What is the explicit formula for this sequence?
1 answer:
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Answer:
49 minutes
Step-by-step explanation:
To find the average time the machine was down per day, we need to add up the total time taken and then divide by the number of days. Since there are 5 days, we have:
= 49
So, the average time per day is 49 minutes.
Hope this helped! :)
The idea here is that $74,900 is Jennifer's annual salary before the deductions (the taxes, social security and medicare). Since she pays 6% in state taxes, 15% in federal taxes, 6.2% in social security and 1.45% in medicare, the deductions total 6% + 15% + 6.2% + 1.45% = 28.65%. To find out what she keeps we do the total (100%) less the deductions (28.65%) which yields 71.35%. That is, she keeps 71.35% of the total amount given ($74,900).
Recall, that percent means out of ("per") 100 ("cent" --> think "century= 100 years). So, 71.35% means 71.35 out of 100. That is
. To find 71.35% of 74,900 we multiply 
. That means that Jennifer keeps $53,441.15 of what she makes.
We are asked for her monthly net income. That is, how much money does she take home per month after the deductions. If we assume that she is paid the same amount each month, to find her monthly net income we divide 53,441.15 by 12.
Jennifer's net monthly income is
Note that when we divide by 12 above we actually get 4,453.42916 but as this is money I rounded to $4,453.43. In reality this is a little bit too high as 4,453.43 times 12 = 53,441.16. That means we overpaid her by one penny. In real life she probably would get 11 paychecks at $4,453.43 and one paycheck at $4,453.42 to make up for the penny, but if this is a textbook problem I expect the rounding up would be acceptable.
Recall, that percent means out of ("per") 100 ("cent" --> think "century= 100 years). So, 71.35% means 71.35 out of 100. That is
We are asked for her monthly net income. That is, how much money does she take home per month after the deductions. If we assume that she is paid the same amount each month, to find her monthly net income we divide 53,441.15 by 12.
Jennifer's net monthly income is
Note that when we divide by 12 above we actually get 4,453.42916 but as this is money I rounded to $4,453.43. In reality this is a little bit too high as 4,453.43 times 12 = 53,441.16. That means we overpaid her by one penny. In real life she probably would get 11 paychecks at $4,453.43 and one paycheck at $4,453.42 to make up for the penny, but if this is a textbook problem I expect the rounding up would be acceptable.