Danny charges $22 for 2 hours of swimming lessons, Martin charges $90 for 5 hours of swimming lessons. Who offers a better deal?
2 answers:
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The standard deviation is 9.27. The typical heart rate for the data set varies from the mean by an average of 9.27 beats per minute.
<h3>How to determine the standard deviation of the data set?</h3>The dataset is given as:
Heart Rate Frequency
60 1
65 3
70 4
75 12
80 8
85 15
90 9
95 5
100 3
Calculate the mean using
Mean = Sum/Count
So, we have
Mean = (60 * 1 + 65 * 3 + 70 * 4 + 75 * 12 + 80 * 8 + 85 * 15 + 90 * 9 + 95 * 5 + 100 * 3)/(1 + 3 + 4 + 12 + 8 + 15 + 9 + 5 + 3)
Evaluate
Mean = 82.25
The standard deviation is
So, we have:
SD = √[1 * (60 - 82.25)^2 + 3 * (65 - 82.25)^2 + 4 * (70 - 82.25)^2 + 12 * (75 - 82.25)^2 + 8 * (80 - 82.25)^2 + 15 * (85 - 82.25)^2 + 9 * (90 - 82.25)^2 + 5 * (95 - 82.25)^2 + 3 * (100 - 82.25)^2)]/[(1 + 3 + 4 + 12 + 8 + 15 + 9 + 5 + 3 - 1)]
This gives
SD = √85.9533898305
Evaluate
SD = 9.27
Hence. the standard deviation is 9.27. The typical heart rate for the data set varies from the mean by an average of 9.27 beats per minute.
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Answer:
Length of the flower garden = 29 meters
Width of the flower garden = 16 meters
Step-by-step explanation:
I have also attached a diagram for your convenience
Now First let us see the data we are given with:
Arif's backyard length = 37 meters
Arif's backyard Width = 24 meters
Area that should be left with grass = 424 m^2
Now lets suppose the width of the stirp of grass be "a"
According the image the area of backyard will be:
Area ABCD = 24 x 37
Area ABCD = 888 m^2
The length LM will be = (37 -2a)
The Width LO will be = (24 -2a)
Area LMNO = (37 -2a) x (24 -2a)
Area LMNO = 888 -74a -48a +4a^2
Area LMNO = 4a^2 -122a + 888
Now in order the to calculate the area of the grass strip we must subtract the area LMNO from the total area ABCD and we already know that the areas the area of grass strip should be 424 m^2
hence, A = Area ABCD - Area LMNO
424 = 888 - (4a^2 -122a + 888)
424 = 888 - 4a^2 +122a - 888
424 = -4a^2 +122a
4a^2 -122a +424=0
(We can solve this quadratic equation by breaking the middle term method)
2(2x-53)(x-4) = 0
2(2x-53) = 0
2x -53 = 0
x = 53/2
x = 26.5 (Not Possible)
x-4 = 0
x = 4
Length of the flower garden = 37 -2(4)
Length of the flower garden = 29 meters
Width of the flower garden = 24 -2(4)
Width of the flower garden = 16 meters
