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 bicycle wheel has a diameter of 28 inches. If one complete rotation of the wheel covers a distance equal to its circumference, what distance will the wheel cover in 10 rotations? a) 879.2 inches b) 1120.4 inches c) 1379.6 inches d) 1669.8 inches First, find the circumference of the wheel using the formula C = πd, where C is the circumference and d is the diameter: C = 3.14 * 28 = 87.92 inches. Next, multiply the circumference by the number of rotations: 87.92 inches * 10 = 879.2 inches. 2 / 5 2. A triangle has one angle that is 20 degrees less than twice the measure of another angle. The third angle is 30 degrees more than the first angle. What is the measure of the largest angle in the triangle? a) 65 b) 72.5 c) 77.5 d) 80 Let's denote the measures of the angles as follows: Let $A$ be the measure of the first angle. Let $B$ be the measure of the second angle. Let $C$ be the measure of the third angle. According to the problem: $B=2A−20$ (One angle is 20 degrees less than twice the measure of another angle). $C=A+30$ (The third angle is 30 degrees more than the first angle). We also know that the sum of the angles in a triangle is always 180 degrees. Therefore: $A+B+C=180$ Now, substitute the expressions for $B$ and $C$ from the first two equations into the third equation: $A+(2A−20)+(A+30)=180$ Combine like terms: $4A+10=180$ Subtract 10 from both sides: $4A=170$ Divide by 4: $A=42.5$ Now that we know $A$, we can find $B$ and $C$: $B=2×42.5−20=85−20=65$ $C=42.5+30=72.5$ So, the measures of the three angles in the triangle are 42.5∘,65∘, and 72.5∘ 3 / 5 3. A container has a capacity of 20 liters. If the container is filled with water to 25% of its capacity, how many liters of water does it contain? a) 2 liters b) 3 liters c) 5 liters d) 7 liters To find the number of liters of water in the container, we multiply the total capacity of the container by the percentage it is filled: 20 liters * 25% = 5 liters. 4 / 5 4. A half empty tank initially contains 500 liters of water. Water is being pumped into the tank at a rate of 8 liters per minute, while water is simultaneously draining out at a rate of 4 liters per minute. How many minutes will it take for the tank to overflow? a) 135 b) 125 c) 225 d) 220 The differential equation is: dV/dt = 8 - 4 Integrating both sides: (1/4)V = t + C Using the initial condition V(0) = 500: (1/4)(500) = 0 + C C = 125 Now we have: (1/4)V = t + 125 Multiply both sides by 4: V = 4t + 500 The tank overflows when V(t) reaches its capacity (1000 liters): 4t + 500 = 1000 Solving for t: 4t = 1000 - 500 t = (1000 - 500)/4 t = 500/4 t = 125 Therefore, it will take 125 minutes for the tank to overflow. 5 / 5 5. A factory produces 800 toys every 8 hours. If the factory operates for 20 hours, but during the last 5 hours, the production rate is increased by 50%, how many toys will the factory produce in total during the 20-hour period? a) 2,000 toys b) 2,250 toys c) 2,750 toys d) 3,000 toys The production rate per hour is 800 toys / 8 hours = 100 toys/hour. For the first 15 hours, the factory produces 15 hours * 100 toys/hour = 1500 toys. During the last 5 hours, the production rate is increased by 50%, so the new production rate is 100 toys/hour + 0.5 * 100 toys/hour = 150 toys/hour. For the last 5 hours, the factory produces 5 hours * 150 toys/hour = 750 toys. The total number of toys produced during the 20-hour period is 1500 toys + 750 toys = 2250 toys. Therefore, after recalculating, the factory will produce a total of 2250 toys during the 20-hour period. Your score is 0% Restart Quiz