Find All Numbers That Satisfy the Following $\mathrm { P } ( \mathrm { x } )$

question 230

Multiple Choice

Find all numbers that satisfy the following.
-The total profit function $\mathrm { P } ( \mathrm { x } )$ for a company producing $x$ thousand units is given by $P ( x ) = - 3 x ^ { 2 } + 45 x - 162$ . Find the values of $x$ for which the company makes a profit. [Hint: The company makes a profit when $\mathrm { P } ( \mathrm { x } ) > 0$ .]

• A) \(x\) is greater than 6 thousand units
• B) \(x\) is less than 9 thousand units
• C) \(x\) is between 6 thousand units and 9 thousand units
• D) \(x\) is less than 6 thousand units or greater than 9 thousand units

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Definitions:

Natural Opening

A passage by which substances or objects can enter or exit an organ or body part naturally.

Artificial Opening

A surgically created opening in the body for the discharge of bodily wastes or other purposes.

Small Incision

A minimal cut or surgical opening in the skin or body tissue, often used in less invasive procedures to reduce healing time and risk of infection.

Internal Ulcer

A sore or lesion forming on the interior lining of an organ, often in the stomach or intestines, causing pain and discomfort.