Page 834 - Algebra 1

SOLUTION
Find the probability of the complement of the balloon hitting the target. P(not hitting the target) = 1 - P(hitting the target)
= 1 - area of the triangle __
= 1 - 2 = 1 - _7
Use the area formulas. Multiply and square 7. Simplify the fraction. Subtract.
school bus
= 1 - _1 7
= _6 7
The probability of not hitting the target is _6 . 7
Application: Zoning
A new school is being built. All students live within a 4-mile radius of the school, and homes are evenly distributed throughout the area. Planners think that students who live within
0.5 mile of the school would walk to school. Students who live between 0.5 and 2 miles would ride a bike, a city bus, or a private car to school. Students who live between 2 and 4 miles from the school would ride the school bus. What is the probability of a student not walking to school?
SOLUTION
Find the complement of a student walking to school.
_1 mile 2
walk
2 miles
area of square wall _ _1 · 4 · 3 . 5
72 49
Example
4
Math Reasoning
Analyze When calculating with the area of circles, why are some answers exact and some approximate?
P(not walking to school) = 1 - = 1 -
=1-
= 1 -
4 miles bike, city bus, car
__ total area
The probability of not walking to school is _63 . 64
= 1 - = 63
π (0.5)2
2 _π ( 4 )
0.25π 16π
_1 64
Use the area formulas. Simplify the powers. Simplify the fraction. Subtract.
_ 64
P(walking to school) area of walking circle
Lesson 120 819