{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":"<span class='basic_left'>Ng\u01b0\u1eddi ta \u0111\u1ebfm m\u1ed9t c\u00e1ch c\u1ea9n th\u1eadn s\u1ed1 c\u00e1nh hoa tr\u00ean $100$ b\u00f4ng hoa v\u00e0 ghi l\u1ea1i nh\u01b0 sau: <br\/> <table><tr><th>S\u1ed1 c\u00e1nh hoa $(x)$<\/th><th>T\u1ea7n s\u1ed1 $(n)$<\/th><\/tr><tr><td>$10-12$<\/td><td>5<\/td><\/tr><tr><td>$13-15$<\/td><td>22<\/td><\/tr><tr><td>$16-18$<\/td><td>48<\/td><\/tr><tr><td>$19-21$<\/td><td>18<\/td><\/tr><tr><td>$22-24$<\/td><td>7<\/td><\/tr><tr><td><\/td><td>$N=100$<\/td><\/tr><\/table> <br\/> <b> C\u00e2u 1. <\/b> S\u1ed1 ph\u1ea7n tr\u0103m nh\u1eefng b\u00f4ng hoa quan s\u00e1t \u0111\u01b0\u1ee3c v\u1edbi s\u1ed1 c\u00e1nh hoa \u00edt h\u01a1n $19,$ ch\u00ednh x\u00e1c l\u00e0: <\/span>","select":["A. $48\\%$","B. $52\\%$","C. $72\\%$ ","D. $75\\%$"],"explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>T\u00ecm s\u1ed1 b\u00f4ng hoa quan s\u00e1t \u0111\u01b0\u1ee3c c\u00f3 s\u1ed1 c\u00e1nh \u00edt h\u01a1n $19$ <br\/> T\u00ednh t\u1ec9 s\u1ed1 ph\u1ea7n tr\u0103m gi\u1eefa s\u1ed1 hoa c\u00f3 s\u1ed1 c\u00e1nh \u00edt h\u01a1n $19$ v\u1edbi s\u1ed1 hoa quan s\u00e1t <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>S\u1ed1 b\u00f4ng hoa quan s\u00e1t \u0111\u01b0\u1ee3c c\u00f3 s\u1ed1 c\u00e1nh \u00edt h\u01a1n $19$ l\u00e0: <br\/> $5+22+48=75$ (b\u00f4ng hoa) <br\/> S\u1ed1 ph\u1ea7n tr\u0103m nh\u1eefng b\u00f4ng hoa quan s\u00e1t \u0111\u01b0\u1ee3c v\u1edbi s\u1ed1 c\u00e1nh hoa \u00edt h\u01a1n $19$ l\u00e0: <br\/> $\\dfrac{75}{100}\\cdot 100\\%=75\\%$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D.<\/span> <\/span>","column":4}]}],"id_ques":1031},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"<span class='basic_left'>Ng\u01b0\u1eddi ta \u0111\u1ebfm m\u1ed9t c\u00e1ch c\u1ea9n th\u1eadn s\u1ed1 c\u00e1nh hoa tr\u00ean $100$ b\u00f4ng hoa v\u00e0 ghi l\u1ea1i nh\u01b0 sau: <br\/> <table><tr><th>S\u1ed1 c\u00e1nh hoa $(x)$<\/th><th>T\u1ea7n s\u1ed1 $(n)$<\/th><\/tr><tr><td>$10-12$<\/td><td>5<\/td><\/tr><tr><td>$13-15$<\/td><td>22<\/td><\/tr><tr><td>$16-18$<\/td><td>48<\/td><\/tr><tr><td>$19-21$<\/td><td>18<\/td><\/tr><tr><td>$22-24$<\/td><td>7<\/td><\/tr><tr><td><\/td><td>$N=100$<\/td><\/tr><\/table> <br\/> <b> C\u00e2u 2. <\/b> Trung b\u00ecnh m\u1ed7i b\u00f4ng hoa c\u00f3 s\u1ed1 c\u00e1nh l\u00e0:<\/span>","select":["A. $15$","B. $16$","C. $17$ ","D. $18$"],"explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>T\u00ecm s\u1ed1 trung b\u00ecnh c\u1ed9ng c\u1ee7a d\u1ea5u hi\u1ec7u \u0111\u00f3 ch\u00ednh l\u00e0 s\u1ed1 c\u00e1nh trung b\u00ecnh c\u1ee7a m\u1ed7i b\u00f4ng hoa. <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3 b\u1ea3ng sau: <br\/><table><tr><th>S\u1ed1 c\u00e1nh hoa $(x)$<\/th><th>Trung b\u00ecnh c\u1ed9ng c\u1ee7a kho\u1ea3ng<\/th><th>T\u1ea7n s\u1ed1 $(n)$<\/th><th>C\u00e1c t\u00edch<\/th><\/tr><tr><td>$10-12$<\/td><td>11<\/td><td>5<\/td><td>55<\/td><\/tr><tr><td>$13-15$<\/td><td>14<\/td><td>22<\/td><td>308<\/td><\/tr><tr><td>$16-18$<\/td><td>17<\/td><td>48<\/td><td>816<\/td><\/tr><tr><td>$19-21$<\/td><td>20<\/td><td>18<\/td><td>360<\/td><\/tr><tr><td>$22-24$<\/td><td>23<\/td><td>7<\/td><td>161<\/td><\/tr><tr><td><\/td><td><\/td><td>$N=100$<\/td><td>T\u1ed5ng: $1700$<\/td><\/tr><\/table> <br\/> Trung b\u00ecnh m\u1ed7i b\u00f4ng hoa c\u00f3 s\u1ed1 c\u00e1nh l\u00e0: <br\/> $\\overline{X}=\\dfrac{1700}{100}=17$ (c\u00e1nh) <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C.<\/span> <br\/> <b>L\u01b0u \u00fd:<\/b> \u0110\u1ed1i v\u1edbi b\u1ea3ng m\u00e0 gi\u00e1 tr\u1ecb \u0111\u1ec3 \u1edf d\u1ea1ng kho\u1ea3ng th\u00ec ta t\u00ednh s\u1ed1 trung b\u00ecnh c\u1ed9ng c\u1ee7a d\u1ea5u hi\u1ec7u nh\u01b0 sau: <br\/> - T\u00ednh s\u1ed1 trung b\u00ecnh c\u1ed9ng c\u1ee7a t\u1eebng kho\u1ea3ng. S\u1ed1 \u0111\u00f3 ch\u00ednh l\u00e0 trung b\u00ecnh c\u1ed9ng c\u1ee7a gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 nh\u1ecf nh\u1ea5t c\u1ee7a kho\u1ea3ng. V\u00ed d\u1ee5 trung b\u00ecnh c\u1ed9ng c\u1ee7a kho\u1ea3ng $150-152$ l\u00e0 $151.$ <br\/> - Nh\u00e2n c\u00e1c s\u1ed1 trung b\u00ecnh v\u1eeba t\u00ecm \u0111\u01b0\u1ee3c v\u1edbi c\u00e1c t\u1ea7n s\u1ed1 t\u01b0\u01a1ng \u1ee9ng. <br\/> - T\u00ecm s\u1ed1 trung b\u00ecnh c\u1ed9ng theo c\u00f4ng th\u1ee9c \u0111\u00e3 h\u1ecdc.<\/span>","column":4}]}],"id_ques":1032},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["5"],["6"]]],"list":[{"point":10,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> Cho b\u1ea3ng s\u1ed1 li\u1ec7u sau: <br\/> <table><tr><th>Gi\u00e1 tr\u1ecb $(x)$<\/th><th>T\u1ea7n s\u1ed1 $(n)$<\/th><\/tr><tr><td>1<\/td><td>2<\/td><\/tr><tr><td>2<\/td><td>$k$<\/td><\/tr><tr><td>3<\/td><td>4<\/td><\/tr><tr><td>4<\/td><td>8<\/td><\/tr><tr><td>5<\/td><td>5<\/td><\/tr><tr><td>6<\/td><td>$y$<\/td><\/tr><\/table> <br\/> Bi\u1ebft s\u1ed1 trung b\u00ecnh c\u1ed9ng c\u1ee7a d\u1ea5u hi\u1ec7u l\u00e0 $3,9$ <br\/> <b>C\u00e2u 1.