sanji8442
29.05.2020 •
Mathematics
Vanessa purchased a smart TV for $1,500 on a payment plan. Four months after purchasing the TV, her balance was $1,200. 7 months after purchasing the TV, her balance was $975. Find an equation that models the balance B(t) after t months. How many months will it take her to pay off the TV loan?
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Ответ:
The expression for her balance is "B(t) = -75*t + 1500". It'll take her 20 months to pay off the loan.
Step-by-step explanation:
We are looking for a function that has the following points:
B(0) = 1500
B(4) = 1200
B(7) = 975
Between B(4) and B(7), there was a variation of 3 months and a variation of -225 on her balance, thefore for each month that passed there was a variation of -75. Thefore, the expression for her ballance is:
B(t) = -75*t + 1500
To check if this expression is valid, we will apply the values provided on the problem:
B(0) = -75*0 + 1500 = 1500 (valid)
B(4) = -75*4 + 1500 = -300 + 1500 = 1200 (valid)
B(7) = -75*7 + 1500 = -525 + 1500 = 975 (valid)
When she pays of her loan, B(t) = 0, so we need to solve for t as shown below:
B(t) = -75*t + 1500 = 0
-75*t + 1500 = 0
75*t = 1500
t = 1500 / 75 = 20 months
It'll take her 20 months to pay the loan.
Ответ:
P(B) = 1/3 => P(B') = 1 - 1/3 = 2/3
(B' is complement of B)
Using the Bayes theorem:
P(A|B') x P(B') = P(A intersect B')
=>P(A|B') = P(A intersect B)/P(B) = (4/9)/(2/3) = 2/3
=> Option A is correct.
Hope this helps!
:)