What is 10+10/10? Please Help
2 answers:
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Answer:
sum is 125,500
sum in summation notation is = (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
where
a is the first term
d is the common difference of arithmetic progression
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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.
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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
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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
sum in summation notation is = (2a+(n-1)d)n/2
If the first gardener can finish the job in 6 hours, it means that every hour he completes 1/6 of the job.
By the same logic, the second gardener completes 1/7 of the job per hour.
So, if they work together, they complete
of the job per hour.
So, after 42/13 of a hour, they'll complete the job. Since one hour is made of 60 minutes, 42/13 of a hour is
So, it will take them about 194 minutes to finish the job, i.e. about 3 hours and 14 minutes.
Answer:
the 8% loan has a principal of $37500
the 12% loan has a principal of $12500
Step-by-step explanation:
Let's start by writing the general equation for the interest hwre I is the interest, P is the principal (in our case would be loan amounts), "r" is the interest rate in decimal form (in our case one would be 0.12, and the other one 0.08), and t is the time in years (in our case 1 year).
Then we write the interest equation coming from each loan at the end of this year (we call I1 the interest coming from the 12% loan and I2 the interest coming from the 8% one). Since we don't know the loan amounts (in fact those are what we need to find) we will name one "x" and the other "y":
Next, we add these last two equations term by term, and replace the addition of both interests by $4500 as given in the information:
This is our first equation in the variables x and y which are our unknowns.
Now we generate the second equation on x and y by writing in agebraic terms the other piece of information we have: "the total of the two loans is $50000. That is the addition of the principals x and y should equal $50000:
We solve for y in this last equation and replace its form in terms of x in the equation of the interest, and solve for the unknown x:
Therefore the amount of the loan at 12% is $12500
Now to find the amount of the second loan "y" we use the equation for the totals of the loans:
Therefore, the loan at 8% is $37500