Correct Answer: B. 45

Explanation

\(^{3^2 + 1}\)C\(_{3+5}\)

\(^{9 + 1}\)C\(_{3+5}\)

\(^{10}\)C\(_{8}\) = \(\frac{10!}{8! 2!}\)

\(\frac{10 * 9 * 8!}{8! 2!}\) = \(\frac{10 * 9}{2}\)

= 45

Correct Answer: A. x<-2

Explanation

Three times a certain number (x) = 3x

minus 2 = -2

is less than =<

the number minus 6 = x -6

Mathematically; 3x - 2< x - 6

collect like terms

3x - x< -6 + 2

2x< -4

x< -2 is the possible values of x

Correct Answer: C. 5m/s

Correct Answer: B. 2.0

Explanation

mean (4) = \(\frac{2x + 4x + 2x - 13 + 6x}{4}\)

16 = 14x - 13

16 + 13 = 14x

x = 29/14 or 2.07

Correct Answer: D. - \(\frac{4}{5}\)

Explanation

Where sinθ = \(\frac{opp}{hyp}\) → \(\frac{-3}{5}\)

opp = -3, hyp = 5

using pythagoras formula

hyp\(^2\) = adj\(^2\) + opp\(^2\)

adj\(^2\) = hyp\(^2\) - opp\(^2\)

adj\(^2\) = 5\(^2\) - 3\(^2\) → 25 - 9

adj\(^2\) = 16

adj = 4

cosθ = \(\frac{adj}{hyp}\) → \(\frac{4}{5}\)

In third quadrant: cosθ is negative → - \(\frac{4}{5}\)

Correct Answer: D. 3cm

Explanation

hyp = 5cm, adj = \(\frac{8cm}{2}\) 4cm, opp = xcm

Pythagoras theorem:

hyp\(^2\) = opp\(^2\) + adj\(^2\)

5\(^2\) = x\(^2\) + 4\(^2\)

x\(^2\) = 25 - 16

x =√9

x = 3cm

Correct Answer: C. \(1111101_{two}\)

Explanation

\((101_{two})^3\) = \((5_{ten})^3\)

5\(^3\) = 125

And 125 = \(1111101_{two}\)

Correct Answer: B. 1

Explanation

y = 1/x; y = \(\frac{k}{x}\)

k =xy → 3 * 4 = 12

x = \(\frac{k}{y}\)

x = \(\frac{12}{12}\) = 1

Correct Answer: C. 2x - y = -5

Explanation

Condition for Parallelism means that their gradient value is same

line 2x - y = 5 is rearranged

As y = 2x - 5 from y = mx + c

: line 2x - y = 5 has the gradient of 2

A parallel line with gradient of 2 and intercept of 5

→ 2x - y = -5

Rearranged as y = 2x + 5

Correct Answer: C. x?2

Explanation

x ? 2 is represented by an arrow with an filled-in dot above the 2.

The arrow points in the direction of all the numbers that are greater than 2.