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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?

1 answer:

weeeeeb [17]3 years ago

7 0

Answer:

Proper Subsets = 1023

Step-by-step explanation:

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

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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3 years ago

I Need to find the Function Operations

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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:

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Combine like terms:

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Add:

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So:

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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:

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3)

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

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Distribute:

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Distribute:

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Combine like terms:

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Simplify:

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

So:

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

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