Correct Answer: D. (3x-4)(2x+5)

Explanation

\(6x^2 + 7x - 20\)

= \(6x^2 + 15x - 8x - 20\)

= \(3x(2x + 5) - 4(2x + 5)\)

= \((3x - 4)(2x + 5)\)

Correct Answer: D. 12

Explanation

To answer this question, you need to know the first ten prime numbers! Remember, prime numbers are all of the integers that are divisible only by themselves and by 1. They do not include 1. So, our list is: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 The median is the middle value. There is no proper middle since we have an even number of values. We need to take the 5th and the 6th elements (the middle two values) and average them. The 5th term is 11 and the 6th is 13; therefore, the median is: 11+13/2=24/2=12

Explanation

(a)

\(< BAD = 106°\) (Given)

\(/AD/ = /AB/\) (given)

\(\therefore < ADC = \frac{180° - 106°}{2} = 37°\) (base angles of an isosceles triangle)

(b) Total card = 20

(i) P(card picked is E) = \(\frac{1}{20}\)

(ii) P(B and A or C or D or E) or P(A or C or D or E and B)

= \(\frac{4}{20} \times \frac{3 + 7 + 5 + 1}{19} + \frac{3 + 7 + 5 + 1}{20} \times \frac{4}{19}\)

= \(\frac{64}{380} + \frac{64}{380} = \frac{32}{95}\)

Correct Answer: B. 95^o

Correct Answer: C. 1/3

Explanation

(a) 2M, 5P, 3C.

(i) Tie same books together

Maths books can be arranged within themselves in 2! ways, Physics books can be arranged in 5! ways, Chemistry books in 3! ways.

The three sets of subjects can be arranged in 3! ways.

\(\therefore\) Total arrangements = 3!2!5!3!

= \(6 \times 2 \times 120 \times 6 = \text{8640 ways}\).

(ii) Tie Physics books together.

There are 1 + 2 + 3 = 6 books to be arranged in 6! ways.

The Physics books can be arranged in 5! ways.

\(\therefore\) Total arrangement = \(6!5! = 720 \times 120 = \text{86,400 ways}\)

(b) p(English speaking) = p = \(\frac{13}{20}\); p(non- English speaking) = q = \(\frac{7}{20}\)

8 persons selected,

\((p + q)^{8} = p^{8} + 8p^{7}q + 28p^{6}q^{2} + 56p^{5}q^{3} + 70p^{4}q^{4} + 56p^{3}q^{5} + 28p^{2}q^{6} + 8pq^{7} + q^{8}\)

p(at least 3 speak English) = 1 - [none + one + two].

= \(1 - [q^{8} + 8pq^{7} + 28p^{2}q^{6}]\)

= \(1 - [(0.35)^{8} + 8(0.65)(0.35)^{2} + 28(0.65)^{2}(0.35)^{2}]\)

= \(1 - [0.0002252 + 0.003346 + 0.1131]\)

= \(1 - 0.001488 = 0.98512\)

\(\approxeq 0.985\) (3 sig. figs).

Correct Answer: B. \(\frac{1 - \sqrt5}{4}\)

Correct Answer: A. 27\(\frac{1}{3}\)^{n - 1}

Correct Answer: A. m = 0, n = 4

Correct Answer: D. 0.1%

Explanation

Length = 59.6m

Breath = 40.3m

Perimeter = (59.6m + 40.3m) x 2

= 99.9 x 2 = 199.8m

Actual measurement

Perimeter = (60 + 40) x 2 = 100 x 2 = 200m

Error = 200m - 199.8m = 0.2

Error =0.2/200 x 100/1

= 0.1%