Find the median of 5,9,1,10,3,8,9,2,4,5,5,5,7,3 and 6
6
5
4
3
Correct answer is B
First arrange the numbers in order of magnitude; 1,2,3,3,4,5,5,5,5,6,7,8,9,9,10 Hence the median = 5
1
2
3
4
Correct answer is D
The number with the highest frequency = 4
The mean of 2 - t, 4 + t, 3 - 2t, 2 + t and t - 1 is
t
-t
2
-2
Correct answer is C
Mean x = \(\frac{\sum x}{n}\)
= [(2 - t) + (4 + t) + (3 - 2t) + (2 + t) + (t - 1)] \(\div\) 5
= [11 - 1 + 3t - 3t] \(\div\) 5
= 10 \(\div\) 5
= 2
Evaluate \(\int (2x + 3)^{\frac{1}{2}} \delta x\)
\(\frac{1}{12} (2x + 3)^6 + k\)
\(\frac{1}{3} (2x + 3)^{\frac{1}{2}} + k\)
\(\frac{1}{3} (2x + 3)^{\frac{3}{2}} + k\)
\(\frac{1}{12} (2x + 3)^{\frac{3}{4}} + k\)
Correct answer is C
\(\int (2x + 3)^{\frac{1}{2}} \delta x\)
let u = 2x + 3, \(\frac{\delta y}{\delta x} = 2\)
\(\delta x = \frac{\delta u}{2}\)
Now \(\int (2x + 3)^{\frac{1}{2}} \delta x = \int u^{\frac{1}{2}}.{\frac{\delta x}{2}}\)
\( = \frac{1}{2} \int u^{\frac{1}{2}} \delta u\)
\( = \frac{1}{2} u^{\frac{3}{2}} \times \frac{2}{3} + k\)
\( = \frac{1}{3} u^{\frac{3}{2}} + k\)
\( = \frac{1}{3} (2x + 3)^{\frac{3}{2}} + k\)
cos 2x + k
\(\frac{1}{2}\)cos 2x + k
\(-\frac{1}{2}\)cos 2x + k
-cos 2x + k
Correct answer is C
\(\int \sin 2x dx = \frac{1}{2} (-\cos 2x) + k\)
\(- \frac{1}{2} \cos 2x + k\)