Tank Capacity Quinary
1. Problem: Find how much less the capacity of tank B is than the capacity of tank A.
Step 1: Let the capacity of tank A be $C_A$ and tank B be $C_B$.
Step 2: The difference in capacity is $C_A - C_B$.
Without specific values given, the answer is the difference $C_A - C_B$.
2. Problem: Convert 484 to a quinary (base 5) number.
Step 1: Divide 484 by 5 repeatedly and record remainders:
$484 \div 5 = 96$ remainder $4$
$96 \div 5 = 19$ remainder $1$
$19 \div 5 = 3$ remainder $4$
$3 \div 5 = 0$ remainder $3$
Step 2: Write remainders in reverse order: $3 4 1 4$.
Step 3: Therefore, $484_{10} = 3414_5$.
3. Problem: If the ratio of boys to girls is 4:5 and girls are 400, find number of boys.
Step 1: Ratio is $\frac{boys}{girls} = \frac{4}{5}$.
Step 2: Girls = 400, so boys $= \frac{4}{5} \times 400 = 320$.
4. Problem: Check if numbers 5, 8, 10, 15 are proportional.
Step 1: For proportion $a:b = c:d$, check if $a\times d = b \times c$.
Check: $5 \times 15 = 75$ and $8 \times 10 = 80$.
Since $75 \neq 80$, numbers are not proportional.
5. Problem: Is a triangle a rational or irrational number?
Step 1: A triangle is a geometric figure, not a number.
Answer: Not applicable.
6. Problem: Write formula to calculate area of parallelogram.
Answer: $\text{Area} = \text{base} \times \text{height}$.
7. Problem: Calculate area of parallelogram with sides 30 cm and 40 cm, and smaller segment 15 cm.
Step 1: Given, base $b=40$ cm and height $h=15$ cm.
Step 2: Area $= b \times h = 40 \times 15 = 600$ cm$^2$.
8. Problem: Express $x^a \times x^b$ as a power of $x$.
Step 1: Use law of exponents: $x^a \times x^b = x^{a+b}$.
Final answers:
- Capacity difference: $C_A - C_B$
- $484_{10} = 3414_5$
- Boys = 320
- Numbers 5,8,10,15 are not proportional
- Triangle: geometric figure, not a number
- Area of parallelogram $= \text{base} \times \text{height}$
- Area of given parallelogram $= 600$ cm$^2$
- $x^a \times x^b = x^{a+b}$