<\/b> Bi\u1ebft $N=30.$ T\u00ecm $k, y.$ <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $k=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{};y=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ <\/span>","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>T\u00ecm m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa $k$ v\u00e0 $y$ theo hai d\u1eef ki\u1ec7n: <br\/> + S\u1ed1 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a d\u1ea5u hi\u1ec7u <br\/> + S\u1ed1 trung b\u00ecnh c\u1ed9ng c\u1ee7a d\u1ea5u hi\u1ec7u <br\/> T\u1eeb \u0111\u00f3 l\u1eadp lu\u1eadn \u0111\u1ec3 t\u00ecm gi\u00e1 tr\u1ecb c\u1ee7a $k$ v\u00e0 $y.$ <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Theo b\u00e0i s\u1ed1 c\u00e1c gi\u00e1 tr\u1ecb $(N)$ l\u00e0 $30.$ <br\/> Khi \u0111\u00f3: <br\/> $\\begin{align} & N=30 \\\\ & \\Leftrightarrow 2+k+4+8+5+y=30 \\\\ & \\Leftrightarrow 19+k+y=30 \\\\ & \\Leftrightarrow k+y=30-19 \\\\ & \\Leftrightarrow k+y=11\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\left( 1 \\right) \\\\ \\end{align}$ <br\/> L\u1ea1i c\u00f3, s\u1ed1 trung b\u00ecnh c\u1ed9ng l\u00e0 $3,9$ n\u00ean: <br\/> $\\begin{align} & \\overline{X}=3,9 \\\\ & \\Leftrightarrow \\dfrac{1.2+2.k+3.4+4.8+5.5+6.y}{30}=3,9 \\\\ & \\Leftrightarrow \\dfrac{71+2k+6y}{30}=3,9 \\\\ & \\Leftrightarrow 71+2k+6y=117 \\\\ & \\Leftrightarrow 2k+6y=46 \\\\ & \\Leftrightarrow k+3y=23\\,\\,\\,\\,\\,\\,\\,\\,\\left( 2 \\right) \\\\ \\end{align}$ <br\/> T\u1eeb (1) v\u00e0 (2) ta c\u00f3: <br\/> $\\begin{align} & k+3y=23 \\\\ & \\Leftrightarrow \\left( k+y \\right)+2y=23 \\\\ & \\Leftrightarrow 11+2y=23 \\\\ & \\Leftrightarrow 2y=12 \\\\ & \\Leftrightarrow y=6 \\\\ & \\Rightarrow k=11-6=5 \\\\ \\end{align}$ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o c\u00e1c \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $5;6$<\/span><\/span>"}]}],"id_ques":1033},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":"<span class='basic_left'>Cho b\u1ea3ng s\u1ed1 li\u1ec7u sau: <br\/> <table><tr><th>Gi\u00e1 tr\u1ecb $(x)$<\/th><th>T\u1ea7n s\u1ed1 $(n)$<\/th><\/tr><tr><td>1<\/td><td>2<\/td><\/tr><tr><td>2<\/td><td>$k$<\/td><\/tr><tr><td>3<\/td><td>4<\/td><\/tr><tr><td>4<\/td><td>8<\/td><\/tr><tr><td>5<\/td><td>5<\/td><\/tr><tr><td>6<\/td><td>$y$<\/td><\/tr><\/table> <br\/> Bi\u1ebft s\u1ed1 trung b\u00ecnh c\u1ed9ng c\u1ee7a d\u1ea5u hi\u1ec7u l\u00e0 $3,9$ <br\/> <b>C\u00e2u 2.