How many different ways can the letters in the name HANK be scrambled so that the newly created “words” start and end with a consonant and are not HANK?

A line through point P(4, 3) is parallel to the line x – 2y = 8. What is the equation of the line through point P? Express your answer in slope-intercept form where the slope is a common fraction. 

Three standard, six-sided dice are rolled. The sum of the three numbers on top is less than 6. What is the probability that all three dice show a 1? Express your answer as a common fraction.

Fantasy gum is sold in 3-ounce and 10-ounce packages. One pound is equal to 16 ounces. If 76 packages were sold at B-Rite Mart last month and the total weight sold was less than 16 pounds, what is the greatest number of 10-ounce packages B-Rite could have sold?

Four children (Alice, Brad, Cathy and Dan) are arranged in a line. If Brad and Cathy cannot be next to each other, in how many ways can the four children be arranged?

If $1000 is invested at 6% annual interest compounded semiannually, how much interest has been earned at the end of one year?

In regular octagon ABCDEFGH, what is the ratio of the area of triangle ADF to the area of triangle AHF? Express your answer as a decimal to the nearest hundredth.

 Exactly one of the following statements is true. Which one? Why? 

A. Exactly one of these statements is false.

B. Exactly two of these statements are false.

C. Exactly three of these statements are false.

D. Exactly four of these statements are false.

E. Exactly five of these statements are false.

 Mr. Davidson lives 30 miles from his office. Driving to work on Monday, he averaged 50 mph. However, during his return trip from work, there was construction that slowed traffic. Mr. Davidson averaged only 20 mph going home. How many hours did Mr. Davidson spend traveling to and from work on Monday? Express your answer as a decimal to the nearest tenth. 

Tria’s new car can get 50% more miles per gallon of gasoline than her old car could. If her new car gets 24 miles per gallon, how many gallons of gasoline will she save using her new car to travel 480 miles to visit relatives in comparison with driving the old car the same distance? Express your answer to the nearest whole number.

If x and y are two triangular numbers less than 100 that when added, produce a sum that is a square number, what is the largest possible value of x or y? 

At Marsh Mel Low Middle School 34 students play soccer, 36 students play football and 29 students play basketball. Of these students 15 play both soccer and football, 18 play both basketball and football and 13 play both soccer and basketball. What is the smallest possible number of students that play all three sports?  

 Suppose that six brothers (George, John, Thomas, Fred, Andrew, Martin) each roll a fair 6-sided die. At least three of them have rolled an even number. What is the probability that John, Fred and Martin have each rolled an even number? Express your answer as a common fraction.

 Of the 2000 students in Houston High School, 70% are male. How many male students must be moved to another school so that 60% of the Houston High student body will be males?

Running at 12 miles per hour burns about 1200 calories per hour. Running at 5 miles per hour burns about 450 calories in an hour. How many minutes longer does one have to run to burn 300 calories at 5 miles per hour than at 12 miles per hour?

 If ABCDEFGH is a regular octagon with sides of length 2 cm, what is the area, in square centimeters, of triangle ABC? Express your answer in simplest radical form.

The cycle shop sells only bicycles and tricycles. All the bicycles have two wheels and all the tricycles have three wheels. If you add up the total wheels on the 67 cycles in the shop, you get 157 wheels. How many tricycles are in the shop?  

What is the units digit of N in the following equation? \(\dfrac{3.3.3.3.3}{N}=\dfrac{1}{2}.\dfrac{1}{3}.\dfrac{1}{3}\)

A rectangle with sides of length 5 units and 6 units that are parallel to the x-axis and y-axis has one vertex at (1, 3). What is the largest possible sum of the coordinates of any of the other vertices of this rectangle?

In base b, 321 – 123 = 154. What is the value of b?