The slope-intercept form: y = mx + b.
m - slope, b - y-intercept
We have the points (0, 75) → y-intercept (b = 75), and (7, 40).
Substitute the coordimates of the points to the formula of a slope:
2 answers:
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Taylor series is
To find the Taylor series for f(x) = ln(x) centering at 9, we need to observe the pattern for the first four derivatives of f(x). From there, we can create a general equation for f(n). Starting with f(x), we have
f(x) = ln(x)
.
.
.
Since we need to have it centered at 9, we must take the value of f(9), and so on.
f(9) = ln(9)
.
.
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Following the pattern, we can see that for ,
This applies for n ≥ 1, Expressing f(x) in summation, we have
Combining ln2 with the rest of series, we have
Taylor series is
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When building a Venn Diagram, I always start from the area with the most overlap to the areas of least overlap. Once you have placed the 3 in the middle, you have counted those people, and therefore you must subtract them from the other surveys. Example: since there are 3 people that like all three subjects, now only have 5 students that like just math and English instead of 8.
Therefore:
A) 36 Students were in the survey
*Add all the numbers within the Venn diagram up. Overlapping doesn't matter because no one is double counted.
B) 6 People liked only Math
*Can't touch any other circle but Math
C) 20 Students liked English and math, but not history
*You add 9+5+6, since these bubbles are not overlapping with history.
I Hope this helps and let me know if you have any further questions!
Therefore:
A) 36 Students were in the survey
*Add all the numbers within the Venn diagram up. Overlapping doesn't matter because no one is double counted.
B) 6 People liked only Math
*Can't touch any other circle but Math
C) 20 Students liked English and math, but not history
*You add 9+5+6, since these bubbles are not overlapping with history.
I Hope this helps and let me know if you have any further questions!