Question

vocabulary
for problems 1 - 5, choose the correct term or terms from the vocabulary box to label each boxed number.
1.
2.
3.
4.
5.
concepts and skills

1. complete the table to show the total changes and the average (mean) daily changes in the prices of four stocks over a 5 - day period.
2. an equation is shown, where ( alt0,cgt0 ), and ( |a|gt|c| ).

( acdot b = c )
which statements about the value of ( b ) are true?
( blt0 )
( |b|lt1 )
( bgt0 )
( |b|lt0 )
( bgt1 )
( |b|gt1 )

1. a horses weight decreases by ( \frac{1}{2} ) pound per week. at this rate, how many weeks will it take for the horse to lose a total of ( 5\frac{1}{2} ) pounds? write an expression that could be used to model the situation. state what strategy and tool you will use to answer the question, explain your choice, and then find the answer.

Explanation:

Step1: Convert mixed number to improper fraction

The total weight loss is \(5\frac{1}{2}\) pounds. Convert it to an improper fraction: \(5\frac{1}{2}=\frac{5\times2 + 1}{2}=\frac{11}{2}\) pounds.

Step2: Set up the division expression

Since the horse loses \(\frac{1}{2}\) pound per week, the number of weeks \(n\) is given by the division of the total weight loss by the weekly weight loss. The expression is \(n=\frac{11/2}{1/2}\).

Step3: Perform the division

When dividing by a fraction, we multiply by its reciprocal. So \(\frac{11/2}{1/2}=\frac{11}{2}\times\frac{2}{1}\). The \(2\) in the numerator and denominator cancel out, and we get \(n = 11\).

Answer:

The expression is \(\frac{5\frac{1}{2}}{\frac{1}{2}}\) (or \(\frac{11/2}{1/2}\)), the strategy is to use the division of fractions (since we want to find out how many times the weekly loss fits into the total loss), and the number of weeks is \(11\).