answer:Let's find out how many widgets Doris puts in each carton first. Each carton contains 3 widgets. We're given that the shipping box is 20 inches wide, 20 inches long, and 20 inches high, which means its internal dimensions are also 20 inches each. A carton (3 widgets in each carton) needs to fit inside the shipping box. To make compact packing, I'll assume that the carton fits in each dimension with 2.5-inch allowance (so 17.5 inches wide, 17.5 inches long, and 17.5 inches tall). Then there will be space at the top and sides of the shipping box to accommodate the cartons. Now, let's set all of those up: Widgets in one carton: 3 Number of Bare Cartons in the Shipping Box: Number of Cartons / Volume of one carton The volume of the shipping box is 20 inches x 20 inches x 20 inches or 8000 cubic inches. The volume of one carton is x inches x 4 inches x 5 inches or 20x cubic inches. So we need to know what x is to calculate how many cartons can fit in the shipping box. Total volume occupied by all the cartons: Number of cartons * Volume of one carton Total Volume in Shipping box: 8000 cubic inches > Number of cartons * 20x cubic inches = 8000 cubic inches This gives us: Number of cartons = 8000 cubic inches / 20x cubic inches = 400 / (2x) cartons. We're given that each carton contains 3 widgets. So, there are 400 / (2x) * 3 widgets in each shipment. We're also given that there are 300 widgets. Hence, 400 / (2x) * 3 = 300. This simplifies to: x = 10 That means each carton needs to be 10 inches wide to fit the 300 widgets inside the shipping box. Final answer: x = 10, First, let's determine how many cartons can fit in the shipping box. Since the shipping box is 20 inches wide, 20 inches long, and 20 inches high, and each carton is 5 inches wide, 4 inches long, and 3 inches high, we can calculate the volume of the shipping box and the cartons: Shipping box volume = 20 inches * 20 inches * 20 inches = 8000 cubic inches Carton volume = 5 inches * 4 inches * x inches = 20x cubic inches Now, we can divide the shipping box volume by the carton volume to find out how many cartons fit in the shipping box: Number of cartons = Shipping box volume / Carton volume Number of cartons = 8000 cubic inches / 20x cubic inches We are told that 300 widgets are in each shipping box, and since Doris packs 3 widgets in each carton, we can divide the total number of widgets by 3 to find out how many cartons are in the shipping box: Number of cartons = 300 widgets / 3 widgets per carton Number of cartons = 100 Now, we can substitute this value into our previous equation to find the value of x: 100 = 8000 cubic inches / 20x cubic inches To solve for x, we can first multiply both sides by 20x: 100 * 20x = 8000 cubic inches Simplifying that expression, we get: 2000x = 8000 Now, we can divide both sides by 2000 to find the value of x: x = 8000 / 2000 x = 4 The value of x is 4 inches, so each carton is 5 inches wide, 4 inches long, and 4 inches tall.,Doris puts 3 widgets in each carton. The dimensions of each widget are x inches wide, 4 inches long, and 5 inches tall. To fit the widgets in a carton, we need to consider the width, length, and height of the carton. The width of the carton should be able to accommodate 3 widgets, so it should be at least 3x inches wide. The length of the carton should be able to accommodate 3 widgets, so it should be at least 3 * 4 = 12 inches long. The height of the carton should be able to accommodate 3 widgets, so it should be at least 3 * 5 = 15 inches tall. The shipping box dimensions are 20 inches wide, 20 inches long, and 20 inches high. To fit the cartons in the shipping box, we need to divide the dimensions of the shipping box by the dimensions of the carton. The number of widgets that can be shipped in each shipping box is the product of the number of cartons that can fit in each dimension: (20/3x) * (20/12) * (20/15). We are given that the number of widgets shipped in each shipping box is 300, so we can write: (20/3x) * (20/12) * (20/15) = 300. Multiplying the fractions and simplifying, we get: (400/9x) = 300. Dividing both sides by 400/9, we get: x = 12/3. Simplifying the right side, we get: x = 4. The value of x is 4. 4 The answer is: 4

