Explanation

To convert kilometers per hour (km/h) to meters per second (m/s), multiply by 1000/3600:

72 km/h = 72 × (1000/3600)

= 72 × 5/18

= 20 m/s

Explanation

To find the ratio c:a, divide the value of c by the value of a:

c:a = 20:5

Simplify the ratio by dividing both numbers by 5:

c:a = 4:1

Explanation

To simplify the expression, follow the rules of exponents:

(x⁴)³ = x^(4×3) = x¹²

Now, divide x¹² by x⁻⁴:

x¹² ÷ x⁻⁴ = x¹² × x⁴ (since dividing by x⁻⁴ is the same as multiplying by x⁴)

= x^(12+4)

= x¹⁶

Explanation

Convert the mixed fraction to an improper fraction:

3 4/5 = (3 × 5 + 4) / 5 = 19/5

The reciprocal of 19/5 is 5/19.

Explanation

The shaded part in the Venn diagram represents Q - P, meaning elements that belong to set Q but not to P.

Explanation

Work done by 10 women in 7 days = 1

Work done by 1 woman in 7 days = 1/10

Work done by 1 woman in 1 day = 1/(10 × 7) = 1/70

Work done by 10 children in 14 days = 1

Work done by 1 child in 14 days = 1/10

Work done by 1 child in 1 day = 1/(10 × 14) = 1/140

Work done by 5 women in 1 day = 5 × 1/70 = 5/70 = 1/14

Work done by 10 children in 1 day = 10 × 1/140 = 10/140 = 1/14

Total work done per day = 1/14 + 1/14 = 2/14 = 1/7

Total days required = 7 days

Explanation

Step 1: Work Done by A and B Together

• A’s 1-day work = 1/10
• B’s 1-day work = 1/15
• A and B’s 1-day work together:
  1/10​+1/15​=3/30​+2​/30=5/30​=1/6​
• Work done by A and B in 5 days:
  5×1​/6=5/6​

Step 2: Work Left for C

• Total work = 1
• Work remaining after A and B worked for 5 days: $$1 - frac{5}{6} = frac{1}{6}$$
• C completes the remaining 1/6 of the work in 2 days, so C’s 1-day work:
  1/6​÷2=1/12​

Step 3: Wages Calculation

• Total amount = Rs. 1500

• Work done ratio:

  • A's total work = $frac{5}{10} = frac{1}{2}$
  • B's total work = $frac{5}{15} = frac{1}{3}$
  • C's total work = $frac{2}{12} = frac{1}{6}$

• Share of wages:

  • A's share = $frac{1}{2} times 1500 = 750$
    
  • B's share = $frac{1}{3} times 1500 = 500$
    
  • C's share = $frac{1}{6} times 1500 = 250$
    

• Daily wages:

  • B worked 5 days, so B’s daily wage = 500/5 = Rs. 100
  • C worked 2 days, so C’s daily wage = 250/2 = Rs. 125
  • 100+125 = 225

Explanation

The property a × (b + c) = a × b + a × c distributes multiplication over addition.

This is called the Distributive Law of Multiplication over Addition.

Explanation

Equations use "=" (equality sign), like 7x - 1 = 0 and ax + b = 0.

In-equations (inequalities) use "<, >, ≤, or ≥", like 5x - 1 < 0.

Explanation

The mean proportional of two numbers is the square root of their product.

Mean proportional = √(4 × 16) = √64 = 8