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malfutka [58]
3 years ago
10

W contains the best franchises of 2015 according to Entrepreneur. If W= {Hampton Hotels, Anytime Fitness, Subway, Jack in the Bo

x, Supercuts, Jimmy Johns, Servpro, Denny's, Pizza Hut, 7-Eleven}, how many proper subsets does W contain?
Mathematics
1 answer:
weeeeeb [17]3 years ago
7 0

Answer:

Proper Subsets = 1023

Step-by-step explanation:

GivenW= \{Hampton\ Hotels, Anytime\ Fitness, Subway, Jack\ in\ the\ Box, Supercuts, \\Jimmy\ Johns, Servpro, Denny's, Pizza\ Hut, 7-Eleven\}

Required

Determine the proper subsets

Proper Subset (P) is calculated using;

P = 2^n - 1

Where

n = number\ of\ elements

In this case;

n = 10

So:

P = 2^n - 1

P = 2^{10} - 1

P = 1024 - 1

P = 1023

Hence;

<em>Proper Subsets = 1023</em>

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A

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3 0
3 years ago
I Need to find the Function Operations​
Alinara [238K]

Answer:

1) (f+g)(x)=2x^2+3x-6

2) (f-g)(x)=2x^2+x

3) (f \cdot g)(x)=2x^3-4x^2-9x+9

Step-by-step explanation:

So we have the two functions:

f(x)=2x^2+2x-3\text{ and } g(x)=x-3

And we want to find (f+g)(x), (f-g)(x), and (f*g)(x).

1)

(f+g)(x) is the same to f(x)+g(x). Substitute:

(f+g)(x)=f(x)+g(x)\\=(2x^2+2x-3)+(x-3)

Combine like terms:

=(2x^2)+(2x+x)+(-3-3)

Add:

=2x^2+3x-6

So:

(f+g)(x)=2x^2+3x-6

2)

(f-g)(x) is the same to f(x)-g(x). So:

(f-g)(x)=f(x)-g(x)\\=(2x^2+2x-3)-(x-3)

Distribute:

=(2x^2+2x-3)+(-x+3)

Combine like terms:

=(2x^2)+(2x-x)+(-3+3)

Simplify:

=2x^2+x

So:

(f-g)(x)=2x^2+x

3)

(f*g)(x) is the same to f(x)*g(x). Thus:

(f\cdot g)(x)=f(x)\cdot g(x)\\=(2x^2+2x-3)(x-3)

Distribute:

=(2x^2+2x-3)(x)+(2x^2+2x-3)(-3)

Distribute:

=(2x^3+2x^2-3x)+(-6x^2-6x+9)

Combine like terms:

=(2x^3)+(2x^2-6x^2)+(-3x-6x)+(9)

Simplify:

=2x^3-4x^2-9x+9

So:

(f \cdot g)(x)=2x^3-4x^2-9x+9

4 0
3 years ago
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