<\/b> V\u1edbi gi\u00e1 tr\u1ecb $k,y$ t\u00ecm \u0111\u01b0\u1ee3c \u1edf c\u00e2u 1 tr\u00ean th\u00ec m\u1ed1t c\u1ee7a d\u1ea5u hi\u1ec7u l\u00e0: <\/span>","select":["A. $8$","B. $6$","C. $5$","D. $4$"],"explain":"<span class='basic_left'>Theo c\u00e2u 1, ta t\u00ednh \u0111\u01b0\u1ee3c $k=5;y=6$ <br\/> Ta c\u00f3 b\u1ea3ng sau khi t\u00ecm \u0111\u01b0\u1ee3c $k$ v\u00e0 $y$ nh\u01b0 sau: <br\/> <table><tr><th>Gi\u00e1 tr\u1ecb $(x)$<\/th><th>T\u1ea7n s\u1ed1 $(n)$<\/th><\/tr><tr><td>1<\/td><td>2<\/td><\/tr><tr><td>2<\/td><td>5<\/td><\/tr><tr><td>3<\/td><td>4<\/td><\/tr><tr><td>4<\/td><td>8<\/td><\/tr><tr><td>5<\/td><td>5<\/td><\/tr><tr><td>6<\/td><td>6<\/td><\/tr><\/table> <br\/> Nh\u00ecn v\u00e0o b\u1ea3ng s\u1ed1 li\u1ec7u tr\u00ean, gi\u00e1 tr\u1ecb $4$ c\u00f3 t\u1ea7n s\u1ed1 l\u1edbn nh\u1ea5t l\u00e0 $8.$ <br\/> Do \u0111\u00f3, m\u1ed1t c\u1ee7a d\u1ea5u hi\u1ec7u l\u00e0 $4.$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D.<\/span> <\/span>","column":4}]}],"id_ques":1034},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["11"]]],"list":[{"point":10,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> Trung b\u00ecnh c\u1ed9ng c\u1ee7a $n$ s\u1ed1 l\u00e0 $80,$ trong \u0111\u00f3 c\u00f3 m\u1ed9t s\u1ed1 l\u00e0 $100.$ Khi b\u1ecf s\u1ed1 $100$ \u0111\u00f3 \u0111i th\u00ec s\u1ed1 trung b\u00ecnh c\u1ed9ng c\u1ee7a c\u00e1c s\u1ed1 c\u00f2n l\u1ea1i l\u00e0 $78.$ T\u00ednh $n.$ <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $n=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ <\/span>","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>T\u00ednh t\u1ed5ng $n$ s\u1ed1 theo $n$. <br\/> T\u00ednh t\u1ed5ng c\u1ee7a $n-1$ s\u1ed1 theo $n$ <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>T\u1ed5ng c\u1ee7a $n$ s\u1ed1 b\u1eb1ng $80n.$ <br\/> T\u1ed5ng c\u1ee7a $n-1$ s\u1ed1 c\u00f2n l\u1ea1i (sau khi b\u1ecf \u0111i s\u1ed1 $100$) b\u1eb1ng $80n-100$ <br\/> Ta c\u00f3: <br\/> $\\begin{align} & \\dfrac{80n-100}{n-1}=78 \\\\ & \\Rightarrow 80n-100=78(n-1) \\\\ & \\Leftrightarrow 80n-78n=100-78 \\\\ & \\Leftrightarrow 2n=22 \\\\ & \\Leftrightarrow n=11 \\\\ \\end{align}$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $11$<\/span><\/span>"}]}],"id_ques":1035},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"<span class='basic_left'>K\u1ebft qu\u1ea3 \u0111i\u1ec1u tra danh t\u00ednh c\u00e1c