Mathematics Questions and Answers

% error = $\frac{Error}{Actual Value}$ x 100%

Student's Value = 18mL

Actual Value = 18.4mL

Error = 18.4 - 18 = 0.4

∴ % error = $\frac{0.4}{18.4}$ x 100% = 2.17%

Average performance rating of Team B = $\frac{7+9+1+9+6}{5} = \frac{32}{5}$ = 6.4

Average performance rating of Team A = $\frac{5+3+6+10+2}{5} = \frac{26}{5}$ = 5.2

∴ The difference in the average performance ratings between Team B and Team A = 6.4 - 5.2 = 1.2

16.54 x 10$^{-5}$ - 6.76 x 10$^{-8}$ + 0.23 x 10$^{-6}$

⇒ 1.654 x 10$^{-4}$ - 6.76 x 10$^{-8}$ + 2.3 x 10$^{-7}$

⇒ 1.654 x 10$^{-4}$ - 0.000676 x 10$^{-4}$ + 0.0023 x 10$^{-4}$

⇒ (1.654 - 0.000676 + 0.0023) x 10$^{-4}$

∴ 1.655624 x 10$^{-4}$ ≃ 1.66 x 10$^{-4}$

T$_3$ = 6

T$_5$ = 12

S$_{12}$ = ?

T$_n$ = a + (n - 1)d

⇒ T$_3$ = a + 2d = 6 ----- (i)

⇒ T$_5$ = a + 4d = 12 ----- (ii)

Subtract equation (ii) from (i)

⇒ -2d = -6

⇒ d$\frac{-6}{-2}$ = 3

Substitute 3 for d in equation (i)

⇒ a + 2(3) = 6

⇒ a + 6 = 6

⇒ a = 6 - 6 = 0

S$_n$ = $\frac{n(2a + (n - 1)d)}{2}$

⇒ S$_{12}$ = $\frac{12(2 \times 0 + (12 - 1)3)}{2}$

⇒ S$_{12}$ = 6(0 + 11 x 3)

⇒ S$_{12}$ = 6(33)

∴ S$_{12}$ = 198

Volume of the cylinder = $\frac{θ}{360} \times \pi r^2h$

θ = 360$^o$ - 90$^o$ = 270$^o$

∴ Volume of the cylinder = $\frac{270}{360} \times \frac{22}{7} \times \frac{14^2}{1} \times \frac{32}{1} = \frac{37,255,680}{2520} = 14,784cm^3$