A Bookstore Is Having a Sale $A X = B$ , Which Can Be Solved to Determine the Price Each

question 141

Multiple Choice

A bookstore is having a sale. All books included in the sale have a colored sticker on them to indicate the sale price. There are green stickers, red stickers, and orange stickers. Bob, Sue, and Fred each make purchases of
Books that are on sale. Each row of the table gives information about the numbers of book purchases and the
Total cost of the purchase (before taxes) .

Use this information to set up a matrix equation of the form $A X = B$ , which can be solved to determine the price each type of sale book. Solve this matrix equation to find the price of a book with a red sticker.
Use the fact that for $A = \left[ \begin{array} { l l l } 1 & 2 & 2 \\ 1 & 3 & 2 \\ 1 & 2 & 3 \end{array} \right] , A ^ { - 1 } = \left[ \begin{array} { r r r } 5 & - 2 & - 2 \\ - 1 & 1 & 0 \\ - 1 & 0 & 1 \end{array} \right]$ .

• A) $6.79
• B) $6.87
• C) $6.50
• D) $6.99

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Definitions:

P < 0.05

Indicates that the probability of obtaining the observed data, or more extreme, under the null hypothesis is less than 5%, suggesting statistically significant results.

Significant Correlation

A statistical relationship between two variables that is unlikely to be due to chance at a specified level of significance.

Causality

The relation between a cause and its effect, often established through a combination of observational studies and experiments.

Three Variables

Refers to any analytic scenario, model, or experiment that involves exactly three different variables affecting outcomes.