The table shows the results of a survey of 200 randomly selected people on whether they like watermelon, cantaloupe, or
both.
Preferences for Types of Melon
Watermelon
Not Watermelon
Total
Cantaloupe
93
109
Not Cantaloupe
66
91
Total
159
200
Which is the marginal relative frequency for the people who do not like cantaloupe?

84.5%

Step-by-step explanation:

Divide the total number of students who do not like cantaloupe by the grand total. Express your answer as a decimal and as a percent.

Marginal rf= Total no of people who do not like cantaloupe ÷ grand total number

169/200= 0.845 =84.5%

Marginal relative frequency for the people who do not like cantaloupe is 0.455

or

Step-by-step explanation:

See below

Step-by-step explanation:

a) By the base case, a∈S. By the recursive step, bsb∈S if s∈S. Then, for s=a, bab∈S.

b) By the base case, ∅∈S. By the recursive step, asa∈S if s∈S. Then, for s=∅, a∅a=aa∈S. By the recursive step, bsb∈S if s∈S. Then, for s=aa, baab∈S.

c) Structural induction: We want to prove that s is palindrome for all s∈S.

Inductive basis: If s=a,b or ∅, then s is palindrome because s has either 0 or 1 characters.

Inductive hypothesis: Suppose that r∈S is a palindrome.

Inductive step: We will prove that every element constructed from r using the recursion is also a palindrome. Because of the restriction, all elements of S are constructed in this way, except for the base case. Thus, combining this with the inductive step, we will prove that every element of S is a palindrome.

Let t be an element constructed from r by recursion. Then t=ara or t=brb. If t=ara, then t is a palindrome, because reversing the word (denote the reverse word by capitals) gives T=aRa, with R being the reverse word of r. But r is a palindrome, hence r=R and T=aRa=ara=t. Again, if t=brb, T=bRb=brb=t.

We have completed the inductive step, hence by structural induction, every element of S is palindrome.

d) By recursion and the restiction, the only elements of S of length 3 are aaa,bbb,aba,bab. abb is none of those, hence abb∉S. (note that abb is not a palindrome, so by part c), abb∉S).