Solve the following mathematics problems: 1. Convert 21 (Base 10) to Base 2. 2. Calculate a 15% discount on…

Question

Solve the following mathematics problems: 1. Convert 21 (Base 10) to Base 2. 2. Calculate a 15% discount on N5,000. 3. List 3 cylindrical and 3 rectangular prism objects. 4. Simplify 5x + 10 − 2x + 4.

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MATHEMATICS

Number Bases: Convert 21 (Base 10) to Base 2. To convert 21 from base 10 to base 2, we perform successive divisions by 2 and record the remainders.
$21 \div 2 = 10 \text{ remainder } 1$ $10 \div 2 = 5 \text{ remainder } 0$ $5 \div 2 = 2 \text{ remainder } 1$ $2 \div 2 = 1 \text{ remainder } 0$ $1 \div 2 = 0 \text{ remainder } 1$
Reading the remainders from bottom to top, we get: The number 21 in Base 10 is $\boxed{\text{10101}_2}$ in Base 2.
Percentages: Calculate the discount. Original cost = N5,000 Discount percentage = 15% Discount amount = $15\%$ of N5,000
$\text{Discount amount} = \frac{15}{100} \times 5000$ $\text{Discount amount} = 15 \times 50$ $\text{Discount amount} = \text{N}750$
The discount is $\boxed{\text{N750}}$ .
Geometry: List 3 cylindrical and 3 rectangular prism objects.
- Cylindrical objects:
  - Can of soda
  - Battery
  - Toilet paper roll
- Rectangular prism objects:
  - Brick
  - Book
  - Cereal box
Algebra: Simplify the expression: $5x + 10 - 2x + 4$ .

Group like terms.
$$ (5x - 2x) + (10 + 4) $$
Combine like terms.
$$ 3x + 14 $$ The simplified expression is $\boxed{\text{3x + 14}}$.
5. Fractions: Fraction of cake left. Fraction eaten on Friday = $\frac{2}{5}$ Fraction eaten on Saturday = $\frac{1}{4}$

Find the total fraction of cake eaten.

$$
\text{Total eaten} = \frac{2}{5} + \frac{1}{4}
$$
Find a common denominator, which is 20.
$$
\text{Total eaten} = \frac{2 \times 4}{5 \times 4} + \frac{1 \times 5}{4 \times 5}
$$
$$
\text{Total eaten} = \frac{8}{20} + \frac{5}{20}
$$
$$
\text{Total eaten} = \frac{8+5}{20} = \frac{13}{20}
$$

Find the fraction of cake left.

$$
\text{Fraction left} = 1 - \text{Total eaten}
$$
$$
\text{Fraction left} = \frac{20}{20} - \frac{13}{20}
$$
$$
\text{Fraction left} = \frac{7}{20}
$$
The fraction of the whole cake left is $\boxed{\text{}\frac{7}{20}\text{}}$.

6. Decimals: Multiply $12.5 \times 0.4$ without using a calculator.

Multiply the numbers as if they were whole numbers.
$$ 125 \times 4 = 500 $$

Count the total number of decimal places in the original numbers.

12.5 has 1 decimal place.  
0.4 has 1 decimal place.  
Total decimal places = $1 + 1 = 2$.

Place the decimal point in the product.

Starting from the right of 500, move the decimal point 2 places to the left.
$$
5.00
$$
The product is $\boxed{\text{5}}$.

7. LCM: Find the Lowest Common Multiple (LCM) of 12, 18, and 24.

Find the prime factorization of each number.

$$
12 = 2^2 \times 3^1
$$
$$
18 = 2^1 \times 3^2
$$
$$
24 = 2^3 \times 3^1
$$

For each prime factor, take the highest power that appears in any of the factorizations.
Highest power of 2 is $2^3$. Highest power of 3 is $3^2$.
Multiply these highest powers together.
$$ \text{LCM} = 2^3 \times 3^2 = 8 \times 9 = 72 $$ The LCM of 12, 18, and 24 is $\boxed{\text{72}}$.
8. Angles: Use a protractor to draw an angle of $120^\circ$ and label it correctly as "Obtuse". * To draw a $120^\circ$ angle: 1. Draw a straight line segment. This will be one arm of the angle. 2. Place the center of a protractor on one endpoint of the line segment (the vertex). Align the baseline of the protractor with the line segment. 3. Locate the $120^\circ$ mark on the protractor. 4. Make a small mark at $120^\circ$ . 5. Draw a second line segment from the vertex to the mark. 6. Label the angle as $120^\circ$ . * An angle of $120^\circ$ is an obtuse angle because it is greater than $90^\circ$ but less than $180^\circ$ .
1. Word Problem: Cloth needed for 6 outfits. Cloth for one outfit = 2.5 meters Number of outfits = 6
  $\text{Total cloth} = 2.5 \text{ meters/outfit} \times 6 \text{ outfits}$ $\text{Total cloth} = 15.0 \text{ meters}$
  15 meters of cloth are needed for 6 outfits.
2. Symmetry: Draw a square and a rectangle. Draw all the lines of symmetry for each shape.
  
  Square: A square has 4 lines of symmetry.
  
  Two lines pass through the midpoints of opposite sides (one horizontal, one vertical).
  
  Two lines pass through opposite vertices (the diagonals).
  
  Rectangle: A rectangle has 2 lines of symmetry.
  
  One line passes through the midpoints of the longer opposite sides (horizontal).
  
  One line passes through the midpoints of the shorter opposite sides (vertical).
DIGITAL TECHNOLOGIES

Task: Open Microsoft Word and type a "Happy Holiday" message to Mr. Victor.

a. Shortcut Challenge: Highlight your name and press Ctrl + B. What happened to the text?
When you highlight text and press Ctrl + B in Microsoft Word, the selected text becomes bold.

b. Press Ctrl + E. Where did your text move to on the page?
When you press Ctrl + E in Microsoft Word, the selected text or the current paragraph is centered on the page.

c. Press Ctrl

Solve the following mathematics problems: 1. Convert 21 (Base 10) to Base 2. 2. Calculate a 15% discount on N5,000. 3. List 3 cylindrical and 3 rectangular prism objects. 4. Simplify 5x + 10 - 2x + 4.

Step-by-step solution

MATHEMATICS

Group like terms.

Combine like terms.

Find the total fraction of cake eaten.

Find the fraction of cake left.

Multiply the numbers as if they were whole numbers.

Count the total number of decimal places in the original numbers.

Place the decimal point in the product.

Find the prime factorization of each number.

For each prime factor, take the highest power that appears in any of the factorizations.

Multiply these highest powers together.

DIGITAL TECHNOLOGIES

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