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If a > 1, which of the following could be the value of $$(1+\frac{1}{a})^{-1}$$?

Indicate all such values.
$$0 < a < b < c$$

Quantity A

The standard deviation of the seven numbers $$-c, -b, -a, 0, a, b, c$$

Quantity B

The standard deviation of the seven numbers $$-c^{2}, -b^{2}, -a^{2}, 0, a^{2}, b^{2}, c^{2}$$




Quantity A

The standard deviation of data set Ⅰ

Quantity B

The standard deviation of data set Ⅱ


$$B_n=\frac{n}{n+1}$$ for all integers $$n$$ > 1.

$$C_n=B_n + B_{n-1}$$ for all integers $$n$$ > 2.

The integer $$k$$ is greater than 2.

Quantity A

$$C_k$$

Quantity B

$$\frac{2k^2-1}{k+k}$$


Sets R, S, and T are nonempty, and each has the same number of elements. The sets R∩S, R∩T, and S∩T are nonempty, and each has the same number of elements. The set R∩S∩T is empty. Set V consists of all the elements in R that are not in S.

Quantity A

3 times the number of elements in V

Quantity B

The number of elements in the set R∪S∪T




BC=DC

Quantity A

x

Quantity B

y




The figure shows a museum display illustrating the movement of a satellite around the Earth.The two circles shown are concentric, where the inner circle of radius 1 meter represents the Earth's equator and the outer circle of radius 2 meters represents the orbit of the satellite. The part of the equator in the range of the satellite is represented by the shorter arc AB. The satellite makes 6 revolutions around the equator per day. During one day,what is the total amount of time, in hours, that each point on the equator is in the range of the satellite?


From December 31, 1986, to December 31, 1995, approximately what was the average (arithmetic mean) annual increase, in square feet per year, of the total shopping area?


The shaded region in the xy-plane represents the surface of a pond. A length of 1 unit in the xy-plane represents 5 meters. The average depth of the water in the pond is 0.8 meter.Of the following, which is the best estimate of the total volume, in cubic meters, of the water in the pond?
From a group of 100 people including Alice and Bob, 40 people are to be randomly selected at the same time to win movie tickets. What is the probability that both Alice and Bob will be selected to win movie tickets?


The length of one side of the above quadrilateral is p, while the length of the other three sides are q, r, and s, respectively.

Quantity A

p

Quantity B

q+r+s


Machine K, working alone at its constant rate, produces 100 units of product Z in 2 hours. Machine L, working alone at its constant rate, produces 100 units of product Z in 3 hours. Machine M, working alone at its constant rate, produces 100 units of product Z in 4 hours.

Quantity A

The amount of time that it takes machines K, L, and M, working simultaneously at their respective constant rates, to produce 100 units of product Z

Quantity B

1 hour


A certain company has 50 printers that print at the same constant rate. Working continuously and simultaneously at that rate, it takes 9 of the printers 5 hours to complete print job A. Working continuously and simultaneously at that rate, it takes n of the printers 3 hours to complete print job A.

Quantity A

n

Quantity B

16




The two circles have centers at B and C, respectively, and are mutually tangent. Each circle has radius r.

Quantity A

The perimeter of quadrilateral ABCD

Quantity B

8r


At a factory, 7 identical machines,working independently, produce cat litter at the same constant rate. Working simultaneously, 5 of the machines take 14 minutes to produce 2,400 pounds of cat litter.How many minutes does it take all 7 machines, working simultaneously, to produce 3,600 pounds of cat litter?


A customer had 6 items dry-cleaned at the prices shown in the table. Each of the items was either a shirt or a pair of pants. If the total price for the dry cleaning was $14.00,how many shirts did the customer have dry-cleaned?
In a certain apartment complex,the probability that a household selected at random will be one that subscribes to newspaper T is 0.5 and the probability that a household selected at random will be one that subscribes to newspaper W is 0.3. If the probability that the selected household will be one that subscribes to both newspaper T and newspaper W is 0.1, what is the probability that the selected household will be one that subscribes to neither newspaper T nor newspaper W?


Quantity A

$$x$$

Quantity B

$$90$$


Let $$k$$ be a positive integer, and let $$n$$ be a random variable whose values are the integers from 1 to $$k$$. The probability distribution of $$n$$ is defined by $$P(n)=\frac{2n-1}{d}$$, where $$d$$ is a constant.

Quantity A

$$d$$

Quantity B

$$k^2$$


The four letters w, x, y, z are to be randomly sequenced.

Quantity A

The probability that w will precede x in the sequence

Quantity B

$$\frac{1}{2}$$


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