Use the Venn diagram to complete the contingency
1 answer:
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Answer/Step-by-step explanation:
a. Using a point on the graph, (6, 12), and the slope of the line, we can first generate an equation in the point-slope form, given as , where,
m = slope, and (a, b) is a point on the line.
Using two points, (6, 12) and (3, 21), let's find slope, m.
Using a point (6, 12) and slope, m = -3, generate an equation in the point-slope form by substituting a = 6, b = 12, and m = -3 in .
✅Equation in point-slope form would be:
Rewrite this to make it be in the slope-intercept form, .
Add 12 to both sides
✅The equation in slope-intercept form is
b. ✍️Based on the linear model, , the 30 represents b = y-intercept.
✅Therefore, it took Peter 30 mins long initially to deliver his package.
✍️Based on the linear model, , "-3" represents the slope.
✅Therefore, Peter's delivery time decreased 3 mins per day.
Roots with imaginary parts always occur in conjugate pairs. Three of the four roots are known and they are all real, which means the fourth root must also be real.
Because we know 3 and -1 (multiplicity 2) are both roots, the last root is such that we can write
There are a few ways we can go about finding , but the easiest way would be to consider only the constant term in the expansion of the right hand side. We don't have to actually compute the expansion, because we know by properties of multiplication that the constant term will be
.
Meanwhile, on the left hand side, we see the constant term is supposed to be 9, which means we have
so the missing root is 3.
Other things we could have tried that spring to mind:
- three rounds of division, dividing the quartic polynomial by , then by
twice, and noting that the remainder upon each division should be 0
- rational root theorem