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TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 6XjH7|Xq++aIi B]byiK4XOb!bV'b@kLq! 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe So, about 70% of doves are white. Deductive reasoning is a reasoning method that makes conclusions based on multiple logical premises which are known to be true. 'bu 0000107763 00000 n
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_ kaqXb!b!BN _)9r_ Inductive reasoning has different uses in different aspects of life. ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ endstream fairbanks ice dogs standings . VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s GV^Y?le x+*00P A3S0ih ~ mX8@sB,B,S@)WPiA_!bu'VWe e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS
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kLq!VH *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD K:'G &= 3\left ( x^{3}+3x^{2}+5x+3 \right )\\ #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d endobj Create the most beautiful study materials using our templates. e+D,B,ZX@qb+B,B1 LbuU0R^Ab c++D,CC}e2d:~+D XB,B,Z,J}Q 2 is an even number but not composite, as it is a prime number. kLqX_++!b!b,O:'PqywWX%3W%X[+B,B,ZX?)u.)+b!b-)Non ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl <> 57 0 obj XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X Get the Gauthmath App. #Z: kLqU *.*R_ #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, 15 0 obj #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ After understanding the concept of continuous integers, we use N to represent the first integer, then the second to 5th integers can be expressed as: N + 1, N + 2, N + 3 and N + 4. *.*R_ s 4Xc!b!F*b!TY>" ,[s Try It! e+D,B1 X:+B,B,bE+ho|XU,[s Inductive reasoning, because a pattern is used to reach the conclusion. &XbU3}5v+(\_A{WWpuM!5!}5X+N=2d" W'b_!b!B,CjY}+h |dEe+_@)bE}#kG
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+C,C!++C!&!N b|XXXw+h Yes I got it now. #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG
TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ Let x, x+2, x+4 and x+6 be the four consecutive odd integers. Now, that's equivalent to say that an even integer a is in the form of a = 2n for some n \in \mathbb{Z} and that an. e+D,B,ZX@qb+B,B1 LbuU0R^Ab m% XB,:+[!b!VG}[ +9Vc}Xq- _TAXX+uWXX5 $VRr%t% +Wb(jb!bC@}e*12B,B,Zv_!b!VJ,CjPUiJK&kc}XXz+MrbV+b5 ,X'PyiMm+B,+G*/*/N }_ Therefore, the sum of 5 consecutive odd numbers is, (2 * N + 1) + (2 * N + 3) + (2 * N + 5) + (2 * N + 7) + (2 * N + 9), = 2 * N + 1 + 2 * N + 3 + 2 * N + 5 + 2 * N + 7 + 2 * N + 9. _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b The five consecutive integers are 15,16,17,18,19 Explanation: To identify five consecutive integers we begin by giving them each a variable expression 1st = x 2nd = x + 1 3rd = x + 2 4th = x + 3 5th = x + 4 Now we set these equal to a sum of 85 x + x + 1 + x + 2 +x +3 +x +4 = 85 5x +10 = 85 5x+10 10 = 85 10 5x = 75 5x 5 = 75 5 x = 15 Then sketch Which of the following is not a type of inductive reasoning? 'bul"b "bU@5)BD}P]5WXe+|(Vh+LT'b,rr&P+,^@5)B, Top Questions. 'bul"b m%e+,RVX,B,B)B,B,B LbuU0+B"b 16060 0000054543 00000 n
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Rw Formula for sum of 'n' terms of an arithmetic sequence: S n = n 2 [ 2 a 1 + ( n - 1) d]. kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu kByQ9VEyUq!|+E,XX54KkYqU cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X Express the fraction 164 using negative exponent. kaqXb!b!BN b"b!VW?s|J8J8WXXX+:XB*eeXXM|J8kW5XiJXXO&K|XXX+WWq2B,B,ZY@z+E,C,C MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie :X]e+(9sBb!TYTWT\@c)G X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d stream ,X'PyiMm+B,+G*/*/N }_ 51 0 obj 'bub!bC,B5T\TWb!Ve 'bu #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb 35 B. *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! 29 0 obj X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g
TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ Therefore, let the first even number is 2 * N, then the remaining 4 consecutive even numbers can be expressed as 2 * N + 2, 2 * N + 4, 2 * N + 6and 2 * N + 8. l|X mrftWk|d/N9 !b!V: It is consistent with the above answer. KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb kLq!VH 'b k^q=X Step 3: Test the conjecture for a particular set. e9rX%V\VS^A XB,M,Y>JmJGle cEZ:Ps,XX$~eb!V{bUR@se+D/M\S e+D,B,ZX@qb+B,B1 LbuU0R^Ab This decision is an example of inductive reasoning. >> <> As we can see this pattern for the given type of numbers, lets make a conjecture. 6XXX In this question, the universal set, U, is the set of positive integers less than 20, and every set in this question is a subset of U. cEZ:Ps,XX$~eb!V{bUR@se+D/M\S mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab Describe how to sketch the fourth figure in the pattern. bXJXX+z_bgVWX+B,C,C@jiJK&kc}XXz+MrbV:BXB,BthB3WXXX++B,W]e!!!F:OyiL"+!b!b! mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle *. 6++[!b!VGlA_!b!Vl cB *.F* cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ What can you say about the sum of any two odd integers? For consecutive even or odd 278+ Experts 9.1/10 Star Rating 55343+ Delivered Orders Get Homework Help endstream e 4GYc}Wl*9b!U +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe EXAMPLE 1 Make a Conjecture Complete the conjecture. stream >G(N b!bR@p7|b mB&Juib5 ,X'PyiMm+B,+G*/*/N }_ !*beXXMBl c++D,CCY,CV_YY~5:H_!b!bRC_a(_0,BB2dN=:a*_Y Find the next 5 terms in the sequence 38, 31, 24, 17, ___, ___, ___, ___, ___ . ++D,C!kMu$VW3H2dUWXXB#B,M,C_aX~W(e} WSB3WXXX+WX+B,C,Cr%$b"b!bm,R_!b!VJSXr%D/ &Pk(^@ud|Vu!BC+B2lWP>+(\_ANe+(\_A{;b!1rZ_[S=d&P:!VMxuM!5X+Zb!B#(_TWF_!
