Jerry worked for one day on a project that he could have completed alone in nine days. Bill joined Jerry the next day, and they worked together for exactly three days to complete the project. How much of the job did Bill do in those three days? Express your answer as a common fraction.
Naming clockwise, regular pentagon COUNT has vertices C, O, U, N, T, respectively. Point X is right in the center of this pentagon so that line segments from X to each vertex create congruent triangles. If point C is rotated 144° counterclockwise about the point X, what original vertex is the image of point C?
The four points A (−4, 0), B (0, −4), X (0, 8) and Y (14, k) are graphed on the Cartesian plane. If segment AB is parallel to segment XY, what is the value of k?
The preimage of square ABCD has its center at (8, −8) and has an area of 4 square units. The top side of the square is horizontal. The square is then dilated with the dilation center at (0, 0) and a scale factor of 2. What are the coordinates of the vertex of the image of square ABCD that is farthest from the origin?
A car is scheduled to make a 616-mile trip in 9 hours. The car averages 60 mph during the first 240 miles and 80 mph during the next 160 miles. What must the average speed of the car be for the remainder of the trip in order for the car to arrive on schedule?
The new Perry Hotter book will have a cover price of $25. The local bookstore is offering two discounts: $4.00 off and 20% off. A clever shopper realizes that the prices will be different depending on the order in which she claims her discounts. How much more money will she save by taking the better-valued approach rather than the other approach? Express your answer in cents.
The area of square I is 1 square unit. A diagonal of square I is a side of square II, and a diagonal of square II is a side of square III. What is the area of square III?
Triangle ABC has vertices with coordinates A(2, 3), B(7, 8) and C(−4, 6). The triangle is reflected about line L. The image points are A’(2, −5), B’(7, −10) and C’(−4, −8). What is the equation of line L?
Ayushi has six coins with a total value of 30 cents. The coins are not all the same. Two of Ayushi’s coins will be chosen at random. What is the probability that the total value of the two coins will be less than 15 cents? Express your answer as a common fraction.
Ryosuke is picking up his friend from work. The odometer on his car reads 74,568 when he picks his friend up, and it reads 74,592 when he drops his friend off at his house. Ryosuke’s car gets 28 miles per gallon, and the price of one gallon of gas is $4.05. What was the cost of the gas that was used for Ryosuke to drive his friend home from work?
A set of data includes all of the positive odd integers less than 100, the positive, two-digit multiples of 10, and the numbers 4, 16 and 64. All included integers appear exactly once in the data. What is the positive difference between the median and the mean of the set of data? Express your answer as a decimal to the nearest thousandth.
A rectangular solid box measures 2.75 feet by 4.05 feet by 480 inches. In cubic yards, what is the volume of the box? Express your answer as a decimal to the nearest tenth.
Rex runs one mile in 5 minutes, Stan runs one mile in 6 minutes and Tim runs one mile in 7 minutes. There are 5280 feet in one mile. By how many feet does Tim trail Stan at the moment that Rex completes a one-mile run? Express your answer as a decimal to the nearest tenth.
What is the 25th number in the pattern: 1, 2, 3, 5, 7, 10, 13, 17, 21, 26 …?
The positive square root of 200 is what percent larger than the positive square root of 121? Express your answer to the nearest whole number.
Due to bowling a score of 204 in his last game, Remy raised his average from exactly 156 to exactly 158. What score must he bowl in the next game to raise his overall average to exactly 159?
Of all the four-digit positive integers containing only digits from the set {2, 4, 6, 8}, what fraction of them have at least one of their digits repeated? Express your answer as a common fraction
Twenty-nine is the shortest leg of a right triangle whose other leg and hypotenuse are consecutive whole numbers. What is the sum of the lengths of the other two sides?
The formula for the volume of a sphere is V = (4/3)πr\(^3\) , where r is the radius of the sphere. Alex places a particular sphere into a cubic box with sides of 10 meters. If the sphere is tangent to each of the box’s faces, what is the volume of the sphere? Express your answer as a decimal to the nearest tenth.