Explanation

To find the value of k:

Rearrange the equation:

6 = 4.8 / k

Multiply both sides by k:

6k = 4.8

Now, divide by 6:

k = 4.8 / 6

k = 0.8

Explanation

To convert 8 1/3 % to a fraction:

First, convert the mixed number to an improper fraction:

8 1/3 = (8 × 3 + 1) / 3

= 25/3

Now, convert the percentage to a fraction:

(25/3) % = (25/3) / 100

= 25 / (3 × 100)

= 25/300

Simplify the fraction:

25/300 = 1/12

Explanation

To find the length of the arc:

First, convert the angle from degrees to radians:

30° = (30 × π) / 180 radians

= π/6 radians

Now, use the formula for arc length:

Arc length = radius × angle (in radians)

= 6 × (π/6)

= π

Approximating π as 3.14:

Arc length ≈ 3.14 cm

Explanation

Using De Morgan's Law:

$$<b><font\; color="\#0000ff">(</font></b>\mathrm{<b><font\; color="\#0000ff">A</font></b>}<b><font\; color="\#0000ff">\cup </font></b>\mathrm{<b><font\; color="\#0000ff">B</font></b>}{<b><font\; color="\#0000ff">)</font></b>}^{\mathrm{<b><font\; color="\#0000ff">\prime </font></b>}}<b><font\; color="\#0000ff">=</font></b>{\mathrm{<b><font\; color="\#ff0000">A</font></b>}}^{\mathrm{<b><font\; color="\#ff0000">\prime </font></b>}}<b><font\; color="\#ff0000">\cap </font></b>{\mathrm{<b><font\; color="\#ff0000">B</font></b>}}^{\mathrm{\prime }}$$

Explanation

Since y varies directly with x, we can write:

y = kx

where k is the constant of proportionality.

Given y = 27 and x = 3:

27 = k(3)

Divide by 3:

k = 9

Now, use this value of k to find y when x = 11:

y = 9(11)

y = 99

Explanation

To find the solution set of 2x² + 2x - 11 = 1:

First, subtract 1 from both sides:

2x² + 2x - 12 = 0

Now, divide by 2:

x² + x - 6 = 0

Factor the quadratic:

(x + 3)(x - 2) = 0

This gives us two possible solutions:

x + 3 = 0 --> x = -3

x - 2 = 0 --> x = 2

So, the solution set is:

(-3, 2)

Explanation

To solve 2(b - 3) + 5 = 3(b - 1):

First, distribute the numbers outside the parentheses:

2b - 6 + 5 = 3b - 3

Combine like terms:

2b - 1 = 3b - 3

Now, isolate b:

2b - 3b = -3 + 1

-b = -2

Multiply both sides by -1:

b = 2

Explanation

To find the price without GST:

Let the original price be x.

The GST amount is 16.5% of x:

GST = 0.165x

The sales price (including GST) is:

4248 = x + 0.165x

4248 = 1.165x

Now, divide by 1.165:

x = 4248 / 1.165

x ≈ 3646.35

Explanation

The equation x = 4 represents a vertical line.

Vertical lines are always parallel to the y-axis.

Explanation

To find the time required to paint 3000m²:

First, find the painter's rate:

250m² / 8 hours = 31.25m²/hour

Now, divide the total area by the rate:

3000m² / 31.25m²/hour ≈ 96 hours