2ab x cos(C) = 7 since
a^2 + b^2 - 2ab x cos(C) = c^2
2ab x cos(C) = a^2 + b^2 - c^2
2ab x cos(C) = 2^2 + 2^2 - 1^2
2ab x cos(C) = 7
He created a scalene triangle.
A scalene triangle has sides and angles that do not measure alike.
The effective annual interest rate calculations yield:
i = (1 + 0.064/12)^12 - 1 = 0.066
For year 1: the interest amounts to $613.80 (calculating $9300 multiplied by 0.066)
For year 2: the interest totals $654.31 (adding year 1’s interest to $9300 and multiplying by 0.066)
For year 3: the interest is $656.98 (following the same process as year 2)
For year 4: the interest is $657.16
The cumulative interest totals: $2582.25
The present value of this sum is:
P = 2582.23 / (1 + 0.066)^4 = $1999.72
Thus, the final answer is $1999.72.
0.183. This problem addresses Binomial Probability. The formula is nCx × p^x × q^(n - x), where p = 0.72 and q = 1 - p = 0.28. With x representing the number of successes equal to 9 and n being 10, we are calculating the probability that at least nine out of ten people utilized an online travel website for booking. At least 9 out of 10 translates to x ≥ 9, so we calculate P(x ≥ 9) for x = 9 and x = 10. This leads to: P(x ≥ 9) = 10C9 × (0.72^9 × 0.28^(10 - 9)) + 10C10 × (0.72^10 × 0.28^(10 - 10)), resulting in approximately P(x ≥ 9) = 0.183.
