Which of the following is a quantitative continuous variable? a. Where a family goes on vacation b. Distance a family travels on vacation c. Number of vacations a family takes per year d. Number of consecutive years that a family goes on a vacation (Let a trip of at least 200 miles from home be defined as a "vacation") e. Amount spent on the vacation, to the nearest $100.

Which of the following is a quantitative continuous variable?

b. Distance a family travels on vacation

e. Amount spent on the vacation, to the nearest $100.

Step-by-step explanation:

Quantitative variables use numbers to express attributes, there are 2 types:

1. Quantitave continuous variables use numbers to express the attributes but, could have an infinite value between its maximum and minimum values, and are able to be divided into smaller values, such as in options b and e.

2. Quantitative discrete, also use numbers to express attributes, but they may have some, but not all the values, and must be integers, such as in options:

c. Number of vacations a family takes per year

d. Number of consecutive years that a family goes on a vacation (Let a trip of at least 200 miles from home be defined as "vacation").

e. Amount spent on the vacation, to the nearest $100.

And there are the cualitative variables, which use words to express attributes, such as in:

a. Where a family goes on vacation.

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}

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with   number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

hence, first option 'a'   is correct.