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Area bounded by y = \(x^2\) - x + 3 and y = 3 The intersection is given as \(x^2\) - x + 3 = 3 \(x^2\) - x = 0 x(x -1) = 0 The graph is sketched between x= 0 and x = 1 \(\int^{1}_{0}\)\(x^2\) - x + 3)dx - \(\int^{1}_{0}\)3dx = \(\int^{1}{0}(x^2\) - x)dx [\(\frac{2x^3}{3} - \frac{x^2}{2}\)] = f(1) - f(0) = [\(\frac{2}{3} - \frac{1}{2}\)] - [0 - 0] = \(\frac{4 - 3}{6}\) = \(\frac{1}{6}\)unit(sq)

\(\int_0^{\frac{\pi}{2}}\)sin 2x dx = [-1/2cos 2x + C]\(_0^{\frac{\pi}{2}}\) =[-1/2 cos 2 * \pi/2 + C] - [-1/2 cos 2 * 0] = [-1/2 cos \pi] - [-1/2 cos 0] = [-1/2x - 1] - [-1/2 * 1] = 1/2 -(-1/2) = 1/2 + 1/2 = 1

Workers who earn above #700 = 4 + 6 + 2 = 12

Angle of Excellence = 360 - (120+80+90) = 360 - 290 = 70o If 360o represents 36 students 1º will represent \(\frac{36}{360}\) 50^\circ will represent \(\frac{36}{360}\) * \(\frac{70}{1}\) = 7

\(mean=\frac{60+5x}{18+x}\\3.5=\frac{60+5x}{18+x}\\\frac{7}{2}=\frac{60+5x}{18+x}\) 7(18+x) = 2(60+5x) 126 + 7x = 120 + 10x 10x - 7x = 126 - 120 3x = 6 x = 2

1.35, 1.25, 1.35, 1.40, 1.35, 1.50, 1.35, 1.50, and 1.20 Modal height = 1.35 Range (r) = 1.50 - 1.20 = 0.30 ∴m + 2r = 1.35 + 2(0.30) = 1.35 + 0.60 = 1.95

\(mean(x) = \frac{20t}{5}\) = S.D = \(\sqrt{\frac{((\overline{x} - x)^2}{\text{n}}}\) \(\sqrt{2}\) = \(\sqrt{\frac{10t^2}{5}}\) 2 = \(\frac{10t^2}{5}\) 10t\(^2\) = 10 t\(^2\) = 1 t = \(\sqrt{1}\) = 1

\(\frac{6!}{2!} = ways =\(\frac{6\times5\times4\times3\times2!}{2!}\) = 6\(\times5\times4\times3\) = 360ways

(n - 1)! = (7 - 1)! = 6! = 6*5*4*3*2*1 = 720 ways

Blue balls = 5 Red balls = 3 White balls = 2 Total = 10 P(Two blue) = 5/10 * 5/10 = 25/100 P(Two Red) = 3/10 * 3/10 = 9/100 ∴P(Two blue or two red balls) = 25/100 + 9/100 = 34/100 = 17/50

U = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20} A = {x/x is divisible by 2} A = {2,4,6,8,10,12,14,16,18,20} B = {x/x is divisible by 3} A ∩ B = {6, 12, 18} P(Number divisible by both 2 and 3) = 3/20

Reproducibility (I) Consistent readings under the same conditions. Sensibility (II) Quick response to small temperature changes. High Accuracy (IV) Measurements close to the true temperature.

since resistance R = \(\frac{p(l)}{a}\) = \(\frac{4 \times 10^{-7} \times 20}{8.0 \times 10^{-6}}\) R = 1.0 Ω

the power of a lens is defined as the reciprocal of the focal length ,expressed in metre.Mathematically, the power of a lens in dioptres is given by:(1)/f(in cm). thus for lens of power of 4.0 dioptres we have that: (1)/(f) = +4.0 f= (1)/(4.0) = 0.25cm

Fractional distillation of liquefied air, with Nitrogen distilling as a vapor at a lower boiling point of -196^\circC while O2 is left as a liquid. In the industrial preparation of nitrogen and oxygen from air, the process of fractional distillation is used. This process separates the components of air based on their boiling points. The boiling points of the main components of air are: - Nitrogen (N\(_2\)): -195.8^\circC - Oxygen (O\(_2\)): -182.96^\circC By cooling air to extremely low temperatures, the components can be separated based on their boiling points, allowing for the production of high-purity nitrogen and oxygen.