According to an almanac, 70% of adult smokers started smoking before turning 18 years old. (a) if 200 adult smokers are rando
1 answer:
Solution: (a) if 200 adult smokers are randomly selected, how many would we expect to have started smoking before turning 18 years old?
Answer: It is expected that in a random sample of 200 adult smokers, will have started smoking before turning 18.
(b) would it be unusual to observe 160 smokers who started smoking before turning 18 years old in a random sample of 200 adult smokers? why?
Answer: Yes, it would be unusual to observe 160 smokers who started smoking before turning 18 years old in a random sample of 200 adult smokers, because 160 is greater than μ + 2σ
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Answer:
Part 1) The equation of the perpendicular bisector side AB is
Part 2) The equation of the perpendicular bisector side BC is
Part 3) The equation of the perpendicular bisector side AC is
Part 4) The coordinates of the point P(0.091,3.727)
Step-by-step explanation:
Part 1) Find the equation of the perpendicular bisector side AB
we have
A(–2, 0), B(0, 8)
<em>step 1</em>
Find the slope AB
The formula to calculate the slope between two points is equal to
substitute the values
<em>step 2</em>
Find the slope of the perpendicular line to side AB
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
therefore
The slope is equal to
<em>step 3</em>
Find the midpoint AB
The formula to calculate the midpoint between two points is equal to
substitute the values
<em>step 4</em>
Find the equation of the perpendicular bisectors of AB
the slope is
passes through the point
The equation in slope intercept form is equal to
substitute
solve for b
so
Part 2) Find the equation of the perpendicular bisector side BC
we have
B(0, 8) and C(4, 2)
<em>step 1</em>
Find the slope BC
The formula to calculate the slope between two points is equal to
substitute the values
<em>step 2</em>
Find the slope of the perpendicular line to side BC
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
therefore
The slope is equal to
<em>step 3</em>
Find the midpoint BC
The formula to calculate the midpoint between two points is equal to
substitute the values
<em>step 4</em>
Find the equation of the perpendicular bisectors of BC
the slope is
passes through the point
The equation in slope intercept form is equal to
substitute
solve for b
so
Part 3) Find the equation of the perpendicular bisector side AC
we have
A(–2, 0) and C(4, 2)
<em>step 1</em>
Find the slope AC
The formula to calculate the slope between two points is equal to
substitute the values
<em>step 2</em>
Find the slope of the perpendicular line to side AC
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
therefore
The slope is equal to
<em>step 3</em>
Find the midpoint AC
The formula to calculate the midpoint between two points is equal to
substitute the values
<em>step 4</em>
Find the equation of the perpendicular bisectors of AC
the slope is
passes through the point
The equation in slope intercept form is equal to
substitute
solve for b
so
Part 4) Find the coordinates of the point of concurrency of the perpendicular bisectors (P)
we know that
The point of concurrency of the perpendicular bisectors is called the circumcenter.
Solve by graphing
using a graphing tool
the point of concurrency of the perpendicular bisectors is P(0.091,3.727)
see the attached figure
