Project Restaurant AS
docx
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School
Front Range Community College *
*We aren’t endorsed by this school
Course
120
Subject
Mathematics
Date
Feb 20, 2024
Type
docx
Pages
6
Uploaded by meghanmcfeely1
Name:
andrew sinclair
Directions:
·
Read the Project Guidelines and Directions in MyCourses
·
Worth 50 points
Coffee Time
1.
You were going to meet a friend for lunch, but you arrived too early. So, you decided to grab some coffee at the Bean Me Up Coffee Shop. The available flavors that day were: Au-
tumn Spice (AS), Chocolate Caramel (CC), Hawaiian Hazelnut (HH), and Vanilla Bean (VB).
a.
(1 pt) Is the set of coffee flavors available that day a well-defined set or not? Explain your answer.
this is a well defined set because it will have only these elements on this day and nothing else. b.
(1 pt) Write the set of available coffee flavors in roster form.
available flavors = {Autumn Spice, Chocolate Caramel, Hawaiian Hazelnut, Vanilla Bean}
c.
(2 pt) What is the cardinal number for the set of available coffee flavors?
n(4)
2.
The manager of the Bean Me Up Coffee Shop was sitting next to you working on business paperwork. You happen to see the following chart.
Non Coffee Items
July Sales (in $)
Cheesecake Cookies (CC)
$1,775
Mini Muffins (MM)
$1,050
Cinnamon Rolls (CR)
$972
Cookie Dough Cake Pops (CDCP)
$802
Double Chocolate Brownies (DCB)
$800
Waffle Cakes (WC)
$649
Chocolate Dipped Twinkies (CDT)
$380
Cream Puffs (CP)
$245
a.
(2 pt) If the manager wanted to find the set of non-coffee items that had at least $800 in
sales, what would be in that set? Write in roster form.
{double chocolate brownies, cookie dough cake pops, cinnamon rolls, mini muffins, cheesecake cookies}
b.
(2 pt) Consider the set {
x
|
x
is a non-coffee item with at most $700 in July sales
}
. Write the items in this set, in roster form.
{waffle cakes, chocolate dipped twinkies, cream puffs}
c.
(2 pt) Consider the set {
x
|
x
is a non-coffee item with no more than $600 in July sales
}
. Write the items in this set, in roster form.
{chocolate dipped twinkies, cream puffs}
Lunch Time
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3.
The restaurant had the following sauces for their wings: Honey BBQ (HBBQ), Spicy Garlic (SG), and Teriyaki (T).
a.
(1 pt) How many
subsets
of wing sauces are there?
6 subsets
b.
(2 pt) List
all the subsets
of this set of sauces. Use roster notation for each subset.
{hbbq}
{sg}
{t}
{hbbq, sg}
{t, hbbq }
{sg, t}
c.
(1 pt) How many
proper subsets
of wing sauces are there?
6 proper subsets d.
(2 pt) List
all the proper subsets
of this set of sauces.
{hbbq}
{sg}
{t}
{hbbq, sg}
{t, hbbq }
{sg, t}
4.
(2 pt) The salad bar at the restaurant had the following toppings: artichokes, broccoli, chick-
peas, eggs, mushrooms, olives, peppers, radishes, sprouts, tomatoes, and zucchini. Lettuce is the base, and is not considered a topping. However, a person could also just have lettuce only. How many different variations of toppings
are possible? Show or explain your steps.
2^11-1=2047
5.
As your server walked by you, they dropped a piece of paper where theye were keeping track of 100 customers in their zone. They had written the following information:
❑
Salad 45
❑
Soup 53
❑
Wings 54
❑
Salad and soup 30
❑
Soup and wings 20
❑
Wings and salad 16
❑
All three 9
(16 pt) In the following Venn diagram, fill in the corresponding values (numbers).
a.
(2 pt) How many customers ordered exactly two of these options? 39
b.
(2 pt) How many customers ordered at least one of these options? 47
9
27
5
21
12
11
7
8
c.
(2 pt) How many customers had only wings or only salad?
35
d.
(2 pt) How many customers did not have soup?
42
For parts e – h, remember that the cardinal number of a set is the number of elements in that set. Examples: n(set of letters in the English alphabet) = 26; there are 26 elements in the given set.
n(set of letters in the English alphabet ∩
set of letters in the word fun) = 3; there are 3 elements in the intersection of the two sets. e.
(2 pt) What is n
(
S et o f t ho se w hohad onl y s ala d
)
?
{8}
f.
(2 pt) What is n
(
Set of those who had soup Set of those who had wings
∪
)
?
{12, 21, 9, 7, 11, 27}
g.
(2 pt) What is n
(
Set of those who had soup ∩ Set of those who had salad
)
?
{21, 9}
h.
(2 pt) What is n
(
Universal set
)
?
{12, 21, 8, 9, 11, 7, 27, 5}
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