answer:To find the remainder when 3^118 is divided by 5, we can examine the pattern of remainders of powers of 3 when divided by 5. Calculating a few powers of 3 modulo 5, we see that 3^1 ≡ 3 (mod 5), 3^2 ≡ 9 ≡ 4 (mod 5), 3^3 ≡ 12 ≡ 2 (mod 5), and 3^4 ≡ 6 ≡ 1 (mod 5). We've reached 1, which means the pattern will repeat every 4 powers. Since 3^4 ≡ 1 (mod 5), we can use this to simplify 3^118. Dividing 118 by 4, we get a quotient of 29 and a remainder of 2. This allows us to express 3^118 as (3^4)^29 * 3^2, which is equivalent to 1^29 * 3^2 modulo 5. Since 1 raised to any power is still 1, and we already calculated 3^2 ≡ 4 (mod 5), the expression simplifies to 4 modulo 5. Therefore, the remainder when 3^118 is divided by 5 is 4.

answer:To find the remainder when 2^145 is divided by 31, we can examine the pattern of remainders of powers of 2 when divided by 31. Calculating a few powers of 2 modulo 31, we notice that we are looking for a power of 2 that results in 1 modulo 31. After calculating several powers, we find that 2^5 = 32 ≡ 1 (mod 31). Since we've reached 1, the pattern will repeat every 5 powers. Now we can express 2^145 as (2^5)^29, which leaves us with no remainder in terms of powers of 2^5. However, 2^145 can be better expressed as (2^5)^29 * 2^0, since 145 equals 5 * 29. This is simply 1^29 * 1 ≡ 1 modulo 31. Therefore, the remainder when 2^145 is divided by 31 is 1.

answer:To solve this problem, we need to determine the value of x, which represents the number of other players Mona joins in a group. Let's break down the information given: Number of groups Mona joined: 9 Number of unique players Mona grouped with: 33 Number of players Mona grouped with multiple times: 2 + 1 = 3 (from the information given) We can set up the equation as follows: Number of unique players Mona grouped with + Number of players Mona grouped with multiple times = Total number of players Mona grouped with 33 + 3 = 9x Let's simplify and solve for x: 36 = 9x To isolate x, we divide both sides of the equation by 9: 36 / 9 = 9x / 9 4 = x The value of x is 4. 4 The answer is: 4

answer:To write the `make_compose` function, we need to understand the definition of function composition. Function composition is the process of combining two or more functions to create a new function. In the given example, we have two functions `g` and `f`. The `make_compose` function takes these two functions and returns a new function that composes them. Here is a Python implementation of the `make_compose` function: ```python def make_compose(g, f): Returns a function that composes `g` and `f`. def composed(x): return g(f(x)) return composed ``` Function composition is achieved by nesting function calls. `g` is called with the result of calling `f` with `x`. The `make_compose` function returns this nested function, which is the composition of `g` and `f`.