answer:Each tank has 4 pregnant fish, so there are a total of 3 * 4 = 12 pregnant fish. Each pregnant fish gives birth to 20 young, so there will be a total of 12 * 20 = 240 young fish. Therefore, Mark has 240 young fish at the end. 240 The answer is: 240

answer:d{v} and bold{a} is given by |bold{v}-bold{a}|. Expanding, we have bold{v}-bold{a} = begin{pmatrix} 2 -3 -3 end{pmatrix} + t begin{pmatrix} 7 5 -1 end{pmatrix} - begin{pmatrix} 4 4 5 end{pmatrix} = begin{pmatrix} 2 -3 -3 end{pmatrix} + begin{pmatrix} 7t 5t -t end{pmatrix} - begin{pmatrix} 4 4 5 end{pmatrix} = begin{pmatrix} 2+7t-4 -3+5t-4 -3-t-5 end{pmatrix} = begin{pmatrix} 7t-2 5t-7 -t-8 end{pmatrix} The distance is |bold{v}-bold{a}| = sqrt{(7t-2)^2 + (5t-7)^2 + (-t-8)^2}. We want to find the value of t that minimizes this distance. To find the minimum, we take the derivative of this expression with respect to t and set it equal to zero. frac{d}{dt} left( sqrt{(7t-2)^2 + (5t-7)^2 + (-t-8)^2} right) = 0 By the chain rule, this is equal to frac{1}{2} left( (7t-2)^2 + (5t-7)^2 + (-t-8)^2 right)^{-1/2} left( 2(7t-2)(7) + 2(5t-7)(5) + 2(-t-8)(-1) right) = 0 Simplifying, (7t-2)(7) + (5t-7)(5) + (-t-8)(-1) = 0 49t-14 + 25t-35 + t+8 = 0 75t-41 = 0 t = frac{41}{75} Therefore, the value of t that makes bold{v} closest to bold{a} is boxed{frac{41}{75}}.The answer is: frac{41}{75}

answer:To solve this problem, we need to determine the value of x, which represents the number of children that the set of marbles can be divided among with no marbles left over. We know that the set of marbles can be divided equally among 2, 3, 4, 6, and x children. The least number of marbles is 60. We can set up the equation as follows: Number of marbles = Least common multiple of 2, 3, 4, 6, and x Number of marbles = LCM(2, 3, 4, 6, x) We are given that the least number of marbles is 60, so we can set up the equation as follows: 60 = LCM(2, 3, 4, 6, x) To find the LCM of 2, 3, 4, 6, and x, we can break down each number into its prime factors: 2 = 2^1 3 = 3^1 4 = 2^2 6 = 2^1 * 3^1 x = x^1 Now, we can find the LCM by taking the highest power of each prime factor: LCM(2, 3, 4, 6, x) = 2^2 * 3^1 * x^1 60 = 2^2 * 3^1 * x^1 60 = 4 * 3 * x 60 = 12x To solve for x, we divide both sides of the equation by 12: 60 / 12 = 12x / 12 5 = x The value of x is 5. The answer is: 5

answer:We can write the given equation as 3(-2) = nabla + 2. Simplifying, we have -6 = nabla + 2. Subtracting 2 from both sides, we get nabla = boxed{-8}. The answer is: -8