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aksik [14]
3 years ago
12

A catering service offers 5 appetizers,4 main courses, and 8 desserts. A customer is to select 4 appetizers,2 main courses,and 3

desserts for a banquet. In how many ways can this be done
Mathematics
1 answer:
Alisiya [41]3 years ago
7 0

Answer:

468 ways

Step-by-step explanation:

Given: A catering service offers 5 appetizers, 4 main courses, and 8 desserts

To find: number of ways a customer is to select 4 appetizers, 2 main courses,and 3 desserts.

Solution:

A permutation is an arrangement of elements such that order of elements matters and repetition is not allowed.

Number of appetizers = 5

Number of main courses = 4

Number of desserts = 8

Number of ways of choosing k terms from n terms = nPk=\frac{n!}{(n-k)!}

Number of ways a customer is to select 4 appetizers, 2 main courses,and 3 desserts =  5P4+4P2+8P3

=\frac{5!}{(5-4)!}+\frac{4!}{(4-2)!}+\frac{81}{(8-3)!}\\=5!+\frac{4!}{2!}+\frac{8!}{5!}\\=5!+(4\times 3)+(8\times 7\times 6)\\=120+12+336\\=468

So, this can be done in 468 ways.

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What kind of transformation converts the graph of f(x) = 10x + 71 - 2 into the graph of
Over [174]

Answer:

A transition down six units

Step-by-step explanation:

-2-6=-8

8 0
3 years ago
What is the equation of the graph below? A graph shows a parabola that opens up with a vertex at negative three comma negative o
Tomtit [17]

Answer:

y=(x+3)^2-1\\y=x^2+6x+8

Step-by-step explanation:

Given:

Vertex of the parabola is, (h,k)=(-3,-1)

Equation of the parabola in vertex form is given as:

y=(x-h)^2+k

Plug in h=-3,k=-1. This gives,

y=(x-(-3))^2+(-1)\\y=(x+3)^2-1

Therefore, the equation of the given graph is

y=(x+3)^2-1\\y=x^2+6x+8.

5 0
3 years ago
HALP PLEASE DO 6 AND 7 PLEASEEE
Harman [31]

Answer:

Step-by-step explanation:

6) Convert mixed fraction to improper fraction and then plugin the values in the formula.

l= 3\frac{1}{3} yard=\frac{10}{3}\\\\w = 1\frac{5}{9} yard=\frac{14}{9}\\\\h =2\frac{1}{4} yard=\frac{9}{4}\\\\Volume of wood shed = l * w *h\\\\= \frac{10}{3}*\frac{14}{9}*\frac{9}{4}\\\\= \frac{5}{3}*\frac{7}{1}*\frac{1}{1}\\\\=\frac{5*7}{3}\\\\=\frac{35}{3}\\\\=11\frac{2}{3} cubic yard

b) 10 cubic yard is less than 11 2/3 cubic yard. So, it will fit in the wood shed.

7) Right side rectangular prism:

l = 16 in

w = 5 in

h =  20 - 14 = 6 in

Volume 1 = 16 * 5 * 6 = 480 cubic inches

Left side rectangular prism:

l = 9 in

w = 5 in

h =14 in

Volume 2 = 9 * 5 * 14 = 630 cubic in

Volume of composite solid = 480 + 630 = 1110 cubic inches

7 0
3 years ago
What is the value of expression 2X plus 5Y when X equals three and Y equal 2
fredd [130]
16, because 2•x would also be 2•3 which is 6, and 5•y is rewritten as 5•2 which equals 10. 10+6=16 :)
3 0
3 years ago
Let f(x) = 3x + 5 and g(x) = -4x + 7. Find.(f.g)(-4)
Shalnov [3]

Answer:

74

Step-by-step explanation:

fg(x)=f[g(x)]

=f(-4x+7)

=3(-4x+7)+5

=-12x+26

When x=-4,

fg(-4)=-12(-4)+26

=74

3 0
3 years ago
Read 2 more answers
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