Answer:
The Schusters will have to pay $2,034 in the sixth month.
Step-by-step explanation:
Since Carpet King is trying to increase sales, and it has instituted a new promotion by which all purchases can be paid on the installment plan with no interest, as long as the total is paid in full within six months, and there is a $20 minimum monthly payment required, if the Schuster family buys carpeting for $2,134 and makes only the minimum payment for five months, to determine how much will they have to pay in the sixth month, the following calculation must be performed:
2134 - (5 x 20) = X
2134 - 100 = X
2034 = X
Therefore, the Schusters will have to pay $ 2,034 in the sixth month.
Well the word “sum” means to add.
Other than that good luck.
Answer: 2343 / 256
Explanation
I will do this for you in two forms: 1) adding each term, and 2) using the general formula for the sum of geometric series.
1) Adding the terms:
4
∑ 3 (3/4)^i = 3 (3/4)^0 + 3 (3/4)^1 + 3 (3/4)^2 + 3 (3/4)^3 + 3 (3/4)^4
i=0
= 3 + 9/4 + 27/16 + 81/64 + 243/256 = [256*3 + 27*16 + 64*9 + 4*81 + 243] / 256 =
= 2343 / 256
2) Using the formula:
n-1
∑ A (r^i) = A [1 - r^(n) ] / [ 1 - r]
i=0
Here n - 1 = 4 => n = 5
r = 3/4
A = 3
Therefore the sum is 3 [ 1 - (3/4)^5 ] / [ 1 - (3/4) ] =
= 3 [ 1 - (3^5) / (4^5) ] / [ 1/4 ] = 3 { [ (4^5) - (3^5) ] / (4^5) } / {1/4} =
= (3 * 781) / (4^5) / (1/4) = 3 * 781 / (4^4) = 2343 / 256
So, no doubt, the answer is 2343 / 256
2x + 5 = 27
2x + 5 (-5) = 27 (-5)
2x = 22
2x/2 = 22/2
x = 11
hope this helps
