Alan

Looks like you and I agree for the "with replacement" case Melody.

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Eventually I might get this right!  Here's my latest attempt:

Now with replacement:

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So, with and without replacement cases require 16 red cards.

$$\\ \frac{6^{2007}-6^{2006}}{30} = \frac{6^{2006}\times 6-6^{2006}}{30} = \frac{6^{2006}(6-1)}{30} = \frac{6^{2006}\times 5}{30}=\frac{6^{2006}}{6}=6^{2005}$$

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Possibly as follows:

7x8 = 56

6x7 = 42

5x6 = 30

4x5 = 20

3x4 = 12

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You need to divide both sides by 10, not multiply:

b = 18/10 

b =1.8

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I think this should be interpreted as:

n + d = 83                         (1)

5n + 10d = 690                 (2)

From (1) we have: n = 83 - d           (3)

Put (3) into (2)

5(83 - d) + 10d = 690

415 -5d + 10d = 690

5d = 275

d = 55

Put this into (3)

n = 83 - 55

n = 28

So there are 28 nickels and 55 dimes

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This can be re-written as (y - 10)² = x + 6,  so y = 10 ± √(x + 6)

This is a parabola.

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First find the price before sales tax:

P = $20000/1.072

The difference between this and the MSRP must equal nine times the cost of the remote keyless entry (4-way power passenger seat + keyless entry), so:

9*K = P - 17980  where K is cost of keyless entry.

9*K = 20000/1.072 - 17980

$${\mathtt{K}} = {\frac{\left({\frac{{\mathtt{20\,000}}}{{\mathtt{1.072}}}}{\mathtt{\,-\,}}{\mathtt{17\,980}}\right)}{{\mathtt{9}}}} \Rightarrow {\mathtt{K}} = {\mathtt{75.190\: \!713\: \!101\: \!160\: \!862\: \!4}}$$

or K ≈ $75

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If we exclude complex numbers, then the domain of f(x) is from 0 to infinity, because we can't take the square root of a negative number.

For the same reason the domain of g(x) is from negative infinity to 1.

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