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hodyreva [135]
3 years ago
13

A cell phone company charges $40 per month for unlimited calling, and $0.20 per text message sent. If t represents the number of

text messages Roxy sent last month, which expression represents the cost of her bill last month before any taxes or additional fees? 40 − 0.2t (40 + 0.2)t 40 + 0.2t (40 − 0.2)t
Mathematics
2 answers:
Zinaida [17]3 years ago
5 0
The expression that represents the cost of her bill last month would be 40 + 0.2t.
The forty represents the forty dollars charged each month for unlimited calling, and the 0.2t represents the amount of money charged for her text messages.
babunello [35]3 years ago
3 0

Answer:  Third option is correct.

Step-by-step explanation:

Let the number of text messages that Roxy sent last month be 't'.

Cost per month of a cell phone company for unlimited calling  = $40

Cost per text message sent = $0.20

So, According to question, the cost of her bill last month before any taxes or additional fees is given by

40+0.20t

Hence, Third option is correct.

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A worker was paid a salary of $10,500 in 1985. Each year, a salary increase of 6% of the previous year's salary was awarded. How
Mazyrski [523]
Note that 6% converted to a decimal number is 6/100=0.06. Also note that 6% of a certain quantity x is 0.06x.

Here is how much the worker earned each year:


In the year 1985 the worker earned <span>$10,500. 

</span>In the year 1986 the worker earned $10,500 + 0.06($10,500). Factorizing $10,500, we can write this sum as:

                                            $10,500(1+0.06).



In the year 1987 the worker earned

$10,500(1+0.06) + 0.06[$10,500(1+0.06)].

Now we can factorize $10,500(1+0.06) and write the earnings as:

$10,500(1+0.06) [1+0.06]=$10,500(1.06)^2.


Similarly we can check that in the year 1987 the worker earned $10,500(1.06)^3, which makes the pattern clear. 


We can count that from the year 1985 to 1987 we had 2+1 salaries, so from 1985 to 2010 there are 2010-1985+1=26 salaries. This means that the total paid salaries are:

10,500+10,500(1.06)^1+10,500(1.06)^2+10,500(1.06)^3...10,500(1.06)^{26}.

Factorizing, we have

=10,500[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]=10,500\cdot[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]

We recognize the sum as the geometric sum with first term 1 and common ratio 1.06, applying the formula

\sum_{i=1}^{n} a_i= a(\frac{1-r^n}{1-r}) (where a is the first term and r is the common ratio) we have:

\sum_{i=1}^{26} a_i= 1(\frac{1-(1.06)^{26}}{1-1.06})= \frac{1-4.55}{-0.06}= 59.17.



Finally, multiplying 10,500 by 59.17 we have 621.285 ($).


The answer we found is very close to D. The difference can be explained by the accuracy of the values used in calculation, most important, in calculating (1.06)^{26}.


Answer: D



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