answer:I want to find the largest odd divisor of 1200, since that would make b as large as possible. To do that, I can factor 1200 into prime factors: 1200 = 2^4 cdot 3 cdot 5^2. Now, I can look at the odd factors of 1200, which are obtained by multiplying any combination of 3 and 5^2, since 2 is even. The largest odd factor of 1200 is 3 cdot 5^2 = 75, so that is the largest possible value of b. To check, I can divide 1200 by 75 and get 16, which is an integer, so a = 16 and b = 75 satisfy the conditions of the problem.,To find the largest possible value of b, I will look for the largest odd multiples of 1200. Since b is an odd integer, I can find the largest odd factor of 1200 and see if it is expressible as a product involving a. The largest odd factor of 1200 is b = 1199, and: 1199 = 1199 cdot 1 = 1199 cdot 1 = a cdot b. This combination gives me the equation ab = 1200 and b is the largest possible odd value for this problem., Since b is an odd integer, it can be written as b = 2k + 1, where k is an integer. Our goal is to find the largest possible value for b. Given that ab = 1200 and a is an integer, we want to find an integer value for a such that the product is maximized while maintaining b as an odd integer. We can rewrite the equation as a(2k + 1) = 1200. Factoring out 2 from the left side gives us 2ak + a = 1200. Since a and b are integers, we know that a must be even because it's being multiplied by an odd integer (b) to give an even product (1200). Let's find the largest possible even value for a. Let a = 2m, where m is an integer. Substituting this into our equation, we get 2mk + 2m = 1200, or mk + m = 600. We can see that m = 600 works since a = 2m = 1200 is an even integer. Thus, b = 2k + 1 = frac{1200 - a}{m} + 1 = frac{1200 - 1200}{600} + 1 = 1. So, the largest possible value of b is 1.

answer:Since the two triangles have equal areas, we can set up the proportion: Area of the first triangle / Area of the second triangle = 1 (1/2 × Base × Height of the first triangle) / (1/2 × Leg1 × Leg2 of the second triangle) = 1 We know the Base of the first triangle is 8 cm, and the Height is 5 cm. So for the first triangle, it becomes: (1/2 × 8 cm × 5 cm) / (1/2 × ( Leg1 of the second triangle) × 20 cm) = 1 Now we can solve for the length of the other leg (Leg2) of the second triangle by first rearranging the equation: Leg1 of the second triangle = 8 cm × 5 cm / 20 cm = 2 cm So, the length of the other leg (Leg2) of the second triangle is 8 cm.,I know that the area of a right triangle is half the product of the lengths of the legs. So, if the first triangle has an area of (1/2)(5)(8) = 20 cm^2, then the second triangle must also have an area of 20 cm^2. That means I can write an equation for the second triangle's area as (1/2)(20)(x) = 20, where x is the length of the other leg. To solve for x, I can multiply both sides by 2 and divide by 20, getting x = 2. So the length of the other leg of the second triangle is 2 cm., Here's how to approach this problem: 1. The area of a right triangle can be calculated using the formula: Area = (base * height) / 2. 2. We know the base and height of the first triangle, so we can find its area.

