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horsena [70]
3 years ago
10

Sage and Tom started the month with the same number of talk minutes on their cell phones. Sage talked for 7 minutes with her dad

. Tom talked for 4 minutes with a friend and 3 more minutes with his mom. Do Sage and Tom have the same number of talk minutes left on their cell phone plans?
Mathematics
1 answer:
Maslowich3 years ago
5 0
Yes because they started with the same amount and they both used 7 minutes
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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



4 0
2 years ago
The value of a car decreases by 20 percent per year. Mr. Sing purchases a $22,000 automobile. What is the value of the car at th
andriy [413]

Answer:

not too sure but I think its C or D

6 0
2 years ago
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What is the value of x?
Ivahew [28]
All 3 angles of a triangle add up too 180, so 80+55= 135, 180-135 is 45, so the value of x is 45
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3 years ago
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John and Brent traveled by train. They traveled 150 kilometers 485 meters, 235 kilometers 82 meters, and 365 kilometers 178 mete
gladu [14]
The answer is 1'495 and how I got that is by adding all the numbers and that's how I got my answer give a thanks and brainiest answer if correct
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A rectangular box has a width of x meters, length of x + 3 meters, and a height of x – 2 meters. Write an expression for its vol
kobusy [5.1K]

Answer:

x(x+3)(x-2)

Step-by-step explanation:

you can't multiply any of them so the expression is that. x cannot be multiplied with x+3 because x+3 are together.

5 0
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