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题目内容
One of the vice presidents will be chosen at random. What is the probability that the vice president chosen will be one whose age is greater than 63 years given that the age of the corresponding president is less than 53 years?

Give your answer as a fraction.
Two bags, A and B, each contain marbles some of which are green. If one marble is selected at random from each bag, the probability is $$\frac{1}{21}$$ that both of the marbles selected will be green. If one marble is selected at random from bag A only, the probability is $$\frac{5}{21}$$ that the marble selected will be green. If one marble is selected at random from bag B only, what is the probability that the marble selected will be green?

Give your answer as a fraction.


In the rectangular coordinate plane, (x, y) is a point on the circle with center O and radius 1, and xy ≠ 0.

Quantity A

|$$x^3 + y^3$$|

Quantity B

1


The total number of calories from carbohydrates in a single serving of Trail Mix is approximately what percent of the total number of calories in the serving?


A certain candy bar contains a total of 28 grams of fat. The total number of grams of fat in the candy bar is what percent greater than the total number of grams of fat in one bag of Trail Mix?


Which of the following expressions gives the number of grams of Trail Mix that contain N grams of saturated fat?


The graph of the ellipse with equation $$x^2+4y^2=4$$ is show in the xy-plane. Circle C (not shown) has its center at the point (-1, 0) and a radius of 1. At how many points does the graph of circle C intersect the graph of the ellipse?


In the rectangular coordinate system shown, how many of the five points $$Q$$, $$R$$, $$S$$, $$T$$, and $$U$$ have coordinates that satisfy the inequality $$y \gt -x+3$$?
In the 3-digit positive integer N, the hundreds digit is m, the tens digit is s, and the units digit is p.

Quantity A

N

Quantity B

m+10s +100p
If x and y are negative integers, which of the following must be a positive integer?
$$P$$, $$Q$$, and $$R$$ are consecutive multiples of 3, and $$P \lt Q \lt R.$$

Quantity A

$$P+Q+3$$

Quantity B

$$Q+R-3$$
y ≠ 0

Quantity A

$$\frac{\frac{2}{3}y+\frac{2}{3}y+\frac{2}{3}y}{3y}$$

Quantity B

$$\frac{2}{3}$$
Grace earned a total of d dollars for completing h hours of work. For completing h-2 hours of work, Mildred earned the same total amount that Grace earned for completing h hours of work. In terms of d and h, by how many dollars did the average amount Mildred earned per hour exceed the average amount Grace earned per hour?
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
Two officers, stationed at opposite ends of a 1.5-mile zone where the speed limit is 40 miles per hour, use stopwatches and two-way radios to check speeds through the zone. A certain driver traveled through the entire zone in exactly 108 seconds. If the penalty for speeding in this zone is $50 plus $10 for each mile per hour that the driver exceeded the speed limit, how much should the penalty be for this driver?
$$2^{3x}=4^{2y}$$[/br] x > 0 and y > 0

Quantity A

x

Quantity B

y

Quantity A

$$(\frac{2^{3}}{3^{2}})^{4}$$

Quantity B

$$(\frac{2^{-3}}{3^{-2}})^{-4}$$
The advertised size of a television is the length of the diagonal of the rectangular viewing screen. For a television advertised as 42-inch, if the ratio of the lengths of the sides of the viewing screen is 16 to 9. approximately what is the area, in square inches, of the viewing screen?


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

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