Let's eat: A fast-food restaurant chain has 597
outlets in the United States. The following table categorizes them by city population size and location, and presents the number of restaurants in each category. A restaurant is to be chosen at random from the
597
to test market a new menu. Round your answers to four decimal places.
Population
of City Region
NE SE SW NW
Under
50,000 26 37 15 4
−50,000500,000 55 95 66 32
Over
500,000 152 23 35 57

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(a) Given that the restaurant is located in a city with a population over
500,000
, what is the probability that it is in the Northeast?
(b) Given that the restaurant is located in the Southeast, what is the probability that it is in a city with a population under
50,000
?
(c) Given that the restaurant is located in the Southwest, what is the probability that it is in a city with a population of
500,000
or less?
(d) Given that the restaurant is located in a city with a population of
500,000
or less, what is the probability that it is in the Southwest?
(e) Given that the restaurant is located in the South (either SE or SW), what is the probability that it is in a city with a population of
50,000
or more?

associative property of multiplication

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500