Explanation

Given the average of 7 quantities is 28:

Step 1: Calculate the sum of the quantities.

Sum = Average × Number of quantities

= 28 × 7

= 196

Explanation

To find the LCM of 90, 110, and 150:

Step 1: Prime factorize each number.

90 = 2 × 3² × 5

110 = 2 × 5 × 11

150 = 2 × 3 × 5²

Step 2: Identify the highest power of each prime factor.

Highest power of 2: 2¹

Highest power of 3: 3²

Highest power of 5: 5²

Highest power of 11: 11¹

Step 3: Calculate the LCM.

LCM = 2 × 3² × 5² × 11

= 2 × 9 × 25 × 11

= 4950

Explanation

Given the area of the square garden is 529 m²:

Step 1: Find the length of one side of the square.

Area = side²

529 = side²

side = √529

side = 23 m

Step 2: Calculate the perimeter of the square.

Perimeter = 4 × side

= 4 × 23

= 92 m

The length of wire required to cover all its sides is equal to the perimeter.

Explanation

To find the fourth proportional of 3, 7, and 15:

Let's denote the fourth proportional as x. We set up the proportion:

3/7 = 15/x

Step 1: Cross-multiply.

3x = 7 × 15

Step 2: Calculate the product of 7 and 15.

3x = 105

Step 3: Solve for x.

x = 105 / 3

x = 35

Explanation

To evaluate the expression 7/12 - 3/8 - 4/9:

Step 1: Find the least common multiple (LCM) of 12, 8, and 9.

The LCM of 12, 8, and 9 is 72.

Step 2: Convert each fraction to have a denominator of 72.

7/12 = (7 × 6) / (12 × 6) = 42/72

3/8 = (3 × 9) / (8 × 9) = 27/72

4/9 = (4 × 8) / (9 × 8) = 32/72

Step 3: Subtract the fractions.

42/72 - 27/72 - 32/72 = (42 - 27 - 32) / 72

= (42 - 59) / 72

= -17/72

Explanation

Given x = -1 and y = -3:

Let's evaluate the expression 5y² - 2(x² - 4xy) - 5y:

1. Calculate 5y² = 5(-3)² = 5(9) = 45

2. Calculate x² = (-1)² = 1

3. Calculate 4xy = 4(-1)(-3) = 12

4. Calculate x² - 4xy = 1 - 12 = -11

5. Calculate -2(x² - 4xy) = -2(-11) = 22

6. Calculate -5y = -5(-3) = 15

Now, combine the results:

5y² - 2(x² - 4xy) - 5y = 45 + 22 + 15

= 82

Explanation

The greatest 6-digit number is 999999.

The smallest 6-digit number is 100000.

The difference is 999999 - 100000 = 899999.

Explanation

Convert to decimals:

  2/3 ≈ 0.666, 1/2 = 0.5, 1/4 = 0.25

Descending order means largest to smallest → 2/3, 1/2, 1/4

Explanation

To round 95 to the nearest 10, look at the units digit (5).

Since it's 5 or more, round up → 95 → 100.

Explanation

The 4×100 meter relay is traditionally held as the final event in many major track competitions.

It adds excitement and team strategy, often closing the athletics program.