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

Explanation

To find the square root of 0.0676:

√0.0676 ≈ 0.26

Explanation

To evaluate 2(-7)²:

First, calculate the exponent:

(-7)² = (-7) × (-7) = 49

Now, multiply by 2:

2 × 49 = 98

Explanation

Set Difference (B A) means the elements in B that are not in A.

Given:

A = {2, 4, 5, 7}

B = {3, 4, 7}

Elements of B are {3, 4, 7}.

4 and 7 are also in A, so they are removed.

3 is not in A, so it remains.

Therefore, B A = {3}