answer：First, I need to determine the total surface area of the cube that needs to be painted. A cube has 6 faces, and each face is a square with an area equal to the side length squared.The side length of the cube is 10 feet, so the area of one face is:Area of one face = side length × side length = 10 ft × 10 ft = 100 sq. ft.Since there are 6 faces on a cube, the total surface area to be painted is:Total surface area = 6 × area of one face = 6 × 100 sq. ft. = 600 sq. ft.Next, I need to calculate how many kilograms of paint are required to cover the total surface area. Given that 1 kg of paint covers 20 sq. ft., the amount of paint needed is:Paint required = total surface area / coverage per kg = 600 sq. ft. / 20 sq. ft. per kg = 30 kgFinally, to find the total cost of the paint, I multiply the amount of paint required by the cost per kilogram:Total cost = paint required × cost per kg = 30 kg × Rs. 40.00/kg = Rs. 1200.00Therefore, the total cost to paint the outside of the cube is Rs. 1200.00.

answer：Okay, so I have this function f(x) = x|x| + bx + c, and I need to check four statements about it. Let me go through each statement one by one.**Statement 1: When c = 0, f(-x) = -f(x) holds.**Alright, let me substitute c = 0 into the function. So f(x) becomes x|x| + bx. Now, let's compute f(-x):f(-x) = (-x)|-x| + b(-x) = (-x)(x) - bx = -x² - bx.Now, let's compute -f(x):-f(x) = -(x|x| + bx) = -x|x| - bx.Since |x| is equal to |-x|, which is just |x|, so x|x| is equal to -x|x| when we plug in -x. Therefore, f(-x) = -x² - bx, which is the same as -f(x). So, yes, when c = 0, f(-x) = -f(x). So statement 1 is correct.**Statement 2: When b = 0 and c > 0, the equation f(x) = 0 has only one real root.**Okay, let's set b = 0. Then f(x) = x|x| + c. Let's write this piecewise:For x ≥ 0: f(x) = x² + c.For x < 0: f(x) = -x² + c.So, let's solve f(x) = 0 for both cases.For x ≥ 0: x² + c = 0. Since c > 0, x² = -c, which has no real solution because x² is always non-negative.For x < 0: -x² + c = 0 ⇒ x² = c ⇒ x = ±√c. But since x < 0, only x = -√c is a solution.Therefore, the equation f(x) = 0 has only one real root at x = -√c. So statement 2 is correct.**Statement 3: The graph of the function y = f(x) is symmetric about the point (0, c).**Hmm, symmetry about a point usually means that if you rotate the graph 180 degrees around that point, it looks the same. For a function to be symmetric about (0, c), it should satisfy f(-x) = 2c - f(x). Let's check this.Compute f(-x):f(-x) = (-x)|-x| + b(-x) + c = (-x)(x) - bx + c = -x² - bx + c.Now, compute 2c - f(x):2c - f(x) = 2c - (x|x| + bx + c) = 2c - x|x| - bx - c = c - x|x| - bx.Compare this with f(-x):f(-x) = -x² - bx + c.Wait, for x ≥ 0, x|x| = x², so f(-x) = -x² - bx + c, and 2c - f(x) = c - x² - bx. These are the same.For x < 0, x|x| = -x², so f(-x) = -x² - bx + c, and 2c - f(x) = c - (-x²) - bx = c + x² - bx. Hmm, wait, that doesn't seem to match.Wait, maybe I made a mistake. Let's re-examine.For x < 0, x|x| = -x², so f(x) = -x² + bx + c.Then, 2c - f(x) = 2c - (-x² + bx + c) = 2c + x² - bx - c = c + x² - bx.But f(-x) when x < 0: Let me substitute x with -x in f(x). Wait, no, f(-x) is computed as above, regardless of whether x is positive or negative.Wait, maybe I need to think differently. Let me take a specific example. Let’s pick x = 1 and x = -1.Compute f(1) = 1*1 + b*1 + c = 1 + b + c.Compute f(-1) = (-1)*1 + b*(-1) + c = -1 - b + c.Now, check if f(-1) = 2c - f(1):2c - f(1) = 2c - (1 + b + c) = c - 1 - b.Compare with f(-1) = -1 - b + c. Yes, they are equal. So for x = 1, f(-1) = 2c - f(1).Similarly, for x = 2, f(2) = 4 + 2b + c.f(-2) = (-2)*2 + b*(-2) + c = -4 - 2b + c.2c - f(2) = 2c - (4 + 2b + c) = c - 4 - 2b, which is equal to f(-2).So it seems that f(-x) = 2c - f(x) holds for all x. Therefore, the graph is symmetric about the point (0, c). So statement 3 is correct.**Statement 4: When x > 0, the function f(x) = x|x| + bx + c has a minimum value of c - b²/2.**Okay, for x > 0, f(x) = x² + bx + c. Let's find its minimum.This is a quadratic function in x, opening upwards (since the coefficient of x² is positive). The vertex occurs at x = -b/(2*1) = -b/2.But wait, x > 0, so if -b/2 > 0, that is, if b < 0, then the vertex is within the domain x > 0. If b ≥ 0, then the minimum occurs at x = 0.Wait, but the statement says "when x > 0", so maybe we are considering x > 0, so the domain is x > 0, and the function is f(x) = x² + bx + c.The minimum occurs at x = -b/2 if -b/2 > 0, i.e., b < 0. If b ≥ 0, the function is increasing on x > 0, so the minimum is at x approaching 0 from the right, which would be f(0) = c.But the statement says the minimum value is c - b²/2. Let's compute the value at x = -b/2:f(-b/2) = (-b/2)² + b*(-b/2) + c = b²/4 - b²/2 + c = -b²/4 + c.Wait, that's c - b²/4, not c - b²/2.Hmm, so the minimum value is c - b²/4 when b < 0, and c when b ≥ 0.But the statement says c - b²/2. That doesn't match. So statement 4 is incorrect.Wait, maybe I made a mistake. Let me double-check.f(x) = x² + bx + c.The vertex is at x = -b/2, and f(-b/2) = (-b/2)² + b*(-b/2) + c = b²/4 - b²/2 + c = -b²/4 + c.Yes, that's correct. So the minimum value is c - b²/4, not c - b²/2. Therefore, statement 4 is incorrect.Wait, but maybe the question is considering the minimum over all x, not just x > 0? No, the statement says "when x > 0", so it's only considering x > 0.Alternatively, maybe I misread the function. Let me check:f(x) = x|x| + bx + c. For x > 0, x|x| = x², so f(x) = x² + bx + c. Correct.So, the minimum value is c - b²/4 when b < 0, and c when b ≥ 0. Therefore, the statement 4 is incorrect because it claims the minimum is c - b²/2, which is not correct.Wait, unless there's a different approach. Maybe completing the square:f(x) = x² + bx + c = (x + b/2)² - b²/4 + c.So the minimum is c - b²/4, which is what I got earlier. So statement 4 is incorrect.Therefore, statements 1, 2, and 3 are correct, and statement 4 is incorrect.

