14. There is a rectangular piece of property that measures 188 ft by 100 ft. On the property there is a circular lake with a diameter of 72 ft. In the center of the lake there is a circular island with radius of 12 ft. The rest of the property is land. What percentage of the property is covered in water? Use 3.14 for and round your answer to the nearest tenth of a percent.=18.8%
15. You deposit $1500 to start a bank account that gives 5.4% interest, compounded annually. If you do not touch the account, how much will you have after 3 years? Make sure you round your answer to the nearest cent.=$1756.35
16. You find an old savings bond that originally cost $50. It has been compounding 3% interest annually for the last 75 years. How much is it worth? Make sure you round your answer to the nearest cent.=$459.00
To solve question 14, we need to find the area of the circular lake and the area of the rectangular property, and then calculate the percentage of the property covered by water.
1. Area of the circular lake: The formula to calculate the area of a circle is A = πr^2, where π is approximately 3.14 and r is the radius of the circle. Given that the diameter of the lake is 72 ft, the radius (r) would be half of that, which is 36 ft. So, the area of the circular lake is A = 3.14 * (36 ft)^2.
2. Area of the rectangular property: To find the area of a rectangle, we multiply its length by its width. Given that the length of the property is 188 ft and the width is 100 ft, the area of the rectangle is A = 188 ft * 100 ft.
3. Total area of the property covered by water: Since the lake is in the center of the property, we can subtract the area of the circular island from the area of the lake to get the total water coverage. The area of the circular island is calculated using the same formula as the lake, A = 3.14 * (12 ft)^2. Therefore, the total water coverage is the area of the lake minus the area of the island.
To calculate the percentage of the property covered by water, we divide the total water coverage by the total area of the property, and then multiply the result by 100. Finally, round the answer to the nearest tenth of a percent.
For question 15, we use the compound interest formula A = P(1 + r/n)^(n*t), where A is the final amount, P is the principal amount, r is the annual interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years. In this case, the principal amount (P) is $1500, the interest rate (r) is 5.4% (or 0.054 as a decimal), the interest is compounded annually (n = 1), and the time period (t) is 3 years. Plug these values into the formula and calculate the final amount (A).
For question 16, we use the same formula as in question 15, but with different values. The principal amount (P) is $50, the interest rate (r) is 3% (or 0.03 as a decimal), the interest is compounded annually (n = 1), and the time period (t) is 75 years. Plug these values into the formula and calculate the final amount (A).