answer:To solve this problem, we need to determine the value of x, which represents the number of Mr. Slinkums in storage. We know that 20% of the Mr. Slinkums were placed on the shelves. This means that 100% - 20% = 80% of the Mr. Slinkums are in storage. We are told that there are 150 Mr. Slinkums in total. We can set up the equation as follows: 80% of the Mr. Slinkums = Number of Mr. Slinkums in storage 80% of 150 = x To find 80% of 150, we multiply 150 by 80%: 0.8 * 150 = x 120 = x The value of x is 120. The answer is: 120

answer:Let the two integers be x and 1998-x. The product is then x(1998-x) = -x^2+1998x. This is a quadratic equation in x and its graph is a downward-opening parabola. The x-coordinate of the vertex gives us the maximum value of the quadratic. The x-coordinate of the vertex is x=frac{-b}{2a}=frac{-1998}{2(-1)}=999. So the greatest product is -999^2+1998(999)=boxed{998001}. The answer is: 998001

answer:To solve this problem, we need to determine the value of x, which represents the number of sons each of Grandma Olga's daughters has. Let's break down the information given: Number of daughters: 3 Number of sons per daughter: x Number of sons: 3 * x Number of sons' daughters: 3 * 5 = 15 Total number of grandchildren: 33 We can set up the equation as follows: Number of sons + Number of sons' daughters = Total number of grandchildren 3 * x + 15 = 33 Let's simplify and solve for x: 3x + 15 = 33 To isolate x, we subtract 15 from both sides of the equation: 3x + 15 - 15 = 33 - 15 3x = 18 To solve for x, we divide both sides of the equation by 3: x = 18 / 3 x = 6 The value of x is 6. 6 The answer is: 6

answer:To simplify, we will rationalize the denominator of the fraction inside the parentheses. Multiplying the numerator and denominator by the conjugate of the denominator, we get [frac{(1 + i)(1 + i)}{(1 - i)(1 + i)} = frac{1 + 2i + i^2}{1 - i^2} = frac{1 + 2i - 1}{1 - (-1)} = frac{2i}{2} = i.] Now, we have [left( frac{1 + i}{1 - i} right)^{1000} = i^{1000}.] Since i has a period of 4, we can simplify this further. Since 1000 div 4 = 250, we have [i^{1000} = (i^4)^{250} = 1^{250} = boxed{1}.] The answer is: 1