Math Quiz -Arithmetic world problems Report a question What's wrong with this question? You cannot submit an empty report. Please add some details. Math Quiz -Aritmetic world problems Covering: real-world scenarios into mathematical expressions using key mathematical concepts like proportions, ratios, and percentages to solve problems. 1 / 5 1. A company produces 500 widgets every day, and the production rate increases by 2% each month. If the company continues to increase its production at the same rate, approximately how many widgets will it produce in the first 8 months? a) 986 b) 616 c) 386 d) 586 To solve this problem, we can use the formula for compound interest to calculate the production rate each month. The formula is: $Future Value=Present Value×(1+Rate_{Time}$ In this case, the present value is the initial production rate of 500 widgets per day, the rate is 2% (or 0.02) per month, and the time is 8 months. $Future Value=500×(1+0.02_{8}$ Let's calculate this: $Future Value=500×(1.02_{8}$ $Future Value≈500×1.171618$ $Future Value≈585.809$ So, if the company continues to increase its production at a rate of 2% each month for the first 8 months, it will produce approximately $585.809$ widgets per day. 2 / 5 2. Tom invests $10,000 in a compound interest account that earns 5% interest per year, compounded quarterly. If the interest is calculated annually, approximately how much money will Tom have after 5 years? a) 12,820 b) 11,320 c) 10,020 d) 14,200 To solve the problem, we'll use the compound interest formula: A = P * (1 + r/n)^(nt) Where: A is the future value of the investment/loan, including interest. P is the principal amount (the initial amount of money). r is the annual interest rate (in decimal form). n is the number of times that interest is compounded per unit t (time in years). t is the time the money is invested or borrowed for, in years. In this case: P = $10,000 r = 0.05 (5% expressed as a decimal) n = 4 (compounded quarterly) t = 5 years Plugging in these values, we get: $A=10000∗(1+40.05 _{×}$ Calculate this expression: $A=10000∗(1+0.0125_{20}$ $A=10000∗1.28203723171$ A \approx $12,820.37 After 5 years, Tom will have approximately $12,820.37 in his compound interest account. 3 / 5 3. The population of a city increases by 10% each year. If the current population is 5,000, what will be the population after 6 years? a) 8,858 b) 8000 c) 7,256 d) 4,434 We can use the formula for exponential growth to solve this problem: P(t) = P₀ * (1 + r)^t Where: P(t) is the population after t years, P₀ is the initial population, r is the growth rate (as a decimal), t is the time in years. In this case: P₀ = 5,000, r = 0.10 (10% expressed as a decimal), t = 6 years. Substitute these values into the formula: P(6) = 5,000 * (1 + 0.10)^6 Calculate this expression: P(6) = 5,000 * (1.10)^6 P(6) = 5,000 * 1.771561 P(6) ≈ 8,857.805 Therefore, the population of the city after 6 years will be approximately 8,857.805. 4 / 5 4. A rectangular garden has a length of 30 feet and a width of 10 feet. What is the perimeter of the garden? a) 60 feet b) 70 feet c) 75 feet d) 80 feet The perimeter of a rectangle is calculated by adding the lengths of all its sides: (2 * length) + (2 * width) = (2 * 30) + (2 * 10) = 60 + 20 = 80 feet. 5 / 5 5. A train travels at an average speed of 60 miles per hour. If it is scheduled to complete a 420-mile trip, how many hours will it take? a) 6 hours b) 7 hours c) 8 hours d) 9 hours Divide the total distance by the average speed: 420 miles / 60 mph = 7 hours. Your score is 0% Restart Quiz