A high school's graduating class has a mean graduating average of 63.7% with a standard deviation of 11.2%.
How many of the 460 graduates would expect to have a graduating average of 85% or higher?
Answer the question without the use of technology.
Explain what the value of the z-score associated with an average of 85% means in terms of the standard deviation
1 mark for showing work to find the probability
1 mark for correct probability
1 mark for correct number of students
1 mark for showing work to calculate the z-score
1 mark for explanation
Alex, Curtis and Michael go boating together on a calm day. They leave the marina dock and travel at a speed of 40 km/h due east for 3 hours. Then, they travel 22° west of south for 2 hours at a speed of 30 km/h. At that point, their boat breaks down and they call the mechanic at the marina dock to come and help them.
To get to them in the shortest time, how far must the mechanic travel and in what direction?
1 mark for an appropriate diagram
1 mark for finding the enclosed angle
1 mark for setting cosine law up properly
1 mark for finding the distances the boats travel
1 mark for finding the measure of angle A
1 mark for giving a correct direction
A company is experimenting with the pricing on a calculator. They currently average 200 daily sales at a price of $10. Research suggests that if they raise the price of the calculator by 50¢ that they will make 5 fewer sales. It costs the company $4 to manufacture a calculator.
a) Find an equation for the revenue the company will make.
b) Given that Profit = Revenue – Cost, find an equation for the profit the company can make.
c) What price should the company charge for a calculator in order to maximize the profit?