Correct Answer: D. - 1\(\frac{37}{48}\)

Explanation

If m = 4, n = 9, r = 16,

then \(\frac{m}{n}\) - 1\(\frac{7}{9}\) + \(\frac{n}{r}\)

= \(\frac{4}{9}\) - \(\frac{16}{9}\) + \(\frac{9}{16}\)

= \(\frac{64 - 256 + 81}{144}\)

= \(\frac{-111}{144}\)

= - 1\(\frac{37}{48}\)

Correct Answer: A. (1, 1)

Correct Answer: (a) Gain of 20%

Correct Answer: A. -1.55, 4.55

Explanation

x² - 3x = 7

x² - 3x - 7 = 0

What can you add to both sides of the equation to give the same value of y = x² - 3x - 3

The number is 4

x² - 3x - 7 + 4 = 4

x² - 3x - 3 = 4

but y = x² - 3x - 3

y = 4; So are y = 4 draw a line parallel to x axis, to cut or intersect the graph. At these points look down to see the corresponding values on x axis

This give -1.55 and 4.55

Correct Answer: D. 25% loss

Explanation

Cost price CP of the 100 oranges = \(\frac{100}{5}\) x N40.00

selling price SP of the 100 oranges = \(\frac{100}{20}\) x N120

= N600.00

so, profit or loss per cent

= \(\frac{SP - CP}{CP}\) x 100%

= \(\frac{600 - 800}{800}\) x 100%

= \(\frac{-200}{800}\) x 100%

Hence, loss per cent = 25%

Correct Answer: C. x=2, y=6

Explanation

The set is already in increasing order. We have six numbers in the set and we need to ensure the set will have a median of 4. When there is an even number in the set, we need to take the two middle numbers by adding them then dividing by two. The two middle numbers represent x and y. Let's set up an equation. x+y2=4. The numerator represents the two middle numbers being added and divided by the denominator. If we multiply both sides by 2 we get the sum of the variables to be 8. So we need to find the sum of x and y to be 8. The only choices are x=2, y=6 and x=?4, y=12. However, x=?4, y=12 doesn't work because 12 is bigger than both 7 and 10 and thus changing the median. x=2, y=6 is good because both of the values are les than 7 but greater than ?5.

Correct Answer: C. 300

Correct Answer: B. 60\(^o\)

Explanation

x + y + m + 2 = 180\(^o\)

\(\frac{x + y + 2}{2} + \frac{m}{2}\) = 90\(^o\)

m + \(\frac{m}{2} = 90^o\)

3m = 2 x 90\(^o\)

\(\frac{3m}{3} = \frac{180^o}{3}\)

m = 60\(^o\)

Correct Answer: D. -1< x ≤ 2

Explanation

(a)

(b) From the above diagram,

\(\sin 37° = \frac{5}{|LM|}\)

\(|LM| = \frac{5}{\sin 37}\)

\(|LM| = \frac{5}{0.6018}\)

= \(8.308 m\)

\(\approxeq 8.31 m\)

\(\cos 37 = \frac{|AM|}{|LM|}\)

\(|AM| = 8.308 \times \cos 37\)

\(|AM| = 8.308 \times 0.7986\)

\(|AM| = 6.6348 m\)

(c) The new |AM| = 6.6348 m - 2 = 4.6348 m

\(\cos y = \frac{4.6348}{8.308}\)

\(\cos y = 0.5579\)

\(y = \cos^{-1} (0.5579)\)

\(y = 56.089°\)

\(y = 56°\) (to the nearest degree).