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3 years ago

One hundred people were asked about their favorite sport.

Mathematics

1 answer:

Makovka662 [10]3 years ago

7 0

Answer:categorical data listed on the left to complete the frequency table. Ways ... 100. B Jenna asked some randomly selected students whether they preferred dogs, cats, or other pets. ... part-time job. The results are shown in the two-way frequency table below. ... Two hundred students were asked about their favorite sport.

Step-by-step explanation:

A two-way table is a useful way to organize data that can be categorized by two variables. Suppose the school board asked 125 households if they would support a tax ... Make a table of the joint and marginal relative frequencies. ... The table shows the results of a survey of 100 randomly selected people entering an.

You might be interested in

You spend $56 dollars on food and beverages. You spent $18 more on food than on beverages.

mylen [45]

Answer:

in to total it is 130 or beverages is 74

Step-by-step explanation:

More means add so you would add 18 to 56

5 0

3 years ago

For the given set, first calculate the number of subsets for the set, then calculate the

vodomira [7]

Answer:

$\fbox{\begin{minipage}{14em}Number of subsets: 16\\Number of proper subsets: 15\end{minipage}}$

Step-by-step explanation:

Given:

The set A = {5, 13, 17, 20}

Question:

Find the number of subsets of A

Find the number of proper subsets of A

Simple solution by counting:

Subset of A that has 0 element:

{∅} - 1 set

Subset of A that has 1 element:

{5}, {13}, {17}, {20} - 4 sets

Subset of A that has 2 elements:

{5, 13}, {5, 17}, {5, 20}, {13, 17}, {13, 20}, {17, 20} - 6 sets

Subset of A that has 3 elements:

{5, 13, 17}, {5, 13, 20}, {5, 17, 20}, {13, 17, 20} - 4 sets

Subset of A that has 4 elements:

{5, 13, 17, 20} - 1 set

In total, the number of subsets of A: N = 1 + 4 + 6 + 4 + 1 = 16

The number of proper subsets (all of subsets, except subset which is equal to original set A): N = 16 - 1 = 15

Key-point:

The counting method might be used for finding the number of subsets when the original set contains few elements.

The question is that, for a set that contains many elements, how to find out the number of subsets?

The answer is that: there is a fix formula to calculate the total number ( $N$ ) of subsets of a set containing $n$ elements: N = $2^{n}$

With original set A = {5, 13, 17, 20}, there are 4 elements belonged to A.

=> Number of subsets of A: N = $2^{4} = 16$

(same result as using counting method)

Brief proof of formula: N = $2^{n}$

Each element of original set is considered in 2 status: existed or not.

If existed => fill that element in.

If not => leave empty.

For i.e.: empty subset means that all elements are selected as not existed, subset with 1 element means that all elements are selected as not existed, except 1 element, ... and so on.

=> From the point of view of a permutation problem, for each element in original set, there are 2 ways to select: existed or not. There are $n$ elements in total. => There are $2^n}$ ways to select, or in other words, there are $2^{n}$ subsets.