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MrMuchimi
3 years ago
12

A DJ tracks the song requests she receives on a Friday night. She noted that the number of requests for country songs was 2 more

than 4/3 times the number of requests for hip-hop songs. There were 18 requests for country. If x represents the number of requests for hip-hop songs, which equation represents this situation? How many requests for hip-hop songs did the DJ receive on Friday night?
Mathematics
1 answer:
gavmur [86]3 years ago
5 0
No. of country songs=4/3x+2
No of hip-hop requests= (18-2)x 3/4=12
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Answer:

l(n) = 80n + 520

Step-by-step explanation:

From the information given in the  question, there is a relationship between the number of new policy sold, n, and earning, I

           For 3 new policies, he earned $760

           For 5 new policies, he earned $920.

The rate of change of IIya's earning with respect to number of new policy sales is

             m = \frac{dI}{dn}

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The linear equation for the relationship is;

             l(n) = mn + b

I(n) is Ilya’s weekly income which is a function of the number of new policies, n

m is the rate of change of I with respect to n

n is the number of new policies,

b is the intial function which is IIya's income when n equals zero

Recall, Ilya earns a commission of $80 for each policy sold during the week. (m = $80 per policy)

                 l(n) = 80n + b

To complete the relationship l, we need to calculate the initial value b.

For 3 new policies, he earned $760,

             760 = 80(3) + b

             760 = 240 + b

             b = 760 - 520

             b = 520

The final equation is l(n) = 80n + 520

From the final equation, we can deduce that Ilya’s weekly salary is $520 and he earns an additional $80 commission for each new policy sold.

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