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d********a
发帖数: 3698 | 2
POSITIVE
A
IS THE
NUMBER
啊 |
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h******g
发帖数: 11250 | 5 6
两个硬币，四种可能，头，头；头，字；字，头；字，字
7
假设袋里共有5n个球，则红球有3n个，
取两个红球概率为(3n/5n)*((3n-1)/(5n-1))=3/10，可得n=1
共有5个球，3个红球，2个白球
8
Janani获胜概率等于1-Manu获胜概率
Manu要获胜，必须连续三次都翻到tail，这个概率为1/2*1/2*1/2=1/8
9
6个cube，从1-6，最有可能的情况是1-6每个数字出现一次，所以总和为21
另一种考虑的方法是先考虑2个，这个和可以从2-12，概率分别为
2: 1+1 1/6*1/6=1/36
3: 2+1 1/6*1/6+1/6*1/6=1/18
4: 1+3 3+1 2+2 2*(1/6*1/6)+(1/6*1/6)=1/12
5: 1+4 4+1 2+3 3+2 1/9
6: 1+5 5+1 2+4 4+2 3+3 5/36
7: 1+6 6+1 2+5 5+2 3+4 4+3 1/6
8: 2+6 6+2 3+5 5+3 4+4 5/36
9: 3+6 6+3 4+5 5+4 1/9
10: 4+6 6+4 5+5 1/12
11: 5... 阅读全帖 |
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a*****g
发帖数: 1320 | 6 写得很清楚详细，我这个老文科生都看到懂了，谢谢！！！ |
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a*****g
发帖数: 1320 | 7 1) The solutions of x2 +bx+c=0 are each 5 more than the solution of x2+7x+3=
0. What are the value of b and c? Express your answer as an ordered pair (b,
c)
2) A cubic equation of the form x3+ bx2+cx+d==0 has solutions x=3, x=4 and x
=5. What are the value of b, c, and d? Express your answer as an ordered
triple (b,c,d)
3) What is the sum of the reciprocals of the solutions of x3-3x2-13x+15=0?
Express your answer as a common fraction
4) What is the sum of the squares of the solutions of x3-15x2... 阅读全帖 |
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m*********y
发帖数: 1735 | 8 1)
假设第二个方程的解是x1,x2，所以第一个方程的解就是(x1+5),(x2+5)
所以，x1+x2=-7,x1*x2=3;
b=-(x1+5)+(x2+5)=-(x1+x2)-10=-3
c=(x1+5)*(x2+5)=x1*x2+5(x1+x2)+25=3-35+25=-7
2)
{27+9b+3c+d=0 (1)
64+16b+4c+d=0;(2)
125+25b+5c+d=0;(3)
}
(2)-(1)=(4)
(3)-(2)=(5)
(5)-(4)=(6)
倒回去
b=-12 c=47; d=-60;
3) 假设三个根是x1,x2,x3
(x-x1)(x-x2)(x-x3)=0
x1x2+x2x3+x1x3=-13
x1+x2+x3=3;
x1x2x3=-15;
1/x1+1/x2+1/x3=(x1x2+x2x3+x1x3)/(x1x2x3)=13/15
4)the same way as above
x1^2+x2^2+x3^2=(x1+x2+x3)^2-(x1x2+x2x3+x1x3)=15^2-66=159
5)
almost the same
first solu... 阅读全帖 |
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a*****g
发帖数: 1320 | 11 1) What is the units digit of N in the following equation?
（3x3x3x3x3）/N =1/2 X 1/3 X 1/3
2) A rectangle with sides of length 5 units and 6 units that are parallel to
the x-axis and y-axis has one vertex at (1,3). What is the largest possible
sum of the coordinates of any of the other vertices of this rectangle? |
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m*********y
发帖数: 1735 | 12
N=(3*3*3*3*3)/(1/2*1/3*1/3)=3^7*2
3*3=9
3*9=27
3*27=81
3*81=243
个位以4为周期循环，所以3^7等于3^3的各位，就是7，乘以2，个位就是4
to
possible
矩形左下角是（1，3）时右上角坐标之和最大，所以右上角是（6，9），之和是15 |
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a*****g
发帖数: 1320 | 13 太感谢了。你解题的思路非常的清晰，简单明了，俺发自心底的葱白。 |
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a*****g
发帖数: 1320 | 15 1.At Marsh Mel Low Middle School 34 students play soccer, 36 students play
football and 29 students play basketball. Of these students 15 play both
soccer and football, 18 play both basketball and football and 13 play both
soccer and basketball. What is the smallest possible number of students
thatplay all three sports?
2. If x and y are two triangular numbers less than 100 that when added,
produce a sum that is a square number, what is the largest possible value of
x or y?
3. Suppose that six b... 阅读全帖 |
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c*b
发帖数: 3126 | 16 1.A -> soccer, B -> football, C -> basketball
假设同时玩ABC的有x人，如何求玩A的有多少人呢？
玩A和B的 + 玩A和C的 - 被重复计算的x <= 34 （因为还可能有人只玩A不玩别的）
15 + 13 - x <= 34
同理，
15 + 18 - x <= 36
13 + 18 - x <= 29 |
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r*******e
发帖数: 7583 | 18 lz是一位辅导孩子数学的文科妈妈，不容易的
play
both
value |
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s*o
发帖数: 257 | 19 那就发一个版面比较好，一文多发，还不是转载，总感觉有点那啥。。。 |
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l******n
发帖数: 55 | 21 这种妈妈一般都是自己把自己感动了，至于效果吗就无所谓了。 |
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a*****g
发帖数: 1320 | 22 Not everybody would like to answer my questions.You know the probability.
Sometimes, their answers are different and I need to dertimine which one is
right. Normally, I post them in SF, Seattle and THU because the smartest
people over there and THU is my priority board. |
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