Question 277058: Please help! I've been trying to figure out the solution to these problems and not understanding how to solve. Please help!
Question 1.
A survey of flower gardeners showed the following:
126 grew roses 20 grew both roses and tulips 11 grew all three types
51 grew tulips 15 grew both orchids and tulips 16 grew none of these three
37 grew orchids 26 grew both roses and orchids
How do you create a Venn diagram to reflect the above data.
(a) How many grew only tulips?
(b) How many grew both tulips and orchids, but not roses?
(c) How many grew only orchids?
(d) How many grew none of these three or only roses?
(e) How many flower gardeners were surveyed?
Question 2
In a survey of 125 dancers, 73 knew the Ballroom dances, 62 knew the Latin dances, and 49 knew the Swing dances. Of these, 23 knew the Ballroom and Swing dances, 35 knew the Ballroom and Latin dances, and 29 knew the Latin and Swing dances. Twelve dancers indicated that they knew all three styles of dance.
How do you create a Venn diagram to reflect the above data.
(a) How many knew only the Ballroom dances?
(b) How many knew only the Swing dances?
(c) How many knew exactly two of the three dances?
(d) How many knew the Latin and Swing dances, but not the Ballroom dances?
(e) How many knew none of these dances?
Question 3
An electronics store surveyed every 7th customer who came onto the store for a week.
Of the 350 people who responded,
144 people watched movies on VHS tapes
239 people watched movies on DVDs.
54 people watched movies both on VHS tapes and DVDs.
How do you create a Venn diagram to reflect the above data.
i. Of those surveyed, how many watched only VHS tapes?
ii. Of those surveyed, how many watched only DVDs?
iii. Of those surveyed, how many watched VHS tapes or DVDs, but not both?
iv. Of those surveyed, how many watched VHS tapes or DVDs, or both?
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! 1. draw three intersecting circles
___ draw a box around the three circles
___ label each of the circles ___ roses, tulips , orchids
___ label the box ___ flower gardners
fill in quantities that are given ___ usually starting with intersection of all groups
___ "11 grew all three types" ___ this number goes in the intersection of the three circles
___ "16 grew none of these three" ___ this number goes outside the circles, but inside the box
quantities must reflect already existing values
___ "20 grew both roses and tulips"
___ there are 20 in the roses/tulips intersection
___ but 11 of those have already been counted because they grow all three
___ so the remaining intersection area gets the quantity 9
similarly fill in orchids/tulips (4) and roses/orchids (15)
now fill in the roses, orchids, and tulips circles ___ taking into account the already existing values
you should now be able to answer (a) through (e) by using the filled in quantities
the other two questions use the same technique
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