Sure, let's solve each part of the question step-by-step.
### Part 1: Finding [tex]\(x\)[/tex] and [tex]\(y\)[/tex]
Given the ordered pair [tex]\((x, x + y) = (2, 7)\)[/tex],
1. We know that [tex]\(x = 2\)[/tex].
2. Substitute [tex]\(x = 2\)[/tex] into the equation [tex]\(x + y = 7\)[/tex]:
[tex]\[
2 + y = 7
\][/tex]
3. Solving for [tex]\(y\)[/tex]:
[tex]\[
y = 7 - 2
\][/tex]
[tex]\[
y = 5
\][/tex]
Thus, [tex]\(x = 2\)[/tex] and [tex]\(y = 5\)[/tex].
### Part 2: Finding the median of the given marks
Given the marks: 27, 28, 30, 18, 29, 16, 25, 23, 2.
1. First, arrange the marks in ascending order:
[tex]\[
2, 16, 18, 23, 25, 27, 28, 29, 30
\][/tex]
2. The number of marks, [tex]\(n\)[/tex], is 9, which is an odd number. Therefore, the median is the middle number in the sorted list.
3. The position of the median is given by:
[tex]\[
\text{Median position} = \frac{n + 1}{2} = \frac{9 + 1}{2} = 5
\][/tex]
4. The 5th number in the ordered list is:
[tex]\[
25
\][/tex]
Thus, the median is [tex]\(25\)[/tex].
### Part 3: Finding the mean of given numbers
Given the numbers: 48, 38, 42, 38.
1. First, find the sum of the numbers:
[tex]\[
48 + 38 + 42 + 38 = 166
\][/tex]
2. Count the number of values, which is 4.
3. Calculate the mean by dividing the sum by the number of values:
[tex]\[
\text{Mean} = \frac{166}{4} = 41.5
\][/tex]
Thus, the mean of the numbers is [tex]\(41.5\)[/tex].
### Summary:
1. [tex]\(x = 2\)[/tex], [tex]\(y = 5\)[/tex].
2. The median of the marks is [tex]\(25\)[/tex].
3. The mean of the numbers is [tex]\(41.5\)[/tex].
These are the detailed solutions to each part of the question.
