answer:Using the compound interest formula, you can expect to have approximately 20,245 in savings after 3 years. This calculation assumes that you make regular monthly contributions and that the mutual fund maintains an average annual return of 7%.

answer:The given expression is a finite geometric series with first term a = -frac{7}{57}, common ratio r = frac{1}{2}, and number of terms n = 6. The sum of a finite geometric series is given by the formula: S_n = frac{a(1 - r^n)}{1 - r} Substituting the values, we get: S_6 = frac{-frac{7}{57}left(1 - left(frac{1}{2}right)^6right)}{1 - frac{1}{2}} S_6 = frac{-frac{7}{57}left(1 - frac{1}{64}right)}{frac{1}{2}} S_6 = frac{-frac{7}{57}left(frac{63}{64}right)}{2} S_6 = -frac{152915}{622592} Therefore, the sum of the given expression is -frac{152915}{622592}. The answer is -frac{152915}{622592}

answer:Let x be the original number of seats in each row. Original number of rows = 240/x After rearranging: Number of seats per row = x - 2 Number of rows = (240/x) + 3 Since the capacity remains the same: 240 = x * (240/x) = (x - 2) * ((240/x) + 3) Simplifying the equation: 240 = (x - 2) * (240 + 3x)/x 240x = (240x + 3x^2 - 480 - 6x) 3x^2 - 6x - 480 = 0 x^2 - 2x - 160 = 0 (x - 10)(x + 16) = 0 x = 10 or x = -16 Since the number of seats cannot be negative, the original number of seats in each row is x = 10.

answer:To find the equation of the plane, we can use the following steps: 1. Find two vectors that lie in the plane. We can do this by subtracting the coordinates of two of the points: overrightarrow{v_1} = langle -2-5, 0-3, -2-(-1) rangle = langle -7, -3, -1 rangle overrightarrow{v_2} = langle 0-5, 1-3, -5-(-1) rangle = langle -5, -2, -4 rangle 2. Find the cross product of the two vectors: overrightarrow{v_1} times overrightarrow{v_2} = begin{vmatrix} mathbf{i} & mathbf{j} & mathbf{k} -7 & -3 & -1 -5 & -2 & -4 end{vmatrix} = mathbf{i}((-3)(-4) - (-2)(-1)) - mathbf{j}((-7)(-4) - (-5)(-1)) + mathbf{k}((-7)(-2) - (-3)(-5)) = mathbf{i}(12 - 2) - mathbf{j}(28 - 5) + mathbf{k}(14 - 15) = 10mathbf{i} - 23mathbf{j} - mathbf{k} 3. The cross product is a vector that is perpendicular to both overrightarrow{v_1} and overrightarrow{v_2}, and therefore perpendicular to the plane. So, the equation of the plane can be written as: 10x - 23y - z + d = 0 4. To find the value of d, we can substitute the coordinates of one of the points into the equation: 10(5) - 23(3) - (-1) + d = 0 50 - 69 + 1 + d = 0 -18 + d = 0 d = 18 Therefore, the equation of the plane is: 10x - 23y - z + 18 = 0 The answer is 10x - 23y - z + 18 = 0