试卷名称:GRE(QUANTITATIVE)综合模拟试卷21

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Martha invited 4 friends to go with her to the movies. There are 120 different ways in which they can sit together in a row of 5 seats, one person per seat. In how many of those ways is Martha sitting in the middle seat?  

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In the xy-plane, find the following. (a)Slope and y-intercept of the line with equation 2y + x = 6 (b)Equation of the line passing through the point(3,2)with y-intercept 1 (c)The y-intercept of a line with slope 3 that passes through the point(-2,1) (d)The x-intercepts of the graphs in(a),(b), and(c)
For the circle(x- 1)2 +(y+ 1)2= 20 in the xy-plane, find the following. (a)Coordinates of the center (b)Radius (c)Area
For each of the following functions, give the domain and a description of the graph y =f(x)in the xy-plane, including its shape, and the x- and y-intercepts. (a)f(x)= -4 (b)f(x)= 100 - 900x (c)f(x)= 5-(x + 20)2 (d)f(x)=[*] (e)f(x)= x+|x|
If the decagon in exercise 4 is regular, what is the measure of each interior angle?
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Suppose that a computer password consists of four characters such that the first character is one of the 10 digits from 0 to 9 and each of the next 3 characters is any one of the uppercase letters from the 26 letters of the English alphabet. How many different passwords are possible?
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Consider an experiment with events A, B, and C for which P(A)= 0.23, P(B)= 0.40, and P(C)= 0.85. Suppose that events A and B are mutually exclusive and events B and C are independent. What are the probabilities P(A or B)and P(B or C)?
A group of 20 values has a mean of 85 and a median of 80. A different group of 30 values has a mean of 75 and a median of 72. (a)What is the mean of the 50 values? (b)What is the median of the 50 values?
Martha invited 4 friends to go with her to the movies. There are 120 different ways in which they can sit together in a row of 5 seats, one person per seat. In how many of those ways is Martha sitting in the middle seat?
A talent contest has 8 contestants. Judges must award prizes for first, second, and third places, with no ties. (a)In how many different ways can the judges award the 3 prizes? (b)How many different groups of 3 people can get prizes?
In a box of 10 electrical parts, 2 are defective. (a)If you choose one part at random from the box, what is the probability that it is not defective? (b)If you choose two parts at random from the box, without replacement, what is the probability that both are defective?
In the figure below, AC = BC. Find the values of x and y. [*]
In the figure below, what is the relationship between x, y, and z? [*]
In the figure below, AB = BC = CD. If the area of triangle CDE is 42, what is the area of triangle ADG? [*]
If W is a random variable that is normally distributed with a mean of 5 and a standard deviation of 2, what is P(W > 5)? Approximately what is P(3 < W < 7)? Which of the four numbers 0.5,0.1,0.05, or 0.01 is the best estimate of P(W < -1)? [*]
DISTRIBUTION OF CUSTOMER COMPLAINTS RECEIVED BY AIRLINE P, 2003 AND 2004 [*] (a)Approximately how many complaints concerning credit were received by Airline P in 2003? (b)By approximately what percent did the total number of complaints decrease from 2003 to 2004? (c)Based on the information in the table, which of the following statements are true? I. In each of the years 2003 and 2004, complaints about flight problems, baggage, and customer service together accounted for more than 50 percent of all customer complaints received by Airline P. II. The number of special passenger accommodation complaints was unchanged from 2003 to 2004. III. From 2003 to 2004, the number of flight problem complaints increased by more than 2 percent.
FINISHING TIMES AND TRAINING INDICES FOR 50 BICYCLISTS IN A RACE [*] A bicycle trainer studied 50 bicyclists to examine how the finishing time for a certain bicycle race was related to the amount of physical training in the three months before the race. To measure the amount of training, the trainer developed a training index, measured in “units“ and based on the intensity of each bicyclists training. The data and the trend of the data, represented by a line, are displayed in the scatterplot above. (a)How many of the 50 bicyclists had both a training index less than 50 units and a finishing time less than 4.5 hours? (b)What percent of the 10 fastest bicyclists in the race had a training index less than 90 units?
[*] The figure above shows a normal distribution with mean m and standard deviation d, including approximate percents of the distribution corresponding to the six regions shown. Suppose the heights of a population of 3,000 adult penguins are approximately normally distributed with a mean of 65 centimeters and a standard deviation of 5 centimeters. (a)Approximately how many of the adult penguins are between 65 centimeters and 75 centimeters tall? (b)If an adult penguin is chosen at random from the population, approximately what is the probability that the penguins height will be less than 60 centimeters? Give your answer to the nearest 0.05.

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