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题目内容
In transit, the probability that plates crack is $$\frac{1}{2}$$, the probability that plates break is $$\frac{2}{3}$$, while the probability that plates crack and break is $$\frac{1}{3}$$. If 80 plates neither crack nor break when a batch of plates arrive, then how many plates arrive in total?
At a certain university, 60% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?
In a graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students that could have taken both algebra and chemistry?
Professor Lopez is teaching three different courses with an average (arithmetic mean) enrollment of 32 students per course. If 5 students are taking two of these courses, 3 other students are taking all three courses, and all of the others are taking only one of the courses, what is the total number of different students enrolled in the three courses?
There are 500 students in a class. 450 of them take Course A, 300 of them take Course B, and 150 of them take Course C. Each student has to take at least one course, and 100 of them take all the three classes simultaneously. The number of students who take both Course A and Course B, but not Course C could be? Indicate
all
such possible values.
Three students need to read 50 proposals. Each proposal has to be read by at least one student. Student A read 38 of them, Student B read 36 of them, while Student C read 28 of them. At least how many proposals are read by at least two students?
List A:
4, 6, 8, 10, 12, 14- The above list of numbers is formed by adding 2 to each of the preceding term What is the 54th term of the list?
The first term of sequence K is 7 and the last term is 217. Each term after the first is 2 greater than the previous term. How many terms are in sequence K?
A certain holiday is always on the fourth Tuesday of Month X. If Month X has 30 days, on how many different dates of Month X can the holiday fall?
In a sequence, for any integer n greater than 1, $$a_{n}$$ is greater than its preceding term by 3 and $$a_{17}$$ is 55.
Quantity A
$$a_{98}$$
Quantity B
300
What is the sum of all the odd integers between 3 and 97, inclusive?
$$Q_{n}=3Q_{n-1}$$
Quantity A
$$Q_{28}$$
Quantity B
$$Q_{11}$$
In a sequence, $$S_{1}=5$$, $$S_{n}=2*S_{n-1}$$
Quantity A:
$$S_{8}$$
Quantity B:
$$S_{21}/S_{13}$$
Sequence $$S$$: $$a_{1}, a_{2}, a_{3},......,a_{n}$$........
In sequence $$S$$, $$a_{1}$$ is an integer and $$a_{n}=2a_{n-1}$$ for all integers n greater than 1. If
no
term of sequence S is a multiple of 100, which of the following could be the value of $$a_{1}$$?
Indicate
all
such values.
In a sequence, $$a_{1}$$=1, for any integer n greater than 1, $$a_{n}$$ is 12 times the square of its preceding term. If $$a_{5}$$=$$12^{n}$$, then what is the value of n
Eugene and Penny started a job in sales on the same day. Eugene's sales for the first month were r dollars and each month after the first his sales for that month were twice his sales for the preceding month. Penny's sales for the first month were 10r dollars, and each month after the first her sales for that month were 10r dollars more than her sales for the preceding month. Which of the following statements are true? Indicate
all
such statements.
In a certain sequence of numbers, each term after the first term is found by multiplying the preceding term by 2 and then subtracting 3 from the product. If the 4th term in the sequence is 19, which of the following numbers are in the sequence? Indicate
all
such numbers.
Sequence A:
1, –3, 4, 1, –3, 4, 1, –3, 4, ... In the sequence above, the first 3 terms repeat without end. What is the sum of the terms of the sequence from the 150th term to the 154th term?
A list of numbers could be summarized into $$S_{n}=n•(-1)^{n}$$ (n is a positive integer), and $$S_{1}=-1$$. What`s the sum of $$S_{1}$$, $$S_{2}$$, $$S_{3}$$, ......, $$S_{97}$$, $$S_{98}$$, $$S_{499}$$?
In a sequence, $$a_{1}=4$$, $$a_{2}=2$$. If for any n greater than 2, $$a_{n}=a_{n-1}+a_{n-2}$$, then how many terms in the first 60 terms are multiples of 3?
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