Based on the data in this two-way table, which statement is true?
type of flower/color red pink yellow total
rose 40 20 45 105
hibiscus 80 40 90 210
total 120 60 135 315

a. a flower being pink and a flower being a rose are independent of each other.
b. a flower being pink is dependent on a flower being a rose.
c. a flower being a rose is dependent on a flower being pink.
d. a flower being pink and a flower being a rose are the same.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for