Answer:
a)
X[bar]= 71.8cm
X[bar]= 72cm
b)
M.A.D.= 8.16cm
M.A.D.= 5.4cm
c) The data set for Soil A is more variable.
Step-by-step explanation:
Hello!
The data in the stem-and-leaf plots show the heights in cm of Teddy Bear sunflowers grown in two different types of soil (A and B)
To read the data shown in the plots, remember that the first digit of the number is shown in the stem and the second digit is placed in the leaves.
The two data sets, in this case, are arranged in a "back to back" stem plot, which allows you to compare both distributions. In this type of graph, there is one single stem in the middle, shared by both samples, and the leaves are placed to its left and right of it corresponds to the observations of each one of them.
Since the stem is shared by both samples, there can be observations made only in one of the samples. For example in the first row, the stem value is 5, for the "Soil A" sample there is no leaf, this means that there was no plant of 50 ≤ X < 60 but for "Soil B" there was one observation of 59 cm.
X represents the variable of interest, as said before, the height of the Teddy Bear sunflowers.
a) To calculate the average or mean of a data set you have to add all observations of the sample and divide it by the number of observations:
X[bar]= ∑X/n
For soil A
Observations:
61, 61, 62, 65, 70, 71, 75, 81, 82, 90
The total of observations is n= 10
∑X= 61 + 61 + 62 + 65 + 70 + 71 + 75 + 81 + 82 + 90= 718
X[bar]= ∑X
/n
= 218/10= 71.8cm
For Soil B
Observations:
59, 63, 69, 70, 72, 73, 76, 77, 78, 83
The total of observations is n= 10
∑X= 59 + 63 + 69 + 70 + 72 + 73 + 76 + 77 + 78 + 83= 720
X[bar]= ∑X
/n
= 720/10= 72cm
b) The mean absolute deviation is the average of the absolute deviations of the sample. It is a summary of the sample's dispersion, meaning the greater its value, the greater the sample dispersion.
To calculate the mean absolute dispersion you have to:
1) Find the mean of the sample (done in the previous item)
2) Calculate the absolute difference of each observation and the sample mean |X-X[bar]|
3) Add all absolute differences
4) Divide the summation by the number of observations (sample size,n)
For Soil A
1) X[bar]= 71.8cm
2) Absolute differences |X-X[bar]
|
|61-71.8|= 10.8
|61-71.8|= 10.8
|62-71.8|= 9.8
|65-71.8|= 6.8
|70-71.8|= 1.8
|71-71.8|= 0.8
|75-71.8|= 3.2
|81-71.8|= 9.2
|82-71.8|= 10.2
|90-71.8|= 18.2
3) Summation of all absolute differences
∑|X-X[bar]
|= 10.8 + 10.8 + 9.8 + 6.8 + 1.8 + 0.8 + 3.2 + 9.2 + 10.2 + 18.2= 81.6
4) M.A.D.=∑|X
-X[bar]
|/n
= 81.6/10= 8.16cm
For Soil B
1) X[bar]= 72cm
2) Absolute differences |X-X[bar]
|
|59-72|= 13
|63-72|= 9
|69-72|= 3
|70-72|= 2
|72-72|= 0
|73-72|= 1
|76-72|= 4
|77-72|= 5
|78-72|= 6
|83-72|= 11
3) Summation of all absolute differences
∑ |X-X[bar]
|= 13 + 9 + 3 + 2 + 0 + 1 + 4 + 5 + 6 + 11= 54
4) M.A.D.=∑ |X
-X[bar]
|/n
= 54/10= 5.4cm
c)
If you compare both calculated mean absolute deviations, you can see M.A.D. > M.A.D.
. As said before, the M.A.D. summary of the sample's dispersion. The greater value obtained for "Soil A" indicates this sample has greater variability.
I hope this helps!
Answer:
Therefore the equation of the line through ( 4 , -8 ) and ( 8 , 5 ) is
13x - 4y = 84.
Step-by-step explanation:
Given:
Let,
point A( x₁ , y₁) ≡ ( 4 ,-8)
point B( x₂ , y₂) ≡ (8 , 5)
To Find:
Equation of Line AB =?
Solution:
Equation of a line passing through Two points A( x₁ , y₁) and B( x₂ , y₂)is given by the formula
Substituting the given values in a above equation we get
Therefore the equation of the line through ( 4 , -8 ) and ( 8 , 5 ) is
13x - 4y = 84.
Answer:
A = ±
Step-by-step explanation:
Given
b²A² - 3g = q ( add 3g to both sides )
b²A² = q + 3g ( divide both sides by b² )
A² = ( take the square root of both sides )
A = ±