A. A triangle has vertices A(2,3), B(x,y) and C(5,1) is translated 3 units right and 2 units down. find the coordinates of the vertices. ii. A coin is tossed twice. list all the possible outcomes if a coin is tossed twice. find the probability of obtaining. a. exactly 2 heads. b. no head

The triangle is translated 3 units right and 2 units down. This means for any point $(x, y)$, the new coordinates $(x', y')$ will be $(x+3, y-2)$.

• For $A(0,0)$: $A'(0+3, 0-2) = A'(3, -2)$
• For $B(2,3)$: $B'(2+3, 3-2) = B'(5, 1)$
• For $C(3,1)$: $C'(3+3, 1-2) = C'(6, -1)$ The new coordinates of the vertices are $\boxed{\textbf{A'(3, -2), B'(5, 1), C'(6, -1)}}$.

A.ii) Coin Toss Probability

The possible outcomes are: HH, HT, TH, TT. There are 4 total possible outcomes.

Only one outcome has exactly 2 heads (HH).

The probability of obtaining exactly 2 heads is \boxed{\textbf{\frac{1}{4}}}.

Only one outcome has no head (TT).

The probability of obtaining no head is \boxed{\textbf{\frac{1}{4}}}.

A.iii) Addition

The numbers are 4,367, 635,486 (assuming 6,35,486 is a typo for 635,486), and 8,039.

The sum of the numbers is $\boxed{\textbf{647,892}}$.

B) Data Analysis
The table shows the marks scored by 7 learners:

B.a) Draw a line graph for the data.

Draw a horizontal axis (x-axis) for the Students and a vertical axis (y-axis) for the Mark scored. Label the x-axis with the names of the students and the y-axis with a suitable scale for marks (e.g., from 0 to 100).

For each student, plot a point corresponding to their mark. For example, plot a point at (Dwo, 60), (Aloa, 65), (Sisimuden, 70), (Loaso, 66), (Abid, 75), (Animfoo, 80), and (Wohohantan, 85).

Draw straight lines connecting the plotted points in the order the students appear in the table.

B.b) Which of them scored the highest mark?

The marks are 60, 65, 70, 66, 75, 80, 85.

The highest mark is 85, which was scored by Wohohantan.
The student who scored the highest mark is $\boxed{\textbf{Wohohantan}}$.

B.c) Which of them scored the least mark?

The marks are 60, 65, 70, 66, 75, 80, 85.

The least mark is 60, which was scored by Dwo.
The student who scored the least mark is $\boxed{\textbf{Dwo}}$.

B.d) Find the total mark scored by Atopa, Sisimuden, and Wohohantan.

Assuming "Atopa" is a typo for "Aloa" from the table:

• Aloa's mark: 65
• Sisimuden's mark: 70
• Wohohantan's mark: 85

The total mark scored by Aloa, Sisimuden, and Wohohantan is $\boxed{\textbf{220}}$.

B.e) What is the difference between the total mark scored by Aloa, Animfoo, Wohohantan, and Dwo, Atopa, Toaso?

• Aloa: 65
• Animfoo: 80
• Wohohantan: 85

Assuming "Atopa" is a typo for "Aloa" and "Toaso" is a typo for "Loaso" from the table:

• Dwo: 60
• Aloa: 65
• Loaso: 66

The difference between the total marks of the two groups is $\boxed{\textbf{39}}$.