Correct Answer: D. x = 0 or x = 3

Explanation

\(3^{2x-2} - 28(3^{x-2}) + 3 = 0\)

\(\frac{3^{2x}}{3^2} - \frac{28.3^x}{3^2} + 3 = 0\)

\(\frac{3^{2x}}{9} - \frac{28.3^x}{9} + 3 = 0\)

let p = 3\(^x\)

\(\frac{p^{2}}{9} - \frac{{28p}}{9} + 3 = 0\)

multiply through by 9

p\(^2\) - 28p + 27 = 0

p\(^2\) - p - 27p + 27 = 0

p (p - 1) - 27(p - 1) = 0

(p-1)(p-27) = 0

p = 1 or 27

when p = 1

p = 3\(^x\)

3\(^x\) = 1

3\(^x\) = 3\(^0\)

x = 0

when p = 27

3x = 27

3x = 33

x = 3

Correct Answer: B. 2

Explanation

T.S.A of the wall \(=2(7\times 5 + 7 \times x + 5 \times x) = 96\\

70 + 14x + 10x = 96 \Rightarrow 24x = 96-70=26\\

x = \frac{26}{24}=\frac{13}{12}\)

Correct Answer: D. No correct option

Correct Answer: C. y + x - 3 ≥ 0, y + x ≤ 0

Correct Answer: C. 4/27

Correct Answer: B. 22

Explanation

\(\text{Total frequency} = 50\)

Median occurs at \(\frac{50}{2} = \text{25th position}\)

= Class 20 - 24 with classmark \(\frac{20 + 24}{2} = 22\)

Explanation

\(\frac{dV}{dt}=3\frac{1}{2}cm^3s^{-1}=3.5cm^3s^{-1}\)

L = 6cm

\(\frac{dL}{dt}=?\)

\(V = L^3\)

\(\frac{dV}{dL}=3L^2\)

\(\frac{dL}{dt}=(\frac{dV}{dL})^{-1}\times \frac{dV}{dt}\)

\(\frac{dL}{dt}=(3L^2)^{-1}\times 3.5\)

At L= 6cm

\(\frac{dL}{dt}=(3(6)^2)^{-1}\times 3.5\)

\(\frac{dL}{dt} =(108)^{-1}\times 3.5\)

\(\frac{dL}{dt}=\frac{1}{108}\times 3.5\)

\(\therefore \frac{dL}{dt}0.032cms^{-1}\)

Correct Answer: A. 67

Explanation

Find the median of the following data set: 66,123,44,78,99,67,143,44,107,12,578,12,67,367,44 Let's begin by putting our data in increasing order: 12,12,44,44,44,66,67,67,78,99,107,123,143,367,578 Now, the median should be pretty straightforward to find. The median will simply be the number in the middle of all the terms. In this case, it is the number in red below 12,12,44,44,44,66,67,67,78,99,107,123,143,367,578 So our answer is 67.

Correct Answer: C. 38208

Correct Answer: D. N35.00

Explanation

Let x = original price

A decrease of 22% = (100-22)% = 78% of the original price.

78% of x = 27.30

= \(\frac{78x}{100} = 27.30\)

78x = 2730

then, x = \(\frac{2730}{78}\)

x = 35

Therefore, the original price of the shoe was N35.00.