Margo is planning a vacation. Assume that they have 2 possible destinations: beach or mountains. There are 2 vacation areas in the beach destination with 5 available condos for 1 of the areas, and 4 available condos for the other areas. There are 3 mountain destinations with 1 available condo for 2 of the areas, and 3 available condos for the other areas. A trip plan involves the selection of a destination, area, and a condo. First, draw out the tree diagram representing making these choices below: Required:
a. How many outcomes are there in the sample space?
b. Write out the event "Margo picks a beach destination" in set notation.

There are 14 outcomes in the sample space.

x= { x/x ∈ b, where b≠0 }

Step-by-step explanation:

The tree diagram is as follows

                                                                                                   Sample Space

Margo→→→→Beach (b)→→→→→→→1 destination→→→→→→→5 condos              5

     ║                   ║→→→→→→→→→→2 destination→→→→→→→→→4 condos       4

     ║

     ║

     ║→→→→→Mountain (m) →→→→→→→→1 destination→→→→→→ 1condo         1

                                    ║→→→→→→→→→→2 destination→→→→→ 1condo         1

                                     ║→→→→→→→→→→ 3destination→→→→→ 3 condos     3

Part a:

There are 14 outcomes in the sample space .

5+4+1+1+3= 14

Part b:

Margo picks a beach destination in set notation is

x= { x/x ∈ b, where b≠0 }

x such that x belongs to b ( beach destination) and b is not equal to zero.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.