Explanation

The radius is half of the diameter, so: 16 cm ÷ 2 = 8 cm.

Radius is the distance from the center of the circle to any point on its edge.

Explanation

Let's solve the quadratic equation 6x² - 17x + 12 = 0.

Using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Here, a = 6, b = -17, and c = 12.

x = (17 ± √((-17)² - 4_6_12)) / (2*6)

x = (17 ± √(289 - 288)) / 12

x = (17 ± √1) / 12

x = (17 + 1) / 12 or x = (17 - 1) / 12

x = 18 / 12 or x = 16 / 12

x = 3/2 or x = 4/3

The solutions are x = 3/2 and x = 4/3.

Explanation

The surface area of a sphere (A) is given by the formula:

A = 4 × π × r²

Given A = 616 m², let's solve for r:

616 = 4 × π × r²

616 = 4 × (22/7) × r²

616 = 88/7 × r²

r² = 616 × 7 / 88

r² = 49

r = √49

r = 7

Explanation

To find the area of the carpeting part, we need to find the area of the inner rectangle (without carpet) and subtract it from the total area.

Length of inner rectangle = 7.8 - 22.3 = 3.2 m

Width of inner rectangle = 6.5 - 22.3 = 1.9 m

Area of the room = 7.8 * 6.5 = 50.7 m^2

Area of inner rectangle = 3.2 * 1.9 = 6.08 m^2

Area of carpet = Total area - Inner area

= 50.7 - 6.08

= 44.62 m^2

Explanation

The correct definition of rational numbers is:

The set of all numbers of the form p/q where p and q are integers and q ≠ 0.

This is because rational numbers are defined as the ratio of two integers, with the denominator (q) being non-zero.

Explanation

The given expression:

(x/x ∈ A and x ∈/ B)

Can be read as:

x is an element of A and x is not an element of B

This represents the set difference between A and B, which is denoted as:

A B or A - B

The correct answer is: AB

Explanation

90 minutes is equivalent to 5400 seconds, and 54 seconds is 1% of that.

The calculation shows that 54 seconds is 1% of 90 minutes.

Explanation

To find the percentage that 3% is of 5%, divide 3% by 5% and multiply by 100:

(3/5) × 100

= 0.6 × 100

= 60%

Explanation

Blouse, Skirt, and Coat are all types of clothing worn on the upper or lower body.

Slipper is footwear, making it the odd one out.

Explanation

Using the identity:

a³ + b³ = (a + b)³ - 3ab(a + b)

Given:

a + b = 4

ab = 3

Substitute the values:

a³ + b³ = (4)³ - 3(3)(4)

= 64 - 36

= 28