nh\u00e2n vi\u00ean trong m\u1ed9t c\u00f4ng ty cho th\u1ea5y: <br\/> - T\u1ec9 s\u1ed1 gi\u1eefa s\u1ed1 nam v\u00e0 s\u1ed1 n\u1eef b\u1eb1ng $\\dfrac{4}{5}$ <br\/> - Tu\u1ed5i trung b\u00ecnh c\u1ee7a nam l\u00e0 $35$ <br\/> - Tu\u1ed5i trung b\u00ecnh c\u1ee7a n\u1eef l\u00e0 $31$ <br\/> Khi \u0111\u00f3, tu\u1ed5i trung b\u00ecnh c\u1ee7a c\u00e1c nh\u00e2n vi\u00ean trong c\u00f4ng ty \u0111\u00f3 l\u00e0 $32.$ <\/span>","select":["\u0110\u00fang","Sai"],"explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>G\u1ecdi s\u1ed1 nam v\u00e0 n\u1eef l\u1ea7n l\u01b0\u1ee3t l\u00e0 $4k; 5k$ (ng\u01b0\u1eddi) <br\/> T\u00ednh t\u1ed5ng s\u1ed1 tu\u1ed5i c\u1ee7a nam theo $k,$ t\u1ed5ng s\u1ed1 tu\u1ed5i c\u1ee7a n\u1eef theo $k.$ <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>G\u1ecdi s\u1ed1 nam l\u00e0 $4k$ (ng\u01b0\u1eddi) th\u00ec s\u1ed1 n\u1eef l\u00e0 $5k$ (ng\u01b0\u1eddi) <br\/> Tu\u1ed5i trung b\u00ecnh c\u1ee7a nam l\u00e0 $35$ n\u00ean t\u1ed5ng s\u1ed1 tu\u1ed5i c\u1ee7a nam l\u00e0: $35.4k=140k$ <br\/> Tu\u1ed5i trung b\u00ecnh c\u1ee7a n\u1eef l\u00e0 $31$ n\u00ean t\u1ed5ng s\u1ed1 tu\u1ed5i c\u1ee7a n\u1eef l\u00e0: $31.5k=155k$ <br\/> Tu\u1ed5i trung b\u00ecnh c\u1ee7a c\u00e1c nh\u00e2n vi\u00ean trong c\u00f4ng ty \u0111\u00f3 l\u00e0: <br\/> $\\dfrac{140k+155k}{4k+5k}=\\dfrac{295k}{9k}=32,78$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 Sai.<\/span> <\/span>","column":2}]}],"id_ques":1036},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["5"]]],"list":[{"point":10,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> B\u1ea3o \u0111\u00e3 c\u00f3 m\u1ed9t s\u1ed1 \u0111i\u1ec3m ki\u1ec3m tra To\u00e1n v\u00e0 t\u00ednh r\u1eb1ng n\u1ebfu b\u00e0i cu\u1ed1i c\u00f9ng s\u1eafp t\u1edbi \u0111\u01b0\u1ee3c $10$ th\u00ec \u0111i\u1ec3m trung b\u00ecnh l\u00e0 $9.$ Nh\u01b0ng b\u00e0i \u0111\u00f3 ch\u1ec9 \u0111\u01b0\u1ee3c $7,5$ \u0111i\u1ec3m n\u00ean \u0111i\u1ec3m trung b\u00ecnh l\u00e0 $8,5.$ H\u1ecfi B\u1ea3o c\u00f3 t\u1ea5t c\u1ea3 bao nhi\u00eau b\u00e0i ki\u1ec3m tra? (k\u1ec3 c\u1ea3 b\u00e0i ki\u1ec3m tra cu\u1ed1i c\u00f9ng)<br\/> <b> \u0110\u00e1p \u00e1n: <\/b> C\u00f3 $\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ (b\u00e0i ki\u1ec3m tra) <\/span>","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>T\u00ednh t\u1ed5ng s\u1ed1 \u0111i\u1ec3m \u0111\u00e3 c\u00f3 (kh\u00f4ng k\u1ec3 b\u00e0i cu\u1ed1i c\u00f9ng) theo c\u1ea3 