Correct Answer: B. 29,250

Correct Answer: C. \(\begin{pmatrix} 13 \\ 11 \end{pmatrix}\)

Explanation

\(\begin{pmatrix} 2 & 3 \\ 4 & 1 \end{pmatrix} \begin{pmatrix} 2 \\ 3 \end{pmatrix}\)

= \(\begin{pmatrix} 2 \times 2 + 3 \times 3 \\ 4 \times 2 + 1 \times 3 \end{pmatrix}\)

= \(\begin{pmatrix} 13 \\ 11 \end{pmatrix}\)

Correct Answer: D. 13

Explanation

(ii)

bi) Median 1/2 of N = 1/2 x 400 = 200

Cumulative frequency level From the curve, it is 118.5cm

(ii) Inter quartile range = upper quartile - lower quartile upper quartile

= 3/4 of N

= 3/4 x 400 = 300

Cumulative frequency level From the curve, it is 126.5cm

lower quartile = 1/4 of N

= 1/4 x 400 = 100

Cumulative frequency level From the curve, it is 111.0cm

Inter quartile range = 126.5cm -111.0cm = 15.5cm

(ii) From the curve, students whose heights are at most 130cm are 240.

Percentage óf students whose heights are at most 130cm = \(\frac{240}{400}\) x 100

= 60%

Correct Answer: D. \(\frac{13}{54}\)

Explanation

\(P(A)=\frac{1}{6},P(T)=\frac{1}{9}\)

Probability that only one of them will hit the target = \(P(A)\times P( \bar T ) + P( \bar A )\times P(T)\)

Where \(P( \bar T )\) is the probability that Tunde will not hit the target and \(P( \bar A )\) is the probability that Atta will not hit the target

\(P( \bar T )=1-\frac{1}{9}=\frac{8}{9}\)

\(P( \bar A )=1-\frac{1}{6}=\frac{5}{6}\)

Pr(only one) =\((\frac{1}{6}\times\frac{8}{9}) + (\frac{5}{6} \times \frac{1}{9}) =\frac{4}{27} + \frac{5}{54}\)

\(\therefore\) pr (only one) = \(\frac{13}{54}\)

Correct Answer: B. Mary walked to school because the school bus arrived late

Explanation

The statement "y ⇒ x" represents a logical implication, where y implies x. This means that if y is true, then x must also be true. In other words, if the condition represented by y is satisfied, the condition represented by x must also be satisfied.

Out of the provided options:

"Emmanuella did not go to school because the school bus arrived late."

In this case, "Emmanuella did not go to school" (not y) is the outcome of the late school bus (x). However, the implication y ⇒ x would mean that if the student walked down to school (y), then the school bus arrived late (x). So this case does not match the y ⇒ x structure.

"The school bus arrived early and Kate ran to school" does not match the y ⇒ x structure, as there's no clear implication between the two events.

"Mary walked to school because the school bus arrived late" can be represented by y ⇒ x because if Mary walked to school (y), it implies that the school bus arrived late (x).

"Either the school bus arrived late or Maryam walked to school" does not match the y ⇒ x structure, as it represents a logical OR relationship rather than an implication.

So, the correct statement that can be represented by y ⇒ x is:

Mary walked to school because the school bus arrived late

Correct Answer: B. \(\frac{-2}{x+3}\)

Explanation

\(\frac{1}{x-3}-\frac{3(x-1)}{x^2 - 9}\\

\frac{1}{x-3}-\frac{3(x-1)}{(x-3)(x+3)}\\

\frac{x+3-3x+3}{(x-3)(x+3)};\frac{-2x+6}{(x-3)(x+3)}\\

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

Correct Answer: D. \(\frac{8}{15}\)

Explanation

Prime number in the experiment are 2,3 and 5 with frequencies 10,14 and 8

P(obtaining a prime number) = \(\frac{10+14+8}{60}\)

= \(\frac{32}{60}\) or \(\frac{8}{15}\)

Correct Answer: (c) 70

Correct Answer: B. 25