The faces of a cube are numbered 1, 2, 3, 4, 5, and 6, respectively. Whenever the cube is rolled, each number is equally likely to appear on the top face after the roll. The cube is to be rolled twice. What is the probability that the number appearing on the top face after the second roll will be different from the number appearing on the top face after the first roll?
Give your answer as a fraction.
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One student is to be selected at random from a class. The probability that the student selected will be male is equal to the probability that the student selected will be an English major. The probability that the student selected will be both male and an English major is 0.35. The probability that the student selected will be neither male nor an English major is 0.15. What is the probability that the student selected will be an English major?
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Marina's total monthly salary consists of a base monthly salary of $400 plus a commission equal to 10 percent of her sales up to a certain amount and a commission of 20 percent on any additional sales in excess of that amount. Last month Marina's sales were $12,000, and her total monthly salary was $2,000. What is the amount of sales at which the commission rate changes from 10 percent to 20 percent?
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A certain teacher determines the grade on an assignment by first finding the percent of questions that are answered correctly and then, if the assignment was handed in late, deducting 7 percentage points from the grade for each day that the assignment was late. If Tim answered 3 of the 25 questions incorrectly and handed the assignment in to this teacher 2 days late, what grade did he receive on the assignment?
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Each salesperson in a retail store is paid a commission based on the amount of his or her daily sales. For daily sales up to and including $200, the commission is $$r$$ percent of the daily sales. For daily sales over $200, the commission is $$2r$$ percent of the daily sales. On Friday, Amanda had daily sales of $300 and Bill had daily sales of $200. If the total of Amanda' s and Bill' s commissions on Friday was $40, what is the value of $$r$$?
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Nancy has a job where she is paid at a regular hourly rate for the first 40 hours that she works each week. For each hour that Nancy works each week in excess of the first 40 hours, she is paid 1.5 times her regular hourly rate. Nancy worked 35 hours during the first week of last month and 50 hours during the second week of last month. If Nancy was paid $270.00 more during the second week than during the first week, what is her regular hourly rate?
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Each time a certain coin is tossed, the coin lands either heads up or tails up. For any given toss, the probability that the coin will land heads up is equal to the probability that the coin will land tails up. The coin is to be tossed $$n$$ times. What is the least possible value of $$n$$ such that the probability of the coin landing heads up $$n$$ times in a row is less than $$0.05$$?
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In a legislature with 360 members, each member is in one of two political parties, either A or B. Party A has 110 members, and Party B has 250 members. In order for a certain bill to pass in the legislature, at least two-thirds of all the members must vote in favor of the bill. If 50 percent of the members of Party A and $$p$$ percent of the members of Party B will vote in favor of the bill, what is the least value of $$p$$ for which the bill will pass?
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A rectangular coordinate grid was created to represent the location of three campsites in a certain flat region. The centers of the three campsites are located at the points (0, 0), (0, 600), and (450, 300) on the grid, where 1 unit on each axis represents 1 meter. The center of a water fountain in the region is equidistant from the centers of the three campsites. What point on the grid represents the location of the center of the water fountain?
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There are two overlapping circular regions on a level field, and the centers of the regions are 40 meters apart. One circular region has a radius of 25 meters, and within the region there is a marker located 5 meters away from its border. The other circular region has a radius of 30 meters, and within the region there is a marker located 7 meters away from its border. What is the greatest possible distance, in meters, between the two markers?
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In a certain city, each of the 30 days last April was classified as either sunny or cloudy. There were 24 sunny days in the city last April, and there were 20 days with a daily maximum temperature of at least 80℉. Which of the following statements individually provide(s) sufficient additional information to determine the number of cloudy days in the city last April with a maximum temperature of less than 80?
Indicate all such statements.
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A collection of pottery shards consists of shards from three archaeological sites, R, S, and T. For the shards from R, the least length is 1.3 centimeters and the range of the lengths is 8.7 centimeters. For the shards from S, the least length is 2.4 centimeters and the range of the lengths is 9.6 centimeters. For the shards from T, the least length is 0.6 centimeter and the range of the lengths is 10.2 centimeters. What is the range of the lengths of all the shards in the collection?
_____centimeters
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The students in a home economics class are making a set of vertical blinds to cover a window that is 6 feet high by 8 feet wide. Each vertical blind in the set is hung so that it is 6 feet high, 2 inches wide, and overlaps each blind next to it by $$\frac{1}{2}$$ inch. What is the least number of blinds needed to cover the window? (12 inches = 1 foot)
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From the time a manufacturer's assembly line begins operating for the day, an inspector checks every $$12^{th}$$ item as it comes off the line, beginning with the $$12^{th}$$ item, and another inspector checks every $$28^{th}$$ item, beginning with the 28th item. If the $$n^{th}$$ item coming off the line is the first item that is checked by both inspectors, what is the value of $$n$$?
$$n$$=__________
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Each of three tall buildings has a light that flashes on its roof to warn low-flying aircraft. One light flashes every 3 seconds, another light flashes every 4 seconds, and the third light flashes every 6 seconds. If the three lights flash at precisely the same moment, what is the least number of seconds after which the three lights will flash again at the same moment?
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Then are between 40 and 70 members in a certain club. If 1 member is absent then the remaining members can be divided into groups of 4 members each with no members left over. If 2 members are absent, then the remaining members can be divided into groups of 5 members each with no members left over. How many members are in the club?
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Last year a youth organization sold candy bars for $1.50 each for a fund-raiser. This year the organization members plan to repeat the fund-raiser, but they project that the number of candy bars sold will be reduced from last year's number by 1/3 of the number sold last year. If this projection is correct, what price per candy bar would result in the same total amount of revenue this year as last year?
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The families that owned directly held stocks in 1992 owned an average (arithmetic mean) of $10,000 per family in these stocks. The families that owned cash-value life insurance owned an average of $4,000 per family in this type of insurance. Which of the following is closest to the ratio of total family assets in directly held stocks to total family assets in cash-value life insurance?
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