answer:The shoebox has a height of 4 inches and a width of 6 inches. The square block inside has sides of length x inches. The area of the square block is x * x = x^2 square inches. The area of the shoebox is 4 * 6 = 24 square inches. The area of the shoebox that is left uncovered is the difference between the area of the shoebox and the area of the square block: 24 - x^2 square inches. We are given that the area left uncovered is 8 square inches, so we can write: 24 - x^2 = 8. Solving for x, we get: x^2 = 16. Taking the square root of both sides, we get: x = 4. The value of x is 4. 4 The answer is: 4, First, let's calculate the area of the bottom of the shoebox (which is a rectangle): 1. Bottom area = length * width 2. Bottom area = 6 inches * 4 inches 3. Bottom area = 24 square inches If Tara places a square block of side length x inches inside the box, then the area of the block would be: 1. Block area = side^2 2. Block area = x^2 To find the area of the shoebox bottom that is not covered by the block, we subtract the block area from the bottom area: 1. Uncovered area = Bottom area - Block area 2. Uncovered area = 24 square inches - x^2 According to the question, the uncovered area is 8 square inches: 1. 8 square inches = 24 square inches - x^2 2. x^2 = 24 square inches - 8 square inches 3. x^2 = 16 square inches 4. x = √(16 square inches) 5. x = 4 inches So, the value of x is 4 inches.,To solve this problem, we need to figure out how many square inches of the shoebox's internal space are left uncovered when the block is inside it. Let's analyze what we know so far: 1. The shoebox is 4 inches tall and 6 inches wide. 2. There is a square block inside with sides of length x inches. 3. The length remaining uncovered on the top of the box when the block is inside equals 4 - x inches (since the block has an x-inch side sticking out of the top). 4. The width remaining uncovered on the box when the block is inside equals 6 - x inches (since the block has an x-inch side sticking out on each side). 5. The remaining space inside the box is equal to the rectangle of the remaining space on top and the remaining space on the sides, which can be represented by (4 - x)(6 - x) square inches. 6. We are given that the remaining space inside the box is 8 square inches. Now, we can set up an equation based on our understanding and solve for x: (4 - x)(6 - x) = 8 This equation simplifies to: 24 - 10x + x^2 - 6x = 8 Combine like terms: x^2 - 16x + 16 = 0 We can divide the equation by 4 to simplify further: x^2 - 4x = 4 Rearranged: x^2 - 4x - 4 = 0 Factoring: (x - 4)(x + 1) = 0 Using the zero-product property, we find the solutions: x - 4 = 0 or x + 1 = 0 x = 4 or x = -1 Since x cannot be negative (the length of the block's side cannot be negative), the only valid solution is: x = 4 So, the value of x is 4.

answer:Out of 300 students, 40% of them are smoking teens, so there are 300 * 0.4 = 120 smoking students. Over the course of a year, 70% of the smoking students are hospitalized, so 120 * 0.7 = 84 smoking students are hospitalized. Therefore, the number of smoking students who have not been hospitalized is 120 - 84 = 36. 36 The answer is: 36, First, let's find out how many smoking teens there are in the class: Smoking teens = Total students * Percentage of smoking teens = 300 * 0.40 = 120 Next, we'll calculate how many of these smoking teens get hospitalized due to smoking-related complications: Hospitalized smoking teens = Smoking teens * Percentage hospitalized = 120 * 0.70 = 84 Since we want to find out how many smoking teens were not hospitalized, we simply subtract the number of hospitalized smoking teens from the total number of smoking teens: Non-hospitalized smoking teens = Smoking teens - Hospitalized smoking teens = 120 - 84 = 36 So, 36 smoking students from the class have not been hospitalized from smoking-related complications.,First, find the number of smoking students in the class: 40% of 300 students = 0.40 * 300 = 120 smoking students Next, find the number of smoking students who were hospitalized: 70% of 120 students = 0.70 * 120 = 84 smoking students Finally, subtract the number of hospitalized students from the total number of smoking students to find the number of smoking students who have not been hospitalized: 120 smoking students - 84 hospitalized students = 36 smoking students who have not been hospitalized So, 36 smoking students from the class have not been hospitalized from smoking-related complications.

answer:The distance between the first and second signs is 625 feet. Here's the reasoning: 1. Matt rode a total of 1000 feet away from his house. 2. He passed the first sign, which was 350 feet away from his house. At this point, Matt has traveled 350 feet. 3. After the first sign, he rode an additional distance before reaching the second sign. Since he traveled a total of 1000 feet, and 350 feet were covered up to the first sign, there are 1000 - 350 = 650 feet left to cover between the two signs. 4. However, after passing the first sign, Matt continued for another 275 feet before reaching the second sign. 5. Therefore, the distance between the first and second signs is 650 - 275 = 625 feet.,To find the distance between the first and second signs, we need to subtract the distance between the stop sign (350 feet) and his house from the total distance he rode (1000 feet), and then subtract the additional 275 feet he rode after passing the second sign. Total distance - Distance from stop sign to house - Additional distance after passing second sign 1000 feet - 350 feet + 275 feet = 925 - 275 = 650 feet The distance between the first and second signs is 650 feet.,Matt rode a total of 1000 feet away from his house. He passed a stop sign that was 350 feet away from his house. After passing the first sign, he rode an additional 275 feet. To find the distance between the first and second signs, we can subtract the distance of the first sign from the total distance Matt rode and then subtract the additional distance he rode. 1000 feet - 350 feet - 275 feet = 375 feet. The distance between the first and second signs is 375 feet. 375 The answer is: 375