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# 一題機率問題，一題三角型問題，一題加法問題

Q2: The sum of the first k positive integers is equal to k(k+1)/2. What is the sum of the integers from n to m, inclusive , where 0<n<m?

答案是：m(m+1)/2-(n-1)n/2

答案為什麼有減號???

題目是問sum， n(n+1)/2+m(m+1)/2

請幫忙解說詳細謝謝!!

Q3: In triangle ABC, point X is the midpoint of side AC and point Y is the midpoint of side BC. If point R is the midpoint of line segment XC and if point S is the midpoint of line segment YC, what is the area of triangular region RCS ?

條件1: The area of triangular region ABX is 32.

條件2: The length of one of the altitudes of triangle ABC is18

答案是：條件1單獨成立。

我不懂耶?? 我RCS圖形劃出來，跟ABC圖形 不一樣，請指導我一下謝謝。為什麼條件1能成立呀!

Q4: On a certain transatlantic crossing ,20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?

答案是50%

0.6-0.2=0.4

為什麼是50% ，請解說謝謝。

### 2 Answers

- 玉米Lv 41 decade agoFavorite Answer
Q2:

The sum of the first k positive integers is equal to k(k+1)/2

這段話是解釋k個等加級數總合的為k(k+1)/2

What is the sum of the integers from n to m, inclusive , where 0<n<m?

題目要求n~m等加級數總合

依上式為(m-n+1)*(n+m)/2,m-n+1為數字個數,n+m為首項+末項

(m-n+1)*(n+m)/2=m(m-n+1)/2+n(m-n+1)/2

=m(m+1)/2-mn/2+mn/2+n(1-n)/2

=m(m+1)/2-n(n-1)/2

Q3:

△ABC的AC邊的中點為X,BC邊的中點為Y

XC邊的中點為R,YC邊的中點為S

△ABC相似△XYC相似△RSC

BC長=2*YC長,所以△ABC=4△XYC(因為底和高皆為△ABC1/2),同理△XYC=4△RSC

△ABX=1/2△ABC

其他的部分好像條件不足

Q4:

條件是實際有20%的乘客有票也有開車搭船

假設60%的乘客有票但沒有開車搭船

問實際有多少的乘客有票:P(T)

因為假設60%的乘客有票但沒有開車搭船:P(t&nc)

所以40%的乘客有票也有開車搭船:P(t&c)

P(T)*P(t&c)=0.2

P(T)*0.4=0.2

P(T)=0.5

Source(s): ME