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How many proper subsets does the following set have? T = {m, a, t, h, i, s, #, 1}  Express answer as a Natural Number 

Given: n(A) = 15   and   n(B) = 23  a.   What is the minimum possible number of elements in A ∩ B?    [A]b.   What is the minimum possible number of elements in A ∪ B?    [B]

List all the proper subsets of the set  G= {g, e, m} Be sure to write your answer using proper notation.

Karen asked 60 coffee drinkers whether they like cream and/or sugar in their coffee.  Twelve said they like both, twenty-nine said they like cream and eight said they like it black. HINT:  Draw a Venn Diagram to help solve the problem. a.  How many drinkers like only sugar in their coffee? [a] b. How many drinkers do not like cream in their coffee?  [b]

If U = {x|x is all people}   and   A = {x|x is a man}  and   B = {x|x is a teacher} then which of the following is the best description of :     

Given: n(A) = 15   and   n(B) = 23  a.   What is the maximum possible number of elements in A ∩ B?    [A]b.   What is the maximum possible number of elements in A ∪ B?    [B]

How many one-to-one correspondences are there between the sets {x, y, z, u, v} and {2, 4, 6, 7, 9} if in each correspondence x must correspond to 7 and  y must correspond to 9?

The following table contains data from a study of two airlines which fly to a small town in USA. If a flight is selected, find P (OnTime and Big Name Airlines).   Number of Airlines that are On Time vs. Late OnTime Late Low Budget Airlines 33 6 Big Name Airlines 43 5  

The pie chart below summarizes the information from a recent survey about social media preference of teenagers. How many variables are summarized in this pie chart? [fill1] According to this survey, what is the most popular social media platform among teenagers? [fill2] What percentage teenagers did not vote “YouTube” as their preference? [fill3] Suppose “X” (previously known as Twitter) was among the “other” category displayed in the pie chart. If 100 teenagers were chosen at random, what is the expected number of teenagers who would prefer X [fill4]

Below is a random sample of hotel room prices/per night at State College during the playoff game weekend in 2024. The data include prices per night from a random sample of 13 hotels in the area. For convenience, the prices are sorted from the smallest to the largest, and the five number summary for the data is provided below. 1294 1312 1347 1358 1493 1494 1507 1534 1551 1592 1596 1602 1612 The cheapest 25% of the hotel rooms fall [fill1] The most expensive 25% of the hotel rooms cost [fill2] The data set is split into two halves at [fill3] The inter-quartile range for the data is [fill4]