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题目内容
Vladimir invested $10,000 for one year. He invested some of the amount at 4 percent simple annual interest and the rest of the amount at 6 percent simple annual interest.

If the total interest earned for the year was between $450 and $550, which of the following statements must be true?.

Indicate all such statements.
The 50 students in an art class were given an assignment to visit two museums,A and B.During the week after the assignment was given, 25 of the students visited Museum A and 10 of those 25 students also visited Museum B.

Which of the following statements individually provide(s) sufficient additional information to determine how many of the students visited Museum B during that week?

Indicate all such statements.
Of the 120 first-semester students entering a certain college, $$\frac{3}{5}$$ registered for a statistics class and $$\frac{1}{2}$$ registered for a calculus class. Which of the following could be the number of first-semester students entering the college who registered for a statistics class but did not register for a calculus class?
Indicate all such possible numbers.
All of the 80 science students at a certain school are enrolled in at least one of three science courses: biology, chemistry, and physics. There are 60 students enrolled in biology, 50 students enrolled in chemistry, and 35 students enrolled in physics. None of the students are enrolled in all three courses. Which of the following could be the number of students enrolled in both chemistry and physics?
Indicate all such numbers.
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.
The sequence $$a_{1},a_{2},a_{3}.....a_{n}$$....is defined by $$a_{1}=2$$, $$a_{2}$$=3, and $$a_{n}$$=$$(a_{n－1})(a_{n－2})$$ for all integers n greater than 2. What is the value of $$a_{8}$$?
S={1, 2, 3}
T={1, 2, 3, 4}

Quantity A

The total number of 4-digit positive integers that can be formed using only the digits in set S

Quantity B

The total number of 3-digit positive integers that can be formed using only the digits in set T
What is the tens digit of $$\frac{39!}{29!}$$?
A telephone system has $$n$$ telephone lines. For each of the $$n$$ lines, the event that the line will fail during a certain reliability test has probability $$0.3$$, and these $$n$$ events are independent. If the probability that at least one of the $$n$$ lines will not fail during the reliability test is greater than $$0.99$$, what is the minimum value of $$n$$?
In 1998, how many of the imported towels were not imported from China?
If the average (arithmetic mean) number of towels imported from China per month was the same for the last 3 months of 2000 as it was for the first 9 months of 2000, approximately how many million dozen towels were imported from China during the 12 months of 2000?
In 1999, the ratio of the number of towels imported from China to the total number of towels imported from countries other than China was closest to which of the following?
For each value $$x$$ in a list of values with mean $$m$$, the absolute deviation of $$x$$ from the mean is defined as $$|x-m|$$.

A certain online course is offered once a month at a university. The number of people who register for the course each month is at least $$5$$ and at most $$30$$. For the past $$6$$ months, the mean number of people who registered for the course per month was $$20$$. For the numbers of people who registered for the course monthly for the past $$6$$ months, which of the following values could be the sum of the absolute deviations from the mean?

Indicate all such values.
How many positive two-digit integers have a remainder of 3 when divided by both 10 and 6?
In a certain election, $$\frac{3}{5}$$ of the voters in District K and $$\frac{1}{2}$$ of the voters in District P voted for the candidate Miguel Garcia. If 4 times as many people voted in District K as voted in District P, what percent of the voters in both districts combined voted for Miguel Garcia?
In a certain university, 60 percent of all sophomores are liberal arts majors, 24 percent are education majors, and the rest are majoring in other subjects or have not yet chosen a major. At the university, 55 percent of all sophomores are currently taking a psychology course. If $$x$$ percent of all sophomores are liberal arts majors who are currently taking a psychology course, what is the least possible value of $$x$$?
By draining 40 gallons of water from a tank, the amount of water in the tank was decreased from $$\frac{1}{5}$$ of the tank 's full capacity to $$\frac{2}{11}$$ of the tanks full capacity. Water was then added to the tank until the tank was full. How many gallons of water were added to the tank?
A tank initially contains $$g$$ gallons of water. Beginning at 1 o'clock in the afternoon, water flows into the top of the tank at a constant rate of $$x$$ gallons per minute and out of the bottom of the tank at a constant rate of $$y$$ gallons per minute. If $$ x \lt y$$, in how many minutes after 1 o'clock in the afternoon is the volume of water in the tank equal to $$\frac{1}{2}g$$, in terms of $$g$$, $$x$$, and $$y$$?
A certain charity is conducting a fund-raiser. For the first $9,000 raised by the charity, Company B will contribute $1 for every $3 collected by the charity. For any amount over $9,000 raised by the charity, Company B will contribute $2 for every $5 collected by the charity. How much money must the charity raise in order to reach a total of $68,000, including the contribution from Company B?
A saltwater solution contains $$25$$ percent salt by weight. To $$1$$ kilogram of this solution, $$x$$ grams of salt and $$4x$$ grams of water are added , where $$x \gt 0$$.

Quantity A

The percent of salt in the resulting solution

Quantity B

$$25%$$

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