Basic Mathematics Homework Help

A small town has three gyms: Fit, Gymie and Hip. Each year Fit retains 70% of its members with 20% moving to Gymie and the rest to Hip. Gymie retains 60%, losing the rest in equal numbers to its rivals. Hip retains just 30% with 40% moving to Fit and 30% moving to Gymie. There are no other changes to the gym membership in the town. (a) If x= [1000, 800, 800] is a 3 x 1 matrix for the current numbers, show that it is possible to work out next year's membership figures by performing a matrix multiplication Ax, where A is a 3 x 3 matrix which should be stated. (b) Use matrix multiplication to work out the number of members in Fit 2 years from now. (a) A =

4) A diesel train traveled to New York and back. On the trip there it traveled 30 mph and on the return trip it went 45 mph. How long did the trip there take if the return trip took ten hours?

5) An aircraft carrier left Hawaii and traveled toward Tahiti at an average speed of 15 km/h. A container ship left three hours later and traveled in the same direction but with an average speed of 20 km/h. Find the number of hours the aircraft carrier traveled before the container ship caught up.

6) Ashley and Ted left the mall at the same time. They traveled in opposite directions. Ted traveled 0 km/h slower than Ashley. After one hour they were 40 km apart. Find Ashley's speed.

8) A container ship traveled to Madagascar and back. It took 2.6 hours less time to get there than it did to get back. The average speed on the trip there was 26.5 km/h. The average speed on the way back was 21.2 km/h. How many hours did the trip there take?

9) Molly can pour a large concrete driveway in seven hours. Matt can pour the same driveway in five hours. If they worked together how long would it take them?

QUESTION : how many cards in the 120th stage (REFER FIGURE ATTACHED )

Q.3) Suppose $50,000 is deposited at the end of each year into an account earning interest at 10% compounded annually. What is the value of the annuity at the end of 20 years?

- 4. A set designer for a play makes a whale tail out of a semicircle with an isosceles triangle cut out of it. What is the area of the whale tail? [ 5 mark] 5. A decorator is wallpapering a wall with a circular window of diameter 1.00 m. What is the area of the wall in square feet? (1 m - 3.2808 feet) [ 6 marks] 26mZ 6. A furniture designer builds a trapezoidal desk with a semicircular cutout. What is the area of the desk?

Chapter 6: The following expressions each represent the area of a parallelogram or rectangle. Draw an area model to represent each expression. For expressions in factored form, write the area. For the expressions in expanded form, write the dimensions. 1. a (a + 3) 2. a² + 10a + 25 3. -r (r+ 3) 4. c² - 25