answer：First, I need to determine the number of employees based on the difference in the bonus distribution.Let ( n ) represent the number of employees.Initially, each employee was supposed to receive 50, but the final distribution was 45 per employee, leaving 95 undistributed.The difference in the bonus per employee is:[50 - 45 = 5 text{ dollars}]Since the total undistributed amount is 95, this represents the total reduction in the bonus distribution:[5n = 95]Solving for ( n ):[n = frac{95}{5} = 19]Now, calculate the initial fund:[text{Initial Fund} = 19 times 50 = 950 text{ dollars}]Finally, verify the final distribution:[19 times 45 = 855 text{ dollars}][950 - 855 = 95 text{ dollars}]The calculations confirm that the initial fund was 950.

answer：First, I need to understand what it means for every question to be unanswered. If a question is unanswered, it implies that there's an additional choice besides the answer options, which is essentially not selecting any answer.Let's denote the number of answer choices for each question as ( n ). Since each question can either be answered or left unanswered, the total number of choices per question becomes ( n + 1 ).Given that there are 4 questions, the total number of ways to complete the test is the product of the number of choices for each question. Therefore, the equation to solve is:[(n + 1)^4 = 625]I know that ( 625 ) is a perfect fourth power, specifically ( 5^4 ). This allows me to simplify the equation:[(n + 1)^4 = 5^4]Taking the fourth root of both sides gives:[n + 1 = 5]Finally, solving for ( n ) by subtracting 1 from both sides:[n = 5 - 1 = 4]Therefore, there are 4 answer choices for each question.

answer：Okay, so I have this problem here: Brenda's mother made cookies for guests. Each guest had a certain number of cookies. She prepared a total of 10 cookies for 5 guests. How many cookies did each guest have? Alright, let's try to figure this out step by step.First, I need to understand what the problem is asking. It says that Brenda's mother made cookies for guests, and there are 5 guests in total. She made 10 cookies altogether. The question is asking how many cookies each guest had. So, essentially, I need to find out the number of cookies per guest.Hmm, okay. So, if there are 10 cookies and 5 guests, I think this is a division problem. Division is about splitting things into equal parts. So, if I have 10 cookies and I want to divide them equally among 5 guests, I need to divide 10 by 5.Let me write that down: 10 ÷ 5. What's 10 divided by 5? Well, 5 times 2 is 10, so 10 divided by 5 is 2. That means each guest would get 2 cookies.Wait, let me make sure I'm not missing anything. The problem says each guest had a certain number of cookies, and the total was 10 for 5 guests. So, yes, dividing the total number of cookies by the number of guests should give me the number of cookies per guest.Is there another way to think about this? Maybe using multiplication to check. If each guest had 2 cookies, then 5 guests would have 5 times 2, which is 10 cookies. That matches the total number of cookies prepared. So, that checks out.I don't think there's anything else to consider here. It seems straightforward. The key is to recognize that we're distributing the cookies equally among the guests, which is a division problem.Just to visualize it, imagine laying out 10 cookies and dividing them into 5 equal groups. Each group would have 2 cookies. That's another way to see that each guest gets 2 cookies.So, after thinking it through, I'm pretty confident that each guest had 2 cookies.

answer：First, I need to determine the perimeter of the triangle by adding the lengths of its three sides: 5 cm, 7 cm, and 10 cm.Next, since the square's perimeter is twice that of the triangle, I will multiply the triangle's perimeter by 2 to find the square's perimeter.After obtaining the square's perimeter, I can find the length of one side of the square by dividing the perimeter by 4, as all sides of a square are equal in length.Finally, to calculate the area of the square, I will square the length of one of its sides.