The rule for the nth term of a sequence is 5n + 16 Find the 10th term of the sequence.
2 answers:
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The ordered pairs (0,13) and (10, 0) are joined to best draw the line of best fit for the given scatter plot. So, option 4 is correct.
<h3>How to draw the line of best fit for a scatter plot?</h3>For the given scatter plot, to draw a line of best fit, the slope is to be calculated. The slope of the required line is calculated by
m = [n(∑xy) - (∑x)(∑y)]/[n(∑x²) - (∑x)²]
Where,
∑xy = sum of the product of x and y values
∑x = sum of x values
∑y = sum of y values
∑x² = sum of square values of x
n = total number of scatter points
And the y-intercept is calculated by
b = [∑y - m(∑x)]/n
Where m is the slope obtained above
<h3>Calculation:</h3>The given scatter plot has the coordinate points:
(0,14), (1, 11), (2, 9), (3, 10),(4, 7), (5, 7), (6, 5), (7, 5), (8, 3), (9, 1), (10, 0)
Such that n = 11
Then the required components are calculated as follows:
∑x = 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
∑y = 14 + 11 + 9 + 10 + 7 + 7 + 5 + 5 + 3 + 1 + 0 = 72
∑xy = (0 × 14) + (1 × 11) + (2 × 9) + (3 × 10) + (4 × 7) + (5 × 7) + (6 × 5) + (7 × 5) + (8 × 3) + (9 × 1) + (10 × 0) = 220
∑x² = 0² + 1² + 2² + 3² + 4² + 5² + 6² + 7² + 8² + 9² + 10² = 385
Then the slope is calculated as follows:
slope m = [n(∑xy) - (∑x)(∑y)]/[n(∑x²) - (∑x)²]
On substituting,
m = [11(220) - (55)(72)]/[11(385) - (55)²]
⇒ m = -14/11 = -1.2727273 ≅ -1.3
∴ m = -1.3
Then calculating the y-intercept:
we have b = [∑y - m(∑x)]/n
On substituting,
b = [72 - -1.3(55)]/11
∴ b = 13
Then the slope-intercept form of the required line is
y = -1.3x + 13
When x = 0,
y = -1.3(0) + 13 = 13
When y = 0,
0 = -1.3x + 13
⇒ 1.3x = 13
⇒ x = 13/1.3 = 10
Therefore, the coordinates (0, 13) and (10, 0) give the best draw for the line of best fit.
Learn more about the scatterplot and the line of best fit here:
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