We are given a series of math problems to solve: 1. A word problem involving learners who like football and hockey, requiring a Venn diagram and calculations.

1. Problem Description

We are given a series of math problems to solve:

1. A word problem involving learners who like football and hockey, requiring a Venn diagram and calculations.

2. Writing numbers in words.

3. A word problem involving the number of oranges in three baskets.

4. Stating real-life applications of skip counting.

5. A word problem calculating the total number of students in a school.

6. Rounding a number to the nearest thousandth and hundred-thousandth.

7. Correcting a number to 3 significant figures and 4 decimal places.

8. Writing a number in scientific notation.

9. Finding the union of two sets.

1

0. Finding the intersection of three sets.

2. Solution Steps

1. i. Venn Diagram: This requires a diagram with two overlapping circles, one for Football (F) and one for Hockey (H).

ii. Let $x$ be the number of learners who like both subjects.

Total learners = Learners who like only Football + Learners who like only Hockey + Learners who like both.

$72 = (45 - x) + (38 - x) + x$

$72 = 45 + 38 - x$

$72 = 83 - x$

$x = 83 - 72$

$x = 11$

So, 11 learners like both subjects.

iii. Learners who like only Football = $45 - x = 45 - 11 = 34$

iv. Learners who like only Hockey = $38 - x = 38 - 11 = 27$

2. 63: Sixty-three

278: Two hundred and seventy-eight

975: Nine hundred and seventy-five

348: Three hundred and forty-eight

692: Six hundred and ninety-two

3. Total oranges = Oranges in the first basket + Oranges in the second basket + Oranges in the third basket

Total oranges = $36 + 251 + 2 = 289$

4. Real-life applications of skip counting:

- Counting money in multiples (e.g., counting quarters by 25s).

- Counting items arranged in groups (e.g., counting chairs in rows of 5).

5. Total students = Number of classes * Students per class

Total students = $8 * 30 = 240$

6. Rounding 14.362745:

i. Thousandth: 14.363 (since the digit after 2 is 7 >= 5, round up)

ii. Hundred Thousandth: 14.36275 (since the digit after 4 is 5, round up)

7. Correcting 14.362745:

i. 3 s.f: 14.4 (since the digit after 3 is 6 >= 5, round up)

ii. 4 d.p: 14.3627 (keep the first four digits after decimal point)

8. Writing 294378.29 in scientific notation:

$2.9437829 \times 10^5$

9. Finding the union of A = {22, 33, 44, 55} and B = {66, 44, 22, 2}:

$A \cup B = \{2, 22, 33, 44, 55, 66\}$

1

0. Finding the intersection of {3, 5, 6, 7}, {3, 5}, {2, 1}:

The intersection is the set of elements that are common to all three sets. There are no common elements in all three sets. Therefore, the intersection is the empty set.

$\{3, 5, 6, 7\} \cap \{3, 5\} \cap \{2, 1\} = \{\}$

3. Final Answer

1. i. Venn Diagram (explained in steps)

ii. 11

iii. 34

iv. 27

2. 63: Sixty-three

278: Two hundred and seventy-eight

975: Nine hundred and seventy-five

348: Three hundred and forty-eight

692: Six hundred and ninety-two

3. 289

4. - Counting money in multiples (e.g., counting quarters by 25s).

- Counting items arranged in groups (e.g., counting chairs in rows of 5).

5. 240

6. i. 14.363

ii. 14.36275

7. i. 14.4

ii. 14.3627

8. $2.9437829 \times 10^5$

9. {2, 22, 33, 44, 55, 66}

1

0. {}