In right triangle ABC, the median to the hypotenuse has length 15 units and the altitude to the hypotenuse has length 12 units. What is the length of the shorter leg of triangle ABC? Express your answer in simplest radical form. 

 Yesterday Alice drove one hour longer than Bob at an average speed that was five miles per hour faster than Bob's speed. Clark drove two hours longer than Bob at an average speed that was ten miles per hour faster than Bob's speed. Alice drove 50 miles more than Bob. How many more miles than Bob did Clark drive? 

 For how many integer values of x is the following inequality true? -5 ≤ 2x – 7 ≤ 21 

Marketing analysts are investigating cylindrical packaging for a new beverage called Star Juice. One member of the design team proposed a can that has a diameter of 6 cm and a height of 20 cm. Another suggested a can that is 17 cm tall and has a diameter of 8 cm. What is the ratio of the smaller volume to the larger volume? Express your answer as a common fraction.

 A jar contains $5.00 in quarters, $5.00 in dimes, $5.00 in nickels and $5.00 in pennies. If Connie randomly chooses one coin from the jar, what is the probability that the coin chosen is a dime? Express your answer as a common fraction.  

 A set of 5 positive integers has a mean of 11, a median of 10 and a unique mode of 7. What is the greatest possible range of the set of integers? 

A manufacturing plant periodically opens a large valve at the top of a tank to pump water into the tank for use in a manufacturing process. When the valve is opened, water is pumped into the tank at a rate of 75 gallons per minute. Another valve, at the bottom of the tank, sends water out of the tank to an assembly line at a rate of 24 gallons per minute. Both valves are opened simultaneously at 7:30 am and begin filling the empty tank. At what time, to the nearest minute, will the tank be filled to its 600-gallon capacity? 

Point P is on the y-axis and is equidistant from the points (1, 3) and (7, 5). What is the y-coordinate of point P? 

Six points are equally spaced around a circle. If three of the points are selected at random, what is the probability that they form a scalene triangle? Express your answer as a common fraction.  

 A bag contains five red marbles, three blue marbles and two green marbles. If six marbles are drawn without replacement from the bag, what is the probability that two marbles of each color are drawn? Express your answer as a common fraction. 

A circular garden is placed inside a rectangular patio that measures 20 feet by 14 feet. The circular garden is tangent to three sides of the rectangular patio, as shown. What percent of the patio is outside of the garden? Express your answer to the nearest whole number. Use \(\dfrac{22}{7}\) as an approximation for π.

Mr. Kelly is building a 60-foot-long ramp that will be 24 feet high at the highest point. He wants to place a vertical support beam under the ramp with its top 15 feet down the length of the ramp. How long does he need to make the support beam?

Isosceles trapezoid ABCD has bases with lengths 12 and 24. Points E and F are the midpoints of legs AB and CD, respectively. Points G and H are the midpoints of bases AD and BC, respectively. If the height of the trapezoid is 6 units, what is the difference between the areas of trapezoid ABCD and parallelogram HFGE? Draw the figure.

Stella sells 30 gismos a month at a price of $20 per gismo. She notices that each time she raises the price of a gismo by $4, she sells 2 fewer gismos per month. What is the maximum amount of revenue, in dollars, that Stella can make in a month of selling gismos? 

In order to send his DVD player back to the manufacturer for repair, Jeremy must pack it securely. He has a packing box with internal dimensions 22” × 18” × 6”. The DVD player is a rectangular prism with dimensions 15” × 12” × 2”. He has a box with external dimensions 3” × 3” × 8” for the power cord, which also will go inside the packing box. How many cubic inches of packing material must he put in the packing box to fill it completely?

How many miles can Scotty ride on a bike, going at the rate of 8 miles per hour, if he must walk back to the starting point at a rate of 3 miles per hour (following the same route he traveled on his bike) and he is to be gone a total of 11 hours?  

Tria paid $11,500 for a new car after the original price was reduced by a rebate of $4500. What percentage of the original price did Tria pay for the car? Express your answer to the nearest tenth

 In math class, the mean test score for the girls was 92 points and the mean test score for the boys was 87 points. If 12 girls and 10 boys took the test, what was the mean test score for the whole class? Express your answer as a decimal to the nearest hundredth. 

Two apples, five bananas and one carrot cost a total of $2.05. Three apples, one banana and four carrots cost a total of $1.89. Three apples, two bananas and three carrots cost a total of $1.98. What is the total cost, in cents, of one apple, one banana and one carrot?  

The graphs of y = x\(^2\) – 8x – 35 and y = –2x\(^2\) + 16x + 3 intersect in two points. What is the sum of the x-coordinates of the two points of intersection?