answer:Let's determine the number of cars that are 4-door and red by using the given information. We know that: - frac{1}{3} of the cars are red, and since there are 30 cars in total, this means 10 cars are red (30 * frac{1}{3}). - 50% of the cars are 4-door, which means 15 cars are 4-door (30 * 0.5). - 8 cars are 2-door and white, but these cars could be either red or white. We have a total of 10 red cars and 15 4-door cars. Now we need to find the number of cars that fit both descriptions: red and 4-door. Since frac{1}{3} of the cars are red, there must be frac{1}{3} of the 15 4-door cars that are also red. By multiplying frac{1}{3} by 15, we can find the number of cars that are both red and 4-door: (1/3) * 15 = 5 So, there are 5 cars that are 4-door and red in the parking lot., Let's break down the information given: 1. There are 30 cars in total. 2. The cars are either red or white. 3. Half of the cars are 4-door (15 cars). 4. There are 8 cars that are 2-door and white. Since there are 15 cars that are 4-door, and we know that 8 of those are white, then there must be: 15 (total 4-door cars) - 8 (white 4-door cars) = 7 cars that are 4-door and red. Therefore, there are 7 cars in the parking lot that are 4-door and red.,I want to find the number of cars that are 4-door and red, so I will use a Venn diagram to represent the different categories of cars. I will draw two circles, one for the color (red or white) and one for the number of doors (2 or 4). The circles will overlap in four regions: red and 2-door, red and 4-door, white and 2-door, and white and 4-door. I will label each region with the number of cars in it, and I will use the given information to find the missing numbers. I know that frac{1}{3} of the cars are red, so that means 10 cars are red and 20 cars are white. I also know that 50% of the cars are 4-door, so that means 15 cars are 4-door and 15 cars are 2-door. I also know that 8 cars are 2-door and white, so I will put 8 in the region where the white circle and the 2-door circle overlap. Now I have three regions filled in, and I can use them to find the other numbers. Since 8 cars are 2-door and white, and 15 cars are 2-door in total, that means 7 cars are 2-door and red. I will put 7 in the region where the red circle and the 2-door circle overlap. Since 7 cars are 2-door and red, and 10 cars are red in total, that means 3 cars are 4-door and red. I will put 3 in the region where the red circle and the 4-door circle overlap. Since 3 cars are 4-door and red, and 15 cars are 4-door in total, that means 12 cars are 4-door and white. I will put 12 in the region where the white circle and the 4-door circle overlap. Now I have all four regions filled in, and I can check that they add up to 30 cars in total. 8 + 7 + 3 + 12 = 30, so I have not made any mistakes. The question asks for the number of cars that are 4-door and red, and I have found that to be 3.

answer:To find the mean of two numbers, I need to add them up and divide by two. So the mean of frac{1}{2} and frac{7}{8} is frac{frac{1}{2} + frac{7}{8}}{2}. To add fractions, I need to have a common denominator. The least common multiple of 2 and 8 is 8, so I can rewrite frac{1}{2} as frac{4}{8}. Now I have frac{frac{4}{8} + frac{7}{8}}{2}. I can add the numerators and keep the denominator: frac{frac{4}{8} + frac{7}{8}}{2} = frac{11}{8} cdot frac{1}{2}. To multiply fractions, I can multiply the numerators and the denominators: frac{11}{8} cdot frac{1}{2} = frac{11}{16}.,To find the mean (average) of frac{1}{2} and frac{7}{8}, we add the two fractions and then divide by the number of fractions (which is 2 in this case): text{Mean} = frac{frac{1}{2} + frac{7}{8}}{2} First, we need to find a common denominator to add the fractions. The least common multiple (LCM) of 2 and 8 is 8, so let's convert frac{1}{2} to a fraction with denominator 8: text{LCM}(2,8) = 8 frac{1}{2} = frac{4}{8} = frac{4}{8} Now we can add the two fractions: frac{4}{8} + frac{7}{8} = frac{4 + 7}{8} = frac{11}{8} Finally, we divide by 2 to find the mean: text{Mean} = frac{frac{11}{8}}{2} = frac{11}{16} So, the mean of frac{1}{2} and frac{7}{8} is frac{11}{16}., To find the mean of two numbers, you add them together and then divide by 2. So, to find the mean of frac{1}{2} and frac{7}{8}, we first add the fractions: frac{1}{2} + frac{7}{8} = frac{1 times 8}{2 times 8} + frac{7 times 2}{8 times 2} = frac{8}{16} + frac{14}{16} = frac{22}{16} We can simplify this common fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: frac{22}{16} = frac{22 div 2}{16 div 2} = frac{11}{8} Therefore, the mean of frac{1}{2} and frac{7}{8} is frac{11}{8}.