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Fractions and Percentages

Mathematical Modelling

Please see the attached file for the fully formatted problems. A long, thin rod is clamped at its lower end and a mass M is attached to its upper end. The coordinates (x,y) of any point on it satisfy the equation. where E, I and a are constants. Given that x = 0 when y = 0 and x = a when y = L show that where H

Terminating and Repeating Decimals

State whether each of the following fractions is a terminating or repeating decimal. If the decimal terminates, state the number of decimal places and show how you decided. If the decimal repeats, write the decimal representation of the fraction. A. 12/13 B. 6/ 2^2 x 5^7 x 3 (there are no brackets in this questions and th

Word Problems : Percentages

A. In five years the price of a house in Vancouver is expected to be about 164% of today's price. If the trend continues, what percent of today's price would you expect the price of a house to be in 15 years? B. The sum of two numbers is 24. One number is increased by 50% while the other is decreased by 50%. The sum of the tw

Order repeating decimals

Determine whether the following are equal. If not, which is smaller, and why? _ 0.2525 (the line should be over the last 25) _ 0.2525 (the line should be over the entire 2525)


5/8, 3/16, 7/5, 9/10. Find the reciprocals of the given numbers and order them from smallest to largest. What do you observe about the order.

A binary relation is defined on the set R of all real numbers. The problem is to prove that that binary relation is indeed an equivalence relation, and that there is a (well-defined) bijection between the set of equivalence classes and the set {x: x is a real number and 0 <= x < 1}.

Show that == (where == is the equivalence relation defined below) is an equivalence on A, and find a (well-defined) bijection %: A== -> B, where (a) A = R (the set of all real numbers) (b) B={x: x is an element of R and 0 <= x < 1} (c) for real numbers x and y, "x==y" (x is equivalent to y) if and only if x - y is an e

Subtraction of Fractions

From central parking it is 9/10 of a mile to the science building. Bob started at central parking and walked 1/5 of a mile toward the science building. He stopped for coffee. When he finished how much farther did he have to walk to reach the science building?

Area Calculation

A hallway measures 8 1/6 yards by 5 1/7 yards. How many square yards is the area of the hallway?

Simulation using the 8 steps model

John decides to set up a music group with his even best friends. The group will work only if at least five of his friends can join. Using simulation, answer the following: 1. If John thinks that there is a 50% chance that each of his friends will join the group, can you estimate the probability of getting at least five frien

One equality

Hello! The attached file is the answer an OTA gave me to a problem I was having. There is one line in the reasoning I do not understand, and I have highlighted it in red. I would be very grateful if someone could explain it to me.

Circle (pie) graph and percentages

Construct a circle graph, with sectors given in percent, to represent the data in the given table. Favorite Restaurant Style / Number of Responses Chinese/ 138 Indian/ 90 Mexican /144 Thai/ 108 Answer the question appropriately. How many people were surveyed?

Circle graph and percentage

Use the circle graph to solve the problem. A survey of the 8263 vehicles on the campus of State University yielded the following circle graph. motorcycles 9% concertibles hatchbacks 16% 35% vans 7%

Calculating the percentage change in an algebraic word problem.

A consumer information magazine estimates that the real juice content of several drinks sold as snack drinks for children was 79.5% in 1999, compared to 86.25% in 1998. The percentage change in real juice content is: a. -7.83% b. -6.75% c. 6.75% d. 8.5%

Understanding sequencing and fraction differences.

Context: It would normally follow on from work on sequences and fractions Question: Ruth was investigating fraction differences. She wrote down this sequence of fractions: 1/1, 1/2, 1/3, 1/4, 1,5 1,6 ... ... Then she worked out the difference between the consecutive fractions: 1/2, 1/6, 1/12, 1/20, 1/30, .. .. Sh