Correct Answer: D. 85

Explanation

To find the median of a set of values, simply place the numbers in order and find the value that is exactly in the middle. Here, we can place the test scores in ascending order to get 61, 72, 85, 85, 92. (Descending order would work just as well.) The median is the middle value, 85. Make sure you don't confuse median with mean (average)! To get the mean value of this set, you would find the sum of the test scores and then divide by the number of values.

Correct Answer: B. 4.606

Explanation

(0,3)\(^x\) = (0.5)\(^8\)

xlog 0,3 = 9 log 0.5

x = \(\frac{8 \log 0.5}{\log 0.3}\)

= 4.606

Correct Answer: D. 29.8cm

Correct Answer: B. 10

Explanation

\(a = 2\frac{1}{2}, nth = a + (n-1)d \Rightarrow 25 = 2\frac{1}{2} + (n-1)2\frac{1}{2}\\

25 = \frac{5}{2}+(n-1)\frac{5}{2} \Rightarrow 22\frac{1}{2} = \frac{5n-5}{2}\Rightarrow \frac{45}{2} = \frac{5n-5}{2}\\

45 = 5n - 5 \Rightarrow 5n = 50 \Rightarrow n = 10\)

Explanation

(a) \(\frac{4.56 \times 3.6}{0.12} \equiv \frac{4.56 \times 360}{12}\)

= \(4.56 \times 30 \)

= \(136.8 \)

= \(1.368 \times 10^{2}\)

(b) \((73.8)^{2} - (26.2)^{2}\)

Using the method of difference of two squares,

= \((73.8 + 26.2) \times (73.8 - 26.2)\)

= \(100 \times 47.6\)

= \(4760\)

(c) \(\sqrt{1\frac{19}{81}}\)

= \(\sqrt{\frac{100}{81}}\)

= \(\frac{10}{9}\)

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

Explanation

P(even in 1 dice) = \(\frac{3}{6} = \frac{1}{2}\)

P(even in 2 fair die) = \(\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}\)

Correct Answer: A. 5.0 cm

Explanation

Total surface area of hemisphere is

3\(\pi r^2\) = 75\(\pi cm^2\)

\(r^2\) = \(\frac{75 \pi}{3 \pi}\)

\(r^2\) = 25

r = \(\sqrt{25}\)

r = 5cm

Explanation

(a)(i) \(\sin 63.35° = 0.8938\)

\(2 \sin 63.35° = 2 \times 0.8938 = 1.7876\)

(ii) \(\log \cos 44.74° = \bar{1}.8514\)

(b) \(\log K - \log (K - 2) = \log 5\)

\(\log (\frac{K}{K - 2}) = \log 5\)

\(\therefore \frac{K}{K - 2} = 5 \implies K = 5(K - 2)\)

\(K = 5K - 10 \implies 10 = 5K - K = 4K\)

\(K = 2\frac{1}{2}\)

(c) \(\frac{(3.68)^{2} \times 6.705}{\sqrt{0.3581}}\)

\(\therefore \frac{(3.68)^{2} \times 6.705}{\sqrt{0.3581}} = 151.7\)

Correct Answer: A. 7.725

Explanation

\(\frac {N + 1}{2} = \frac {107 + 1}{2}\) th = 54th value i.e the median age is in the interval "7 - 8" (29 + 25 = 54)

Median = \(1_m + (\frac {^{\sum f} /_2 - f_b}{f_m})\)c

\(l_m\)=lower class boundary of the median age = 6.5

\(\sum f\) = 107

\(f_b\) = sum of all frequencies before the median age = 29

\(f_m\)=frequency of the median age = 40

c = class width = 8.5 - 6.5 = 2

Median = 6.5 + \((\frac {^{107}/_2 - 29}{40})\) x 2

= 6.5 + \((\frac {53.5 - 29}{40})\) x 2

= 6.5 + \((\frac {24.5}{40})\) x 2

= 6.5 + 1.225

\(\therefore\) median age = 7.725

Correct Answer: A. 907