In each of the following situations, indicate whether f = O(g), or f = (g), or both (in which case f = (g)). f(n) g(n) (a) n − 100 n − 200 (b) n1/2 n2/3 (c) 100n + log n n + (log n)2 (d) nlog n 10nlog 10n (e) log 2n log 3n (f) 10 log n log(n2) (g) n1.01 nlog2 n (h) n2/ log n n(log n)2 (i) n0.1 (log n)10 (j) (log n)log n n/ log n (k) √n (log n)3 (l) n1/2 5log2 n (m) n2n 3n

Check the explanation

Step-by-step explanation:

a)

f(n)=theta(g(n))

b) f=O(g)

c)

f(n)=theta(g(n))

d)

f(n)=theta(g(n))

e)

f(n)=theta(g(n))

f)

f(n)=theta(g(n))

g) f=omega(g)

h) f=omega(g)

i) f=omega(g)

j) f=omega(g)

k) f=omega(g)

l) f=O(g)

m) f=O(g)

n) f=theta(g)

o) f=omega(g)

p) f=O(g)

q) f=theta(g)

answer:

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

explanation:

service only with 20% tip  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the  

service

−−−−−−  

so technically the answer is  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

however, the intention of the question provider may have been that your answer is to be  

$

87.12

(

1

+

8

100

)

=

$

94.09

to 2 decimal places.

'

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge  

.

→

$

72.60

20% tip  

20

100

×

$

72.60

=

$

14.52

−−−−−−  

←

add

$

87.12

tax  

8

100

×

$

87.12

=

$

6.97

−−−−−  

←

add

$

94.09

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