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question:Layla is feeding her pet fish. She has two Goldfish which each get one teaspoon of fish food. Her 3 Swordtails each get 2 teaspoons of food. Her 8 Guppies each eat half a teaspoon of food. How much food does she have to give to her fish in total?
answer:Layla has 2 Goldfish, so they need 2 * 1 = 2 teaspoons of food. She also has 3 Swordtails, so they need 3 * 2 = 6 teaspoons of food. Layla has 8 Guppies, so they need 8 * 0.5 = 4 teaspoons of food. In total, Layla needs to give her fish 2 + 6 + 4 = 12 teaspoons of food. 12 The answer is: 12
question:The spacecraft Gibraltar is a mountain-sized intergalactic vehicle for transporting equipment, building materials, and families to establish colonies on far-away planets. At full capacity, the vehicle can carry 300 family units with four people per family. The space flight is expected to take years, and it is expected that the size of families will grow during the space voyage. Therefore, when the spacecraft leaves the earth, it will carry x people less than one-third of the ship's capacity. There will be 300 people on the ship to start the journey. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the number of people less than one-third of the ship's capacity. Let's break down the information given: Capacity of the spacecraft: 300 family units * 4 people per family = 1200 people Number of people less than one-third of the ship's capacity: x Number of people on the ship to start the journey: 300 We can set up the equation as follows: Number of people on the ship to start the journey + Number of people less than one-third of the ship's capacity = Capacity of the spacecraft 300 + x = 1200/3 Let's simplify and solve for x: 300 + x = 400 To isolate x, we subtract 300 from both sides of the equation: 300 + x - 300 = 400 - 300 x = 100 The value of x is 100. 100 The answer is: 100
question:Which value of x will result in the minimum value of the expression 2x^2 - 12x + 3?
answer:We can find the minimum value of the expression by finding the x-coordinate of the vertex of the parabola defined by the expression. The x-coordinate of the vertex can be found using the formula x = -frac{b}{2a}, where a, b, and c are the coefficients of the quadratic expression. In this case, the expression is 2x^2 - 12x + 3, so a = 2, b = -12, and c = 3. Plugging these values into the formula, we get x = -frac{-12}{2(2)} = -frac{-12}{4} = frac{12}{4} = 3. Therefore, the value of x that will result in the minimum value of the expression is boxed{3}.The answer is: 3
question:A laboratory has 22 beakers of liquid in a fume hood, and 8 of the beakers have copper ions in them. Adding x drops of a solution will turn the liquid in a beaker blue if there are copper ions present. If the beakers are tested one by one for copper ions and 45 drops are used before all 8 beakers with copper ions are found, 7 beakers without copper ions were tested. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the number of drops needed to turn the liquid in a beaker blue. Let's break down the information given: Total number of beakers: 22 Number of beakers with copper ions: 8 Number of beakers tested without copper ions: 7 Total number of drops used: 45 We can set up the equation as follows: Number of drops used to test beakers without copper ions + Number of drops used to test beakers with copper ions = Total number of drops used 7x + 8x = 45 Let's simplify and solve for x: 15x = 45 To isolate x, we divide both sides of the equation by 15: 15x / 15 = 45 / 15 x = 3 The value of x is 3. 3 The answer is: 3