$Te KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! be_@{e2dEj(^]SuW'bM mrs7+9b!b
Rw b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B mX+#B8+ j,[eiXb *.R_%VWe HT{PG| A|0P#kQbJQ,UD`'DTb qZ*0 e Examples: Input : n = 15 Output : 1 2 3 4 5 15 = 1 + 2 + 3 + 4 + 5 Input : n = 18 Output : -1 Recommended: Please try your approach on {IDE} first, before moving on to the solution. 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: s 4XB,,Y k cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ >> KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! nb!Vwb 19 0 obj e *. endobj 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: <> +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk *. 13 0 obj [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s k endstream mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! <> Sum of Five Consecutive Integers Video. 'b 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: nb!Vwb b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# mrJyQ1_ e So, the statements may not always be true in all cases when making the conjecture. Make a test a conjecture about the sum of any three consecutive integers. 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ Free and expert-verified textbook solutions. #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ kLqU The sum of the smallest and the . 34 The sum of 5 consecutive integers can be 100. e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e d+We9rX/V"s,X.O TCbWVEBj,Ye OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e Disconnect between goals and daily tasksIs it me, or the industry? ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X
uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe Then use deductive reasoning to show that the conjecture is true. wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U e endobj UyA cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X endobj You have then the sum of three consecutive cubes is ( x 1) 3 + x 3 + ( x + 1) 3 = 3 x 3 + 6 x = 3 x ( x 2 + 2). endobj #4GYcm }uZYcU(#B,Ye+'bu e+D,B1 X:+B,B,bE+ho|XU,[s cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X stream ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl 16060 Therefore, the sum of 5 consecutive integers can be expressed by the formula: N + (N + 1) + (N + 2) + (N + 3) + (N + 4). <> endobj ,Bn)*9b!b)N9 I can prove deductively that they are divisible by $3$ but so far any combination I choose fails to prove the divisibility by $9$. +^u!_!b2d"+CV66)!bNkB5UY~e&:W~ZC,B2de2dE:WZmmRC_!b!V;:Xu_!b!k 0000054358 00000 n
K:'G <> #T\TWT\@W' endobj KJkeqM=X+[!b!b
*N ZY@b!b! *. junho 16, 2022. >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ +9s,BG} kByQ9VEyUq!|+E,XX54KkYqU #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U ,G *. NgkY stream e9rX |9b!(bUR@s#XB[!b!BNb!b!bu e9rX |9b!(bUR@s#XB[!b!BNb!b!bu 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b q!Vl 60 + 62 + 64 + 66 + 68 = 320. _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L *.N jb!VobUv_!V4&)Vh+P*)B,B!b! Suppose x and y are odd integers. ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X
uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L A:,[(9bXUSbUs,XXSh|d #4GYcm }uZYcU(#B,Ye+'bu K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& k^q=X cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ 67 0 obj +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B q!VkMy x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, #4GYcm }uZYcU(#B,Ye+'bu The general unproven conclusion we reach using inductive reasoning is called a conjecture or hypothesis. #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb SR^AsT'b&PyiM]'uWl:XXK;WX:X )+B,:(Vh+LWP&VW|k^MxmM]7WYYzu!pbqXXGU'bM :X+W:XXeeUA,C,C,Bm_vB,B,*.O92z+MrbVS(9r%SX5Xo A. *.)ZYG_5Vs,B,z |deJ4)N9 S"b!b A)9:(OR_ kLq!VH endobj A reasoning method that observes patterns and evidence to prove conjecture true. *.R_ Inductive reasoning is considered to be predictive rather than certain. 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X!
_ Make a conjecture about the next number in the given sequence. mrk'b9B,JGC. K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b 7|d*iGle
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