1) Quaterly interes = 3% / 4 = 0.03 / 4
2) Values:
after 1 quarter: 2000 (1 + 0.03/4)
after 2 quarters: 2000 (1 + 0.03/4)^2
after 3 quarters: 2000 (1 + 0.03/40^4
after 4 quarters = 2000 (1 + 0.03/4)^4
You could have used the future value formula directly:
A = C * (1 + r/n) ^ n*t
where r = 3% = 0.03
n = number of periods in a year: 4
t = number of years = 1
C = initial investment = 20000
=> A = 2000 (1 + 0.03/4)^4
Answer: option D. A = 2000 ( 1 + 0.03 /4) 4
Part A
Either Nathan picked 0, or Sonia picked 0, or both.
This is because multiplying nonzero numbers together gets a nonzero result. So one of them must have picked 0.
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Part B
It's the same idea as part A. It's not clear what the nonzero values are, but one (or more) person picked 0 as their secret number.
If they picked something like 1, 2 and 3, then the product is 1*2*3 = 6 which is nonzero and the product is larger than the three original values. This is because each value is 1 or larger. If someone picked a small decimal value like 0.1 then 0.1*2*3 = 0.6 is the product. It's closer to 0, but not 0 itself.
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Part C
Zero Product Property:
If m*n = 0, then either m = 0 or n = 0 or both.
This idea says that if the product of two numbers is 0, then at least one of the numbers must be 0 itself. It can be extended to three or more numbers.
This idea is useful when it comes to solving factored quadratic equations.
In the case of 2x^2 + 5x - 12, it factors to (2x-3)(x+4)
So using the zero product property, we can solve the quadratic equation like this
2x^2 + 5x - 12 = 0
(2x-3)(x+4) = 0
2x-3 = 0 or x+4 = 0
2x = 3 or x = -4
x = 3/2 = 1.5 or x = -4
The use of the zero product property happens in step 3
If dy / dt = 1, then y = t. If y = t, then y = 2/3, and then you could do 3 /2/3, getting us 3/2
The answer correct response for this x=-32
Answer:
840,000
If it was 500 or more, it would be 841,000.
But since it is below 500, it is 840,000.
Hope it helps!
