answer:To calculate the total cost of buying m bottles of mineral water and n boxes of yogurt, we follow these steps: 1. First, we calculate the cost of m bottles of mineral water. Since each bottle costs 2.5 yuan, the total cost for the mineral water is 2.5 times m yuan. 2. Next, we calculate the cost of n boxes of yogurt. Each box costs 4 yuan, so the total cost for the yogurt is 4 times n yuan. 3. To find the total cost, we add the cost of the mineral water to the cost of the yogurt: [2.5m + 4n] Therefore, the total cost of buying m bottles of mineral water and n boxes of yogurt is boxed{2.5m + 4n} yuan.

answer:To find out how much John made before the raise, we can set up the following equation: Let x be the amount John made before the raise. After the raise, John makes x + 0.3333x (which is the 33.33% increase of his original salary). So, the equation is: x + 0.3333x = 80 Combining like terms, we get: 1.3333x = 80 Now, we can solve for x by dividing both sides of the equation by 1.3333: x = 80 / 1.3333 x ≈ 60 Therefore, John made boxed{60} per week before the raise.

answer:Grant scored 100 points on his math test. Since Grant scored 10 points higher than John, we can determine John's score by subtracting 10 from Grant's score. John's score = Grant's score - 10 points John's score = 100 points - 10 points John's score = 90 points Now, we know that John received twice as many points as Hunter. To find out how many points Hunter scored, we divide John's score by 2. Hunter's score = John's score / 2 Hunter's score = 90 points / 2 Hunter's score = 45 points Therefore, Hunter scored boxed{45} points on his math test.

answer:Let's solve the problem step-by-step, starting with the information provided and using geometric properties and formulas for the areas of polygons. 1. **Define the side of the equilateral triangle:** Let the side of the equilateral triangle be ( a ). 2. **Calculate the area of the equilateral triangle:** The formula for the area ( S_1 ) of an equilateral triangle with side length ( a ) is: [ S_1 = frac{a^2 sqrt{3}}{4} ] 3. **Determine the radius of the inscribed circle in the triangle:** The radius ( r ) of the circle inscribed in an equilateral triangle is given by: [ r = frac{a sqrt{3}}{6} ] 4. **Relate the radius to the side of the hexagon:** In an equilateral triangle, the radius of the inscribed circle is equal to the side of the regular hexagon that is inscribed in the circle. Therefore, the side ( a_6 ) of the hexagon is: [ a_6 = frac{a sqrt{3}}{6} ] 5. **Calculate the area of the inscribed hexagon:** The area ( S_2 ) of a regular hexagon with side length ( a_6 ) is given by: [ S_2 = 6 times text{Area of one equilateral triangle with side } a_6 ] The area of one equilateral triangle with side ( a_6 ) is: [ text{Area} = frac{a_6^2 sqrt{3}}{4} ] Therefore, the total area ( S_2 ) of the hexagon is: [ S_2 = 6 times frac{a_6^2 sqrt{3}}{4} = 6 times frac{left(frac{a sqrt{3}}{6}right)^2 sqrt{3}}{4} ] Simplify ( S_2 ): [ S_2 = 6 times frac{left(frac{a^2 cdot 3}{36}right) sqrt{3}}{4} = 6 times frac{a^2 cdot 3 sqrt{3}}{144} = frac{6 a^2 sqrt{3}}{48} = frac{a^2 sqrt{3}}{8} ] 6. **Find the ratio of the areas ( frac{S_1}{S_2} ):** [ frac{S_1}{S_2} = frac{frac{a^2 sqrt{3}}{4}}{frac{a^2 sqrt{3}}{8}} = frac{a^2 sqrt{3}}{4} times frac{8}{a^2 sqrt{3}} = 2 ] # Conclusion: The ratio of the areas of the triangle and the hexagon is [ boxed{2} ]