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Acurate-Maths-Obj

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**Maths-Theory**

**PLS NOTE THIS SYMBOLS**

**^ means Raise to power**

*** means multiplication**

**√ means Sqr root**

**/ means division or divide**

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**================================**

**12a)**

**9x+10=28**

**9x=28-10**

**9x=18**

**x=18/9**

**x=2**

**-6x+4y=4**

**-6(2)+4y=4**

**4y=4+12**

**4y=16**

**y=16/4=4**

**================================**

**13ai)**

**x*y=x+y+2xy**

**2*3=2+3+2*2*3**

**=5+12=17**

**(2*3)*5=17*5**

**17+5+2*17*5**

**=22+170=192**

**ii)x*7=x+7+2(x)(7)**

**=x+7+14x**

**=15x+7**

**x*5=x+5+2(x)(5)**

**=x+5+10x**

**=11x+5**

**(x*5)*2=(11x+5)*2**

**=11x+5+2+2(11x+5)^2**

**=11x+5+2+44x+20**

**=55x+27**

**15x+7=55x+27**

**15x-55x=22-7**

**-40x=20**

**x=-20/40=-1/2**

**================================**

**2a)**

**A=P(1+r/100)^n**

**A=2,205,000**

**n=2**

**r=5%**

**p=?**

**2205000=p(1+5/100)^2**

**2205000m=p(1.05)^2**

**p=2205000/(1.05)^2=N2,000,000**

**2b)**

**area=30cm^2 h/b=3/2**

**area=1/2bh**

**b=2h/3**

**30=1/2*2h/3*h**

**2h^2=30*2*3**

**h^2=30*2*3/2**

**h^2=90**

**h=√90=9.49m**

**================================**

**4)****area of shaded portion=area of sector pqs-area of triangle pqs**

**=(θ/360*pieR^2)-(1/2r^2sinθ)**

**(60/360*22/7*14^2)-(1/2*14^2sin60)**

**102.2667-84.8705**

**=17.796**

**=17.8cm^2**

**7a)**

**log6Y+2log6x=3**

**log6y+log6x^2=3**

**log6(x^y)=3**

**x^y=6^3**

**x^y=216**

**y=216/x^2**

**7bi)**

**draw**

**7bii)**

**percentage who liked football and volleyball but not boxing=20**

**ii)percentage who liked exactly two part=40+20+10=70**

**iii)summing**

**5+5+10+40+20+10+5+x=100%**

**x+95=100**

**x=100-95=5%**

**percentage who like none=5%**

**================================**

**9a)**

**diagrams**

**9b)**

**|CA|^2=300^2+100^2-2(300)(100)cos 120degree**

**=9000+10000-60000(-cos60)**

**=100000+30000**

**KA|^2=130000**

**KA|=√130000**

**KA|=360.56KM**

**9bii)**

**Using sine rule**

**|AB|/sinC=|AC|/sin120**

**100/sinC=360.56**

**sinC=100sin60/360.56**

**sinC=0.2402**

**C=sin^-1(0.2402)=13.90degree**

**bearing=270+13.90=283.9degree = 284degree**

**1a)**

**[2(1/2)+1(3/4)/1(2/5)]/[2(1/4)-1(1/2)]**

**[5/2+7/4/7/5]/[9/4-3/2]**

**=[5/2+7/4*5/7]/[9/4-3/2]**

**[5/2+5/4]/[9/4-3/2]**

**=[(10+5/4)/(9-6/4)]**

**=(15/4)/(3/4)**

**=15/4*4/3**

**=5**

**1b)**

**From tan60/1*PR/3root2**

**PR=3root2*1/root3**

**=3root2/root3*root3/root3**

**=3root6/3=root6**

**From sin45/1*root6/x**

**x=root6*root2**

**=root12**

**=root4*3**

**=2root3**

**================================**

**5a)**

**Daigrams**

**5b)**

**Median = ((N + 1) / 2)th item Where: N = 31**

**40, 40, 40, 40, 40, 40, 40, 41, 41, 41, 41, 42, 42, 42, 42, 42, 42, 43, 43, 44, 44, 44, 44, 45, 45, 46, 46, 46, 46, 46, 46**

**Data table**

**F 7 4 6 2 4 2 6**

**X 40 41 42 43 44 45 46**

**Median = ((31 + 1) / 2)th item**

**Median = (32 / 2)th item**

**Median = 16th item**

**Arranging the discrete data in ascending order, We go get:**

**40, 40, 40, 40, 40, 40, 40, 41, 41, 41, 41, 42, 42, 42, 42, 42, 42, 43, 43, 44, 44, 44, 44, 45, 45, 46, 46, 46, 46, 46, 46**

**Median = 42**

**================================**

**3)**

**2x/1 – 2/5 y = 2y/1**

**LCM = 5**

**10x – 2y = 10y**

**10x = 10y + 2y**

**10x = 12y**

**X = 12y/10 ————-1**

**2x – 2/5y + 2 1/4x + 1/2y + 2y = 180**

**LCM = 20**

**40x – 8y + 45x + 10y + 40y = 3600**

**40x + 45x + 10y – 8y + 50y = 3600**

**95x + 42y = 3600**

**95 (6y/5) + 42y =3600**

**19(6y) + 42y = 3600**

**114y + 42y = 3600**

**156y = 3600**

**Y = 3600/156**

**Y = 23.08**

**Sub for y in eq 1**

**X = 6(23.08)/5**

**X = 27.69**

**================================**

**11)**

**A={4,5,6,7,8,9,10,11,12}**

**B={10,11,12,13,14,15,16,17,18,19,20,21,22,23,24}**

**M={4,8,12,11,6,20,24,28}**

**a)prob (A)=3/7**

**b)prob( B)=7-4/7=3/7**

**c)prob(AuB)=n(AuB)/n(m)**

**but (AuB)={4,8,12,11,6,20,24,}**

**prob(AuB)=6/7**

Maths-Theory

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