The question consists of two parts: Part 1: Evaluate the expression $75.0785 - 34.624 + 9.83$ and round the result to two decimal places. Part 2: Given two sets $X = \{x: x < 7\}$ and $Y = \{y: y \text{ is a factor of } 24\}$ that are subsets of $\mu = \{1, 2, 3, ..., 10\}$, find the intersection of the two sets, $X \cap Y$.

1. Problem Description

The question consists of two parts:

Part 1: Evaluate the expression $75.0785 - 34.624 + 9.83$ and round the result to two decimal places.

Part 2: Given two sets $X = \{x: x < 7\}$ and $Y = \{y: y \text{ is a factor of } 24\}$ that are subsets of $\mu = \{1, 2, 3, ..., 10\}$, find the intersection of the two sets, $X \cap Y$.

2. Solution Steps

Part 1:

First, perform the subtraction: $75.0785 - 34.624 = 40.4545$.

Next, perform the addition: $40.4545 + 9.83 = 50.2845$.

Finally, round the result to two decimal places: $50.2845 \approx 50.28$.

Part 2:

First, define set X based on the given condition $x < 7$ and the universal set $\mu$. $X = \{1, 2, 3, 4, 5, 6\}$.

Next, define set Y based on the condition that $y$ is a factor of 24 and the universal set $\mu$. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and

2

4. Since $Y$ is a subset of $\mu = \{1, 2, 3, ..., 10\}$, $Y = \{1, 2, 3, 4, 6, 8\}$.

The intersection of sets X and Y, $X \cap Y$, consists of elements that are in both X and Y.

$X \cap Y = \{1, 2, 3, 4, 6\}$.

3. Final Answer

Part 1: C. 50.28

Part 2: B. {1, 2, 3, 4, 6}