answer:The probability of winning the car by switching doors is 2/3. Here's the reasoning: 1. Initially, the probability of choosing the correct door (with the car) is 1/3, and the probability of choosing a wrong door (with a goat) is 2/3. 2. When the host reveals a goat behind one of the remaining doors, it doesn't change the initial probabilities. However, it does give us new information about the remaining unopened door. 3. If the contestant initially chose a wrong door (which had a 2/3 probability), switching to the other unopened door would now result in choosing the car. 4. Therefore, the probability of winning the car by switching doors is equal to the initial probability of choosing a wrong door, which is 2/3.

answer:To find the derivative of g(x) = 5x^3 - 7x^2 + 2x - 8, we will use the power rule for differentiation. The power rule states that if f(x) = x^n, where n is a constant, then the derivative f'(x) = nx^(n-1). Step 1: Identify each term in the function and its corresponding exponent. The terms are 5x^3, -7x^2, 2x, and -8, with exponents 3, 2, 1, and 0, respectively. Step 2: Apply the power rule to each term. For 5x^3, the exponent is 3, so using the power rule, we get (3)(5)x^(3-1) = 15x^2. For -7x^2, the exponent is 2, so using the power rule, we get (2)(-7)x^(2-1) = -14x. For 2x, the exponent is 1, so using the power rule, we get (1)(2)x^(1-1) = 2. For -8, the exponent is 0, and since the derivative of a constant is always 0, this term has no effect on the derivative. Step 3: Combine the results from Step 2. g'(x) = 15x^2 - 14x + 2 So, the derivative of g(x) = 5x^3 - 7x^2 + 2x - 8 is g'(x) = 15x^2 - 14x + 2.

answer:The ages of the daughters are 2, 2, and 9 years old. Here's the reasoning behind this: 1. We know that the product of their ages is 36. So, we need to find all the sets of whole numbers whose product equals 36: (1,1,36), (1,2,18), (1,3,12), (1,4,9), (1,6,6), (2,2,9), and (2,3,6). 2. We also know that the sum of their ages is equal to the house number across the street. Since we don't have a specific number for this, we can't use it directly to eliminate any options yet. 3. However, we do know that there's an oldest daughter, which means there must be a unique oldest age among the three daughters. This eliminates the sets (1,1,36) and (1,6,6) because they both have two daughters with the same oldest age. 4. Now, we are left with five possible sets: (1,2,18), (1,3,12), (1,4,9), (2,2,9), and (2,3,6). If we look at the sums of these sets, we get 21, 16, 14, 13, and 11 respectively. The fact that there are different sums indicates that there is only one correct set, as the house number across the street is fixed. 5. Considering that the man could identify the ages of his daughters by knowing the house number across the street, there must be only one set with a unique sum. In our case, the only non-unique sum is 13 (which corresponds to the set (2,2,9)), as all other sums appear just once in our list. 6. Therefore, the ages of the daughters must be 2, 2, and 9 years old.

answer:Here's a simple Golang program that calculates the factorial of an input integer and handles invalid inputs: ```go package main import ( "fmt" "strconv" ) func main() { var input string fmt.Print("Enter an integer: ") fmt.Scan(&input) n, err := strconv.Atoi(input) if err != nil { fmt.Println("Invalid input. Please enter an integer.") return } if n < 0 { fmt.Println("Error: Factorial is not defined for negative integers.") } else { factorial := calculateFactorial(n) fmt.Printf("The factorial of %d is %dn", n, factorial) } } func calculateFactorial(n int) int { if n == 0 || n == 1 { return 1 } return n * calculateFactorial(n-1) } ``` To run this program, save it in a file named `factorial.go` and then execute the following command in your terminal: ```sh go run factorial.go ``` This will prompt you to enter an integer, and it will return the factorial value if the input is valid. If the input is invalid (e.g., non-integer or negative), it will display an appropriate error message.