Asurvey was conducted to determine the popularity of 3 foods among students. the data collected from 75 students are summarized as below:
48 like pizza
45 like hoagies
58 like tacos
28 like pizza and hoagies
37 like hoagies and tacos
40 like pizza and tacos
25 like all three food
what is the number of students who like none or only one of the foods?
a. 4
b. 16
c. 17
d. 20
e. 23

Option D.

Step-by-step explanation:

Total number of students = 75

48 like Pizza, 45 like Hoagies, 58 like tacos, 28 like pizza and hoagies,

37 like hoagies and tacos, 40 like pizza and tacos, 25 like all three food

Using these information we get

Like pizza and hoagies  but not tacos = 28-25=3

Like hoagies and tacos  but not Pizza = 37-25=12

Like pizza and tacos but not hoagies = 40-25 = 15

Only Pizza = 48- 3 -15 -25 = 5

Only Hoagies = 45- 3 -12 -25 = 5

Only tacos = 58 - 12 - 15 - 25 = 6

Number of students who like none = 75 - 48 - 45- 58+28+37+40-25 = 4

The number of students who like none or only one of the foods is

Therefore, the correct option is D.

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step-by-step explanation:

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: