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题目内容
In a large gym class, the teacher plans to group the students into teams for either volleyball or baseball. The volleyball teams would consist of 6 players each, while the baseball teams would consist of 9 players each. If the teacher attempts to group the students into volleyball teams, then there will be 2 students remaining who are not on a team. If the teacher instead attempts to group the students into baseball teams, which of the following could be the number of students remaining who are not on a team?
A rectangular plastic box with inside dimensions 6 inches by 5 inches by 4 inches is 85 percent full of water and contains nothing else.Several spherical lead balls with radius 1 inch will be placed in the water until the box is at least 90 percent full but less than 95 percent full. How many of these lead balls will be placed in the water? (Note: The volume of a sphere of radius r is $$\frac{4πr^3}{3}$$.)


In the triangle, $$r$$ is greater than 0.

Quantity A

$$t$$

Quantity B

$$5$$
In a poll, 600 people answered either “acceptable" or “not acceptable" to each of two questions; 514 answered "acceptable" to the first question, and 388 answered "acceptable" to the second question.

Quantity A

The number of polled people who answered "acceptable" to the first question and answered "not acceptable" to the second question

Quantity B

213
If $$0 \lt |x|-2x \lt 3$$, which of the following is true?
A shipment of 50 radios contains 2 that are defective. What is the probability that 2 radios picked at random and without replacement from the shipment will both be defective?
What is the units digit of the product $$(11^{10})(12^5)(13^3)(15)$$?


A social scientist conducted two experiments, experiment I and experiment II, in which the values 0, 1, 2, 3. and 4 were observed with the frequencies shown in the table above. Which of the following statistics are the same for the distribution of values observed in experiment I as they are for the distribution of values observed in experiment II?

Indicate all such statistics.
Each of Rachelle' s clients is a resident of one of four cities-$$R, S, T$$, or $$W$$. Of these clients, 20 percent are residents of City $$R$$, 25 percent are residents of City $$S$$, and $$x$$ percent are residents of City $$T$$. Which of the following expressions represent, for all possible values of $$x$$, the number of Rachelle's clients who are residents of City $$W$$ as a fraction of all her clients?

Indicate all such expressions.


In the figure above, $$AB$$, $$CD$$, and EF are circular arcs of radius 2, centered at the vertices of the triangle. What is the sum of the lengths of the three arcs?
For how many of the categories shown was the dollar amount of the expenditures in 1995 less than $1 billion?
Approximately what was the ratio of the dollar amount of the expenditures for prescriptions in 1995 to the dollar amount of the expenditures for prescriptions in 1970?
From 1970 to 1995, the dollar amount of expenditures for nursing home care increased by approximately what percent?
$$x$$ is a positive even integer.

Quantity A

The units digit of $$5x^3$$

Quantity B

2
Consider the numbers $$q$$, $$r$$, and $$s$$, where $$0 \lt q \lt r \lt 1 \lt s$$. Which of the following shows the five numbers $$r-q$$, $$\sqrt{r-q}$$, $$\sqrt{s+q}$$, $$(r-q)^{2}$$, and $$(s+r)^{2}$$ listed in order from least to greatest?
A gardener plans to cover a rectangular plot of land with pine bark mulch to a depth of 4 inches.The plot measures 8 feet by 12 feet, and the gardener will buy mulch packed in bags. If each bag contains 3.5 cubic feet of mulch and costs $6,what is the cost of the least number of bags that the gardener will need to cover the plot? (Note: 1 foot=12 inches.)
$$k=11,112,222,334$$ and $$n=111,122,334$$

Quantity A

The number of different 11-digit positive integers that are obtained by all possible orderings of the digits of the integer $$k$$

Quantity B

$$9$$ times the number of different 9-digit positive integers that are obtained by all possible orderings of the digits of the integer $$n$$
If $$n$$ is a number greater than $$1,000$$, which of the following is closest to the value of $$\frac{n^2-n-6}{n^2-9}$$?

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