Week 12/1 - 12/7 - Mix #2

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant value that relates two proportional quantities. It can be found by dividing one quantity by the other.

Front

If Lamont completed 1/8 of his science project in 2/3 of an hour, how do you find the total time to complete the project?

Back

To find the total time, set up a proportion: if 1/8 of the project takes 2/3 hours, then the total time (T) can be found using the equation: \( \frac{1/8}{T} = \frac{2/3}{1} \). Solving gives T = 5 1/3 hours.

Front

How do you calculate the total capacity of a phone's text message inbox if it is 88% full with 44 texts?

Back

To find the total capacity (C), use the equation: \( 0.88C = 44 \). Solving gives C = 50.

Front

What does a ratio of 5 to 3 represent in a real-world context?

Back

A ratio of 5 to 3 means that for every 5 dogs, there are 3 cats. This can be used to find the number of cats if the number of dogs is known.

Front

How do you calculate the total cost including sales tax?

Back

To calculate the total cost, add the prices of the items and then multiply by (1 + sales tax rate). For example, for a shirt costing $23.50 and a hat costing $15.25 with a 6.5% tax: Total = (23.50 + 15.25) * 1.065 = $41.27.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. It can be used to solve for unknown values.

Front

How do you find the constant of proportionality from a graph?

Back

The constant of proportionality can be found by selecting two points on the line, calculating the change in y (dependent variable) and the change in x (independent variable), and then dividing the change in y by the change in x.

Front

What is the formula for finding the total time if a part of a task is completed?

Back

The formula is: Total Time = (Time taken for part) / (Fraction of task completed).

Front

How do you set up a proportion to find an unknown quantity?

Back

To set up a proportion, write two ratios equal to each other. For example, if you know the ratio of dogs to cats and the number of dogs, you can set up: \( \frac{dogs}{cats} = \frac{5}{3} \).

Front

What is the significance of percentages in real-life applications?

Back

Percentages are used to express how much of a whole is represented by a part, such as discounts, tax rates, and statistics.