th\u1ef1c t\u1ebf v\u00e0 gi\u1ea3 \u0111\u1ecbnh. <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>G\u1ecdi s\u1ed1 b\u00e0i ki\u1ec3m tra l\u00e0 $n\\, (n \\ge 2)$ <br\/> T\u1ed5ng s\u1ed1 \u0111i\u1ec3m \u0111\u00e3 c\u00f3 (kh\u00f4ng k\u1ec3 b\u00e0i cu\u1ed1i c\u00f9ng) l\u00e0: $9n-10,$ c\u0169ng l\u00e0 $8,5n-7,5$ <br\/> Do \u0111\u00f3: <br\/> $\\begin{align} & 9n-10=8,5n-7,5 \\\\ & \\Leftrightarrow 9n-8,5n=10-7,5 \\\\ & \\Leftrightarrow 0,5n=2,5 \\\\ & \\Leftrightarrow n=5 \\\\ \\end{align}$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $5$<\/span><\/span>"}]}],"id_ques":1037},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"<span class='basic_left'>M\u1ed9t c\u00e2y khi m\u1edbi tr\u1ed3ng cao $x$ m\u00e9t, m\u1ed7i n\u0103m c\u00e2y cao th\u00eam $y$ m\u00e9t. Ng\u01b0\u1eddi ta \u0111o chi\u1ec1u cao c\u1ee7a c\u00e2y h\u1eb1ng n\u0103m v\u00e0 trong l\u1ea7n \u0111o cu\u1ed1i th\u00ec c\u00e2y cao $17m.$ C\u1eb7p gi\u00e1 tr\u1ecb $(x;y)$ l\u00e0 c\u1eb7p s\u1ed1 n\u00e0o trong c\u00e1c c\u1eb7p s\u1ed1 $(4;2), (5;3), (6;5), (7;4)?$ Khi \u0111\u00f3 c\u00e2y m\u1edbi tr\u1ed3ng cao bao nhi\u00eau m\u00e9t v\u00e0 sau m\u1ed7i n\u0103m c\u00e2y cao th\u00eam bao nhi\u00eau m\u00e9t?<\/span>","select":["A. $(4;2),$ c\u00e2y m\u1edbi tr\u1ed3ng cao $4$ m\u00e9t v\u00e0 m\u1ed7i n\u0103m c\u00e2y cao th\u00eam $2$ m\u00e9t.","B. $(5;3),$ c\u00e2y m\u1edbi tr\u1ed3ng cao $5$ m\u00e9t v\u00e0 m\u1ed7i n\u0103m c\u00e2y cao th\u00eam $3$ m\u00e9t.","C. $(6;5),$ c\u00e2y m\u1edbi tr\u1ed3ng cao $6$ m\u00e9t v\u00e0 m\u1ed7i n\u0103m c\u00e2y cao th\u00eam $5$ m\u00e9t.","D. $(7;4),$ c\u00e2y m\u1edbi tr\u1ed3ng cao $7$ m\u00e9t v\u00e0 m\u1ed7i n\u0103m c\u00e2y cao th\u00eam $4$ m\u00e9t."],"explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>L\u1eadp b\u1ea3ng \u0111\u1ec3 ki\u1ec3m tra c\u00e1c c\u1eb7p gi\u00e1 tr\u1ecb $(x;y)$ \u0111\u00f3 c\u00f3 th\u1ecfa m\u00e3n l\u1ea7n \u0111o cu\u1ed1i c\u00e2y c\u00f3 chi\u1ec1u cao l\u00e0 $17m$ hay kh\u00f4ng. <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> L\u1eadp b\u1ea3ng chi\u1ec1u cao c\u1ee7a c\u00e2y h\u1eb1ng n\u0103m: <br\/> <table><tr><th>$x\\,(m)$<\/th><th>$y\\,(m)$<\/th><th>Chi\u1ec1u cao c\u1ee7a c\u00e2y h\u1eb1ng n\u0103m<\/th><\/tr><tr><td>4<\/td><td>2<\/td><td>$4;6;8;10;12;14;16;18;20;...$<\/td><\/tr><tr><td>5<\/td><td>3<\/td><td>$5;8;11;14;17;20;..$.<\/td><\/tr><tr><td>6<\/td><td>5<\/td><td>$6;11;16;21;...