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.

36 is the final answer! : )

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}