A survey of 106 households was done to investigate the type of pets in the house. The results are shown in the Venn diagram below. If a household was selected at random, which of the following would be the probability the house would have cats given they don't have dogs? *
35 cats, 24 dogs, 19 both, 28 is the number outside the diagram

5/9

Step-by-step explanation:

35 households have only cats, 24 have only dogs, 19 have both cats and dogs, and 28 have neither.

The total number of households without dogs is 35 + 28 = 63.

The number of these households that have cats is 35.

So the probability is 35/63 = 5/9.

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.