$<\/td><\/tr><tr><td>7<\/td><td>4<\/td><td>$7;11;15;19;...$<\/td><\/tr><\/table> <br\/> Theo b\u1ea3ng tr\u00ean, ch\u1ec9 c\u00f3 c\u1eb7p s\u1ed1 $(5;3)$ cho gi\u00e1 tr\u1ecb chi\u1ec1u cao c\u1ee7a c\u00e2y l\u00e0 $17m.$ V\u1eady khi m\u1edbi tr\u1ed3ng, c\u00e2y cao $5m$ v\u00e0 sau m\u1ed7i n\u0103m c\u00e2y cao th\u00eam $3m$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span><\/span>","column":1}]}],"id_ques":1038},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":"<span class='basic_left'>N\u1ebfu m\u1ed7i gi\u00e1 tr\u1ecb c\u1ee7a d\u1ea5u hi\u1ec7u t\u0103ng th\u00eam $5$ \u0111\u01a1n v\u1ecb th\u00ec s\u1ed1 trung b\u00ecnh c\u1ed9ng c\u1ee7a d\u1ea5u hi\u1ec7u \u0111\u00f3 t\u0103ng th\u00eam bao nhi\u00eau \u0111\u01a1n v\u1ecb?<\/span>","select":["A. $20$","B. $15$","C. $10$","D. $5$"],"explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>Vi\u1ebft c\u00f4ng th\u1ee9c t\u00ednh s\u1ed1 trung b\u00ecnh c\u1ed9ng c\u1ee7a $k$ gi\u00e1 tr\u1ecb d\u1ea1ng t\u1ed5ng qu\u00e1t. <br\/> Sau \u0111\u00f3 th\u00eam m\u1ed7i gi\u00e1 tr\u1ecb $5$ \u0111\u01a1n v\u1ecb v\u00e0 t\u00ednh s\u1ed1 trung b\u00ecnh m\u1edbi. <br\/> So s\u00e1nh s\u1ed1 trung b\u00ecnh c\u0169 v\u00e0 s\u1ed1 trung b\u00ecnh m\u1edbi <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: <br\/> ${{\\overline{X}}_{\\text{\u0111}}}=\\dfrac{{{x}_{1}}{{n}_{1}}+{{x}_{2}}{{n}_{2}}+\\cdots +{{x}_{k}}{{n}_{k}}}{N}$ v\u1edbi $N={{n}_{1}}+{{n}_{2}}+\\cdots +{{n}_{k}}$ <br\/> M\u1ed7i gi\u00e1 tr\u1ecb c\u1ee7a d\u1ea5u hi\u1ec7u t\u0103ng th\u00eam $5$ \u0111\u01a1n v\u1ecb th\u00ec: <br\/> $\\begin{align} & {{\\overline{X}}_{s}}=\\dfrac{\\left( {{x}_{1}}+5 \\right){{n}_{1}}+\\left( {{x}_{2}}+5 \\right){{n}_{2}}+\\cdots +\\left( {{x}_{k}}+5 \\right){{n}_{k}}}{N} \\\\ & \\,\\,\\,\\,\\,\\,\\,=\\dfrac{{{x}_{1}}{{n}_{1}}+5{{n}_{1}}+{{x}_{2}}{{n}_{2}}+5{{n}_{2}}+\\cdots +{{x}_{k}}{{n}_{k}}+5{{n}_{k}}}{N} \\\\ & \\,\\,\\,\\,\\,\\,\\,=\\dfrac{\\left( {{x}_{1}}{{n}_{1}}+{{x}_{2}}{{n}_{2}}+\\cdots +{{x}_{k}}{{n}_{k}} \\right)+\\left( 5{{n}_{1}}+5{{n}_{2}}+\\cdots +5{{n}_{k}} \\right)}{N} \\\\ & \\,\\,\\,\\,\\,\\,\\,=\\dfrac{{{x}_{1}}{{n}_{1}}+{{x}_{2}}{{n}_{2}}+\\cdots +{{x}_{k}}{{n}_{k}}}{N}+\\dfrac{5{{n}_{1}}+5{{n}_{2}}+\\cdots +5{{n}_{k}}}{N} \\\\ & \\,\\,\\,\\,\\,\\,=\\overline{{{X}_{\\text{\u0111}}}}+\\dfrac{5\\left( {{n}_{1}}+{{n}_{2}}+\\cdots {{n}_{k}} \\right)}{N} \\\\ & \\,\\,\\,\\,\\,\\,=\\overline{{{X}_{\\text{\u0111}}}}+\\dfrac{5N}{N} \\\\ & \\,\\,\\,\\,\\,=\\overline{{{X}_{\\text{\u0111}}}}+5 \\\\ \\end{align}$ <br\/> $\\Rightarrow$ S\u1ed1 trung b\u00ecnh c\u1ed9ng l\u00fac sau t\u0103ng $5$ \u0111\u01a1n v\u1ecb so v\u1edbi s\u1ed1 trung b\u00ecnh c\u1ed9ng l\u00fac \u0111\u1ea7u. <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D.