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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The answer is r = 2. hope this helps :)
<u><em>Answer:</em></u>
The intersection point is (-4,-19)
<u><em>Explanation:</em></u>
<u>The two given equations are:</u>
y = 5x + 1
y = 2x - 11
<u>To find the intersection point, we will start by equating the two given equations and solving for x</u>
<u>This is done as follows:</u>
5x + 1 = 2x - 11
5x - 2x = -11 - 1
3x = - 12
x = -4
<u>Then, we will use the x and substitute in any of the equations to get the value of y</u>
<u>Using the first equation:</u>
y = 5x + 1 = 5(-4) + 1 = -19
<u>Check using the second equation:</u>
y = 2x - 11 = 2(-4) - 11 = -19 ................? checked
<u>Therefore:</u>
The intersection point between the two given equations is (-4,-19)
Hope this helps :)
We can solve this using the formula nth term = a+(n-1)d
so the 10th term will be 87
75th term will be 132
and nth will be 9n-3
The first reflection reverses the orientation and alters the direction of the vectors representing the sides of the quadrilateral. The second reflection does the same thing. The end result is that the orientation is unchanged by two reflections, and the direction of the sides of the quadrilateral is changed.
The appropriate choice is ...
... B. The resulting image will be a rotation of the pre-image.
_____
The center of rotation will be the point where the lines cross. (That is the invariant point.)
In the attachment, the green quadrilateral RESP is reflected across the line y=2x+7 (blue) to form the blue quadrilateral R'E'S'P'. That is then reflected across the line y = -12x +5 (orange) to give the orange quadrilateral R"E"S"P", which is a rotation of the pre-image.
The amount of rotation is double the angle between the lines, about 62.7°.
