Question

essential question how can you construct and interpret a two - way table? 1 exploration: completing and using a two - way table work with a partner. a two - way table displays the same information as a venn dia a two - way table, one category is represented by the rows and the other category is represented by the columns. the venn diagram shows the results of a survey in which 80 students were asked wh they play a musical instrument and whether they speak a foreign language. use the v diagram to complete the two - way table. then use the two - way table to answer each c survey of 80 students (venn diagram with play an instrument: 25, overlap 16, speak a foreign language: 30, outside both 9) (two - way table with rows: speak a foreign language, do not speak a foreign language, total; columns: play an instrument, do not i an instru) a. how many students play an instrument? b. how many students speak a foreign language? c. how many students play an instrument and speak a foreign language? d. how many students do not play an instrument and do not speak a foreign language? e. how many students play an instrument and do not speak a foreign languag

Explanation:

Step1: Analyze the Venn diagram

The Venn diagram has three regions for "Play an instrument" (25 only, 16 both), "Speak a foreign language" (30 only), and outside both (9). Total students are 80.

Step2: Solve part a (Play an instrument)

To find students who play an instrument, add the only play and both play & speak: $25 + 16 = 41$.

Step3: Solve part b (Speak a foreign language)

Add the only speak and both: $16 + 30 = 46$.

Step4: Solve part c (Play and speak)

The overlapping region is 16, so 16 students.

Step5: Solve part d (Neither)

Total students minus (play only + both + speak only): $80 - (25 + 16 + 30) = 80 - 71 = 9$.

Step6: Solve part e (Play and do not speak)

The "only play" region is 25, so 25 students.

Answer:

a. 41
b. 46
c. 16
d. 9
e. 25