Let the cost price be x. Selling price = cost price - loss = x - (0.10 * x) = 0.90x. Setting this equal to $90 gives 0.90x = $90, so x = $100.

Let the marked price be x. After a 20% discount, the selling price is x - (0.20 * x) = 0.80x. Setting this equal to $80 gives 0.80x = $80, so x = $100.

Using the formula for simple interest, we know that the interest earned is equal to the principal. Therefore, if the principal doubles in 5 years, the rate of interest can be calculated as (100 * Interest) / (Principal * Time) = (100 * Principal) / (Principal * 5) = 20%. Thus, the rate of interest is 20%.

Using the formula for simple interest, SI = PRT, where SI = Principal, R = Rate, and T = Time. If the principal doubles in 5 years, then SI = P. Therefore, P = PRT implies R = 1/5 = 20%. Hence, the rate of interest is 10%.

Using the rule of 72, we estimate the time to double as 72/12 = 6 years.

Using SI = PRT, SI = 8000 * 0.06 * 4 = $1920.

Thursday is the latest start day as the task will then complete by Saturday, which is not allowed.

The number of ways to choose 4 players from 10 is given by 10C4 = 210.

Points = (2 wins * 3 points) + (3 draws * 1 point) + (1 loss * 0 points) = 6 + 3 + 0 = 9 points.

a * b ≡ 2 * 3 ≡ 6 (mod 5), which is equivalent to 1.

All operations (addition, subtraction, multiplication) maintain congruence under modular arithmetic.

Since not all mammals are dogs, it follows that some cats, being mammals, cannot be dogs.

Supplementary angles sum up to 180 degrees. Therefore, angle B = 180 - 45 = 135 degrees.

The exponent zero indicates the multiplicative identity, meaning any non-zero number raised to the power of zero equals one.

Using the property of exponents, a^3 * a^(-2) = a^(3 - 2) = a^1, hence x = 1.

Substituting a = 2, we have 2^3 * b^2 = 64, which simplifies to 8b^2 = 64. Thus, b^2 = 8, leading to b = 4.

If a = b, then a^x = b^y implies x must equal y for the equality to hold.

Since A cannot sit next to B, C, D, or E can be seated next to A. Therefore, C is a valid option.

Since W is to the immediate left of Y and Y is to the immediate right of Z, Y must be in the middle of the arrangement.

P is between Q and R, which means Q is on one side of P and R on the other. Since S is opposite T, the only person next to R must be P.

The arrangement is B-A-C. The person sitting opposite B would be E.

The arrangement is E-D-F. The person sitting opposite E would be I.

If L is to the right of M, and N is to the left of L, we can deduce that H is sitting opposite M.

With M between N and O, and P opposite M, N will be to the left of P.

The arrangement is Q-P-R. Therefore, P is sitting next to R.

With R between S and T, and U opposite R, T will be to the right of U.

Given that T is next to U and V is opposite T, W must be next to V.

Since X is between Y and Z, and W is opposite Y, the only person who can be next to W is Z.

Since P is between Q and R, the arrangement can be visualized as Q-P-R. If S is opposite P, then T and U must be next to S. Thus, R is next to S.

Since A is in chair 1, B in chair 2, and C in chair 3, B is indeed sitting in the middle.