answer:The reaction between magnesium (Mg) and carbon dioxide (CO2) to form magnesium oxide (MgO) and carbon (C) can be represented by the following balanced chemical equation: 2 Mg + CO2 → 2 MgO + C From the balanced equation, we can see that 2 moles of magnesium react with 1 mole of carbon dioxide to produce 2 moles of magnesium oxide and 1 mole of carbon. If the number of moles of magnesium oxide formed is equal to the number of moles of magnesium used, then for every 1 mole of magnesium used, 1 mole of magnesium oxide is formed. Since the balanced equation shows that 2 moles of magnesium are required to react with 1 mole of carbon dioxide, the number of moles of magnesium required to react with 1 mole of carbon dioxide is boxed{2} moles. This will result in the formation of 2 moles of magnesium oxide and 1 mole of carbon.

answer:1. **Calculate the volume of one small ball**: The volume ( V ) of a sphere is given by [ V = frac{4}{3} pi r^3 ] Substituting ( r = 3 ) inches, the volume of one small ball is [ V_{text{small}} = frac{4}{3} pi (3)^3 = 36pi ] 2. **Calculate the total volume of the small balls**: Ten balls each have a volume of ( 36pi ). [ V_{text{total}} = 10 times 36pi = 360pi ] 3. **Calculate the radius of the larger ball**: Equating the volume of the larger ball ( V_{text{large}} ) to the total volume, we get [ frac{4}{3} pi R^3 = 360pi ] Solving for ( R^3 ), [ R^3 = frac{360pi times 3}{4pi} = 270 ] Taking the cube root, [ R = sqrt[3]{270} approx 6.47 text{ inches} ] Thus, the radius of the large ball is ( boxed{6.47} ) inches.

answer:To solve the given system of inequalities, we will tackle each inequality step by step. **Step 1: Solve the first inequality** Given: frac{9-5x}{4} > 1 Multiply both sides by 4 to eliminate the denominator: [9 - 5x > 4] Subtract 9 from both sides: [-5x > -5] Divide both sides by -5 (remember, dividing by a negative number flips the inequality sign): [x < 1] **Step 2: Analyze the second inequality** Given: x < a This inequality tells us that x is less than some value a. **Step 3: Combine the inequalities to find the range of a** The solution set of the system is x < 1. For this to be true, considering x < a, a must be greater than or equal to 1. If a was less than 1, it would contradict our solution set from the first inequality. Therefore, the range of values for a must satisfy a geqslant 1. **Conclusion:** The correct answer, based on the analysis, is boxed{D: a geqslant 1}.

answer:To find the largest number, we arrange the digits in descending order: 9321. To find the least number, we arrange the digits in ascending order: 1239. Now, we subtract the least number from the largest number: 9321 - 1239 = 8082 The difference between the largest number and the least number written with the digits 9, 3, 1, 2 is boxed{8082} .