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Nezavi [6.7K]
3 years ago
10

one video rental club charges $25 to become a member and 2.50 to rent each video another charges no membership fee but charges $

3.25 to write each video how many videos must you run to make the first Club more economical
Mathematics
1 answer:
ladessa [460]3 years ago
8 0

The total charges for the first club as a function of the number of rentals (x) are

... f1 = 25 + 2.50x

The total charges for the second club are

... f2 = 3.25x

We want to find x so that f1 < f2.

... f1 < f2

... 25 + 2.50x < 3.25x

.. 25 < 0.75x . . . . . . . . . . subtract 2.50x

... 25/0.75 < x . . . . . . . . . divide by the coefficient of x

... 33 1/3 < x

You must rent 34 videos or more to make the first club more economical.

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Calculate the sum of the multiples of 4 from 0 to 1000
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Answer:

sum is 125,500

sum in summation notation is \sum\limits_{n=0}^n a+nd= (2a+(n-1)d)n/2

Step-by-step explanation:

This problem can be solved using concept of arithmetic progression.

The sum of n term terms in arithmetic progression is given by

sum = (2a+(n-1)d)n/2

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d is the common difference of arithmetic progression

_____________________________________________________

in the problem

series is multiple of 4 starting from 4 ending at 1000

so series will look like

series: 0,4,8,12,16..................1000

a is first term so

here a is 0

lets find d the common difference

common difference is given by nth term - (n-1)th term

lets take nth term as 8

so (n-1)th term = 4

Thus,

d = 8-4 = 4

d  can also be seen 4 intuitively as series is multiple of four.

_____________________________________________

let calculate value of n

we have last term as 1000

Nth term can be described

Nth term = 0+(n-1)d

1000 =   (n-1)4

=> 1000 = 4n -4

=> 1000 + 4= 4n

=> n = 1004/4 = 251

_____________________________________

now we have

n = 1000

a = 0

d = 4

so we can calculate sum of the series by using formula given above

sum = (2a+(n-1)d)n/2

       = (2*0 + (251-1)4)251/2

       = (250*4)251/2

     = 1000*251/2 = 500*251 = 125,500

Thus, sum is 125,500

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