<\/span><\/span>","column":2}]}],"id_ques":1039},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["4"],["1"]]],"list":[{"point":10,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> Cho b\u1ea3ng t\u1ea7n s\u1ed1 c\u1ee7a m\u1ed9t d\u1ea5u hi\u1ec7u. Bi\u1ebft s\u1ed1 trung b\u00ecnh c\u1ed9ng c\u1ee7a d\u1ea5u hi\u1ec7u l\u00e0 $3,15.$ T\u00ednh $m$ v\u00e0 $n.$ <br\/> <table><tr><th>Gi\u00e1 tr\u1ecb $(x)$<\/th><th>1<\/th><th>2<\/th><th>3<\/th><th>4<\/th><th>5<\/th><th><\/th><\/tr><tr><td>T\u1ea7n s\u1ed1 $(n)$<\/td><td>m<\/td><td>n<\/td><td>8<\/td><td>2<\/td><td>5<\/td><td>$N=20$<\/td><\/tr><\/table> <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $m=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{};n=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$<\/span>","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>Vi\u1ebft m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa $m$ v\u00e0 $n$ th\u00f4ng qua hai d\u1eef ki\u1ec7n: <br\/> + S\u1ed1 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a d\u1ea5u hi\u1ec7u <br\/> + S\u1ed1 trung b\u00ecnh c\u1ed9ng c\u1ee7a d\u1ea5u hi\u1ec7u <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: <br\/> $\\begin{align} & N=20 \\\\ & \\Leftrightarrow m+n+8+2+5=20 \\\\ & \\Leftrightarrow m+n+15=20 \\\\ & \\Leftrightarrow m+n=5\\,\\,\\,\\,\\,\\left( 1 \\right) \\\\ \\end{align}$ <br\/> Ta l\u1ea1i c\u00f3: <br\/> $\\begin{align} & \\overline{X}=3,15 \\\\ & \\Rightarrow \\dfrac{1.m+2.n+3.8+4.2+5.5}{20}=3,15 \\\\ & \\Rightarrow \\dfrac{m+2n+57}{20}=3,15 \\\\ & \\Rightarrow m+2n+57=63 \\\\ & \\Rightarrow m+2n=6\\,\\,\\,\\,\\,\\,\\,\\left( 2 \\right) \\\\ \\end{align}$ <br\/> T\u1eeb (1) v\u00e0 (2) ta c\u00f3:<br\/> $\\begin{align} & m+2n=6 \\\\ & \\Rightarrow m+n+n=6 \\\\ & \\Rightarrow 5+n=6 \\\\ & \\Rightarrow n=1 \\\\ & \\Rightarrow m=5-1=4 \\\\ \\end{align}$ <br\/> V\u1eady $m = 4; n=1$ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o c\u00e1c \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $4;1.$<\/span><\/span>"}]}],"id_ques":1040}],"lesson":{"save":0,"level":3}}