Answer:
d. $350.00
Step-by-step explanation:
A constant is a number that does not have any variables. The additional cost would depend on the number of persons at attendance so the cost would be $10.00p which is not the constant here. Thus, $350.00 is the only constant in this situation.
Answer:
Step-by-step explanation:
1/2(7x - 6) = 6x - 10
7/2x - 3 = 6x - 10 .....multiply by 2
7x - 6 = 12x - 20
-6 + 20 = 12x - 7x
14 = 5x
14/5 = x <===
Answer:
Step-by-step explanation:
First digit 2,3,4,5 = 4 different digits.
Second digit 2,3,4,5 = 4 different digits.
Third digit = 1,2,3,6,7,9 = 6 different digits.
Total number of possibilities = 4*4*6 = 96
If f(x) has an inverse on [a, b], then integrating by parts (take u = f(x) and dv = dx), we can show
Let 
. Compute the inverse:
![f\left(f^{-1}(x)\right) = \sqrt{1 + f^{-1}(x)^3} = x \implies f^{-1}(x) = \sqrt[3]{x^2-1}](https://tex.z-dn.net/?f=f%5Cleft%28f%5E%7B-1%7D%28x%29%5Cright%29%20%3D%20%5Csqrt%7B1%20%2B%20f%5E%7B-1%7D%28x%29%5E3%7D%20%3D%20x%20%5Cimplies%20f%5E%7B-1%7D%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%5E2-1%7D)
and we immediately notice that ![f^{-1}(x+1)=\sqrt[3]{x^2+2x}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%2B1%29%3D%5Csqrt%5B3%5D%7Bx%5E2%2B2x%7D)
.
So, we can write the given integral as
Splitting up terms and replacing 
in the first integral, we get
Answer:
27 years
Step-by-step explanation:
The formula for the number of payments can be used:
N = -log(1 +0.05(1 -1000000/65000))/log(1.05) +1 = 27.03
There will be a couple thousand dollars left after the 27th payment.
The winnings will last 27 years.
