answer:To update a dictionary with the contents of another dictionary, we can use the `update` method. This method takes another dictionary as an argument and updates the current dictionary with its contents. To shallow copy the existing dictionary and remove all the keys that are not in the provided dictionary, we can use the `copy` method to create a shallow copy of the existing dictionary, and then use the `keys` method to get the list of keys in the provided dictionary. We can then use a list comprehension to filter out the keys that are not in the provided dictionary, and then use the `del` keyword to remove them from the shallow copy. Here's how we can implement this: ```python def update_and_remove(dict1, dict2): dict1_copy = dict1.copy() for key in [key for key in dict1_copy.keys() if key not in dict2]: del dict1_copy[key] dict1_copy.update(dict2) return dict1_copy ```

answer:1. Identify when n and n+3 are coprime: - If n and n+3 are coprime (i.e., gcd(n, n+3) = 1), there will be no lattice points (points with integer coordinates) on the line segment OA_n other than the endpoints. 2. Identify when n and n+3 are not coprime: - If n and n+3 are not coprime, they share a common factor of 3, i.e., n = 3k for some integer k. Thus, gcd(3k, 3k+3) = 3. 3. Find intermediate lattice points for n = 3k: - When n = 3k, the line segment OA_{3k} joins (0, 0) and (3k, 3k+3). - The line segment OA_{3k} has a slope of frac{3k+3}{3k} = 1 + frac{1}{k}. Note that this line segment will pass through lattice points for integer values of k. 4. Identify the intermediate lattice points on OA_{3k}: - For n = 3k, the intermediate lattice points between (0, 0) and (3k, 3k+3) will be at (k, k+1) and (2k, 2k+2). 5. Conclusion for f(n): - If n and n + 3 are coprime, f(n) = 0. - If n = 3k, then f(n) = 2, because there are exactly two intermediate lattice points on OA_{3k}. 6. Calculate f(1) + f(2) + cdots + f(1990): - The relevant n values that are multiples of 3 in the range between 1 and 1990 are 3, 6, 9, ldots, 3 times 663. - The number of such terms is 3 times 663 = 1990. Therefore, there are 663 terms. - Sum of f(n) values for these terms: [ f(3) + f(6) + f(9) + cdots + f(3 times 663) = 2 + 2 + 2 + cdots + 2 = 2 times 663 = 1326 ] # Conclusion: [ boxed{1326} ]

answer:Encoding a string to hexadecimal form is a standard way of representing data as a sequence of hexadecimal values. Hexadecimal encoding can be useful in different scenarios, such as data transmission, database storage, or generating cryptographic hashes. To encode a string to hexadecimal form in Python, we can use the built-in function `bytes.hex()`. This function takes a byte string as input and returns its hexadecimal representation as a string. To decode a hexadecimal string back to its original form, we can use the built-in function `bytes.fromhex()`. This function takes a hexadecimal string as input and returns a byte string that can be decoded back to its original form. Here is the implementation of the program: ```python def encode_hex(text: str) -> str: encoded_hex = text.encode().hex() return encoded_hex def decode_hex(hex_string: str) -> str: decoded_text = bytes.fromhex(hex_string).decode() return decoded_text ```

answer:You can achieve this in Python using the filter() function along with a lambda expression. The filter() function takes two arguments - the lambda expression that specifies the condition for filtering and the array to be filtered. Here's an example implementation: ```python def remove_odd(arr): return list(filter(lambda num: num % 2 == 0, arr)) ``` In this code, the lambda expression `lambda num: num % 2 == 0` checks if the number `num` is divisible by 2 (i.e., an even number). The filter() function applies this lambda expression to each element in the input array `arr` and only keeps the elements that satisfy the condition. Finally, the filtered elements are converted back to a list and returned. You can use the function like this: ```python my_array = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] result = remove_odd(my_array) print(result) ``` Output: ``` [2, 4, 6, 8, 10] ``` The resulting `result` array contains only the